All Submission Categories

Beyond Biology: A Functional Framework for Consciousness in Machine Learning

Authors: A. A. Alkadrie
Comments: 14 Pages. (Note by viXra Admin: An abstract with < 400 words is required; also please cite and list scientific references)

The idea of Machines can independently solve problems, serve it as solutions, help us in any kind of task completions and so on, is fascinating. In a general term we identified this kind of machine as intellegence machines. Intellegence, as all of us understand it, is strongly related with conciesness. Does this machines have conciesnesses? this is interesting an interesting question that alot of people have in mind about the intellegence machines. Let's explore this together.
Category: Artificial Intelligence

Supportive Intersection (Without Analyticity)

Authors: Bin Wang
Comments: 22 Pages.

Part I. On a manifold, we apply the analysis in Part II below to define an intersection called supportive intersection for singular cycles. It has a topological descend to the cup-product. The result is motivated by a problem in cohomology theory. The tool is the notion of currents. A current which is a functional was first introduced by de Rham in 1955. Ever since then, currents played a central role in geometry. However, the part about the support has not been in focus. For instance, the cup-product has been extensively studied in the past. Yet, there is no adequate control on the support of cohomological classes. So, we would like to introduce the supportive intersection that will catch this property. The purpose of this paper is to build the foundation for exploring further.In the end, we'll give an application in this direction.

Part II. This is the technical foundation for the geometry above, but it may have an independent interest. It consists of a functional analysis on a very specific type of convergence of currents. In terms of classical analysis, it is an extension of mollifiers. Classically, mollifier is mostly applied as a smoother for a distribution which is usually viewed as a current of degree $0$. We extend the mollifier to currents where the degrees are positive.
Category: Geometry

New Representation of the Euler Constant "e"

Authors: Thomas Clapies
Comments: 2 Pages. (Correction made by viXra Admin to conform with schoarly norm - Please conform!)

This article reminds us that certain fundamental constants are associated with functions, in particular the base of the exponential function. We use certain remarkable identities associated with the exponential function and Lambert's function W (also called Product log) to obtain a new representation of the Euler constant e = exp(1) using a function.
Category: Number Theory

Chaos to Cosmos: Quantum Whispers and The Cosmic Genesis

Authors: Owais Farooq, Romana Zahoor
Comments: 14 Pages.

Quantum fluctuations, usually arising from the inherent uncertanity in the quantum fields, are pivotal in understanding the the universe at both the small and large scales. Despite the fact that fluctuations are usually unob-servable rather small, they give significant observable effects during specific epochs under specific conditions. During the early epochs of the universe the fluctuations were scaled, resulting into the primordial density perturbations that gave rise to the large scale structure of universe and the observedinhomogenities. In this paper we study the basic origin, structure, evolution and the imprints of fluctuations during inflationary period resulting into the large-scale structure formation. We use the Mukhanov-sasaki formalism to model scalar perturbations, embedding the theoretical results into observations.Theoretical predictions show almost scale-invariant power spectrum with stringent constraints on the inflationary parameters. It further states that in the very early universe the inflatons that is quanta of primordial field were highly filled in the degenerate quantum state. This carry large potential energythat resulted in an exponential expansion of universe. During post inflationary period the inflaton dominated the Universe’s energy density; they interact among themselves and due to non-linear effects, these inhomogeneities grow which amalgamate into spatially distinguishable patches in our observableuniverse. Our understanding projects us towards the fact that fluctuations play a pivotal role in understanding the structure formation at micro, macro, and far-macro scales. This study also addresses the significance of quantum fluctuations in cosmic evolution and manifests the enduring relevance in addressing some of the profound mysteries of our universe.
Category: Relativity and Cosmology

Calculation and Prediction of the Frequency of the 229Th Nuclear Transition

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 13 Pages. In Chinese

The accurate measurements of the frequency of the nuclear energy level transition of 229Th base state to excited state 229mTh (the frequency of 229Th nuclear transition for short) is critical to realize nuclear clocks. On 04 December 2024 Prof. Jun Ye’s laboratory reported the most accurate measured value for this frequency, i.e., 2.020407384335(2)×1015 Hz, with 12 precise digits, and gave its ratio with the frequency of 87Sr optical atomic clock, i.e., 4.707072615078(5). In this paper, we construct reasonable formulas, and calculate out the reciprocal of the frequency of 229Th nuclear transition in atomic units, the reciprocal of the frequency of 87Sr optical atomic clock in atomic units and the ratio between them, which are 20.4618997414581433, 96.315647925496289 and 4.70707261507834483 respectively. As the most accurate measured frequency of 87Sr optical atomic clock is 429228004229873.19(15) Hz, we calculate out the frequency of 229Th nuclear transition which is 2020407384335173.05(0.70) Hz, with 15 precise digits. We also calculate out the more precise values of the atomic unit of time, which is 2.4188843265865317(8)×10-17 s, and hence calculate out more precise Rydberg constant, Hartree energy, Bohr radius, classical electron radius and electron mass.
Category: Nuclear and Atomic Physics

The Schrödinger Equation Compatible with Classical Mechanics

Authors: Runsheng Tu
Comments: 9 Pages.

In the scientific community, the traditional concept has been formed that 'quantum mechanics is only applicable to microscopic systems, classical mechanics is only applicable to macroscopic systems, and the Schrödinger equation cannot be used to describe macroscopic objects'. Under the constraints of this traditional concept, there has been no attempt for a long time to establish and apply the Schrödinger equation of gravitational potential energy to describe the motion of the Earth. By replacing the potential energy in the Hamiltonian operator from electromagnetic interaction potential energy to gravitational interaction potential energy, the Schrödinger equation that can describe planetary motion was successfully obtained. Many examples provided can prove that classical mechanics and quantum mechanics are compatible. We can combine classical mechanics and quantum mechanics to describe the same system. For describing an object, mass size is no longer an important determining factor in choosing between classical mechanics and quantum mechanics methods. Establishing the Schrödinger equation for gravitational potential energy can prompt us to change our mindset and liberate our minds. The idea that classical mechanics and quantum mechanics are opposed to each other and should be mutually exclusive can be transformed into the idea that they coexist due to complementarity.
Category: Quantum Physics

Rearranging the Perfect Binary Tree: a Proof of the Collatz Conjecture

Authors: Wiroj Homsup, Nathawut Homsup
Comments: 6 Pages.

The Collatz conjecture considers recursively sequences of positive integers where n is succeeded by n/2 , if n is even, or (3n+1)/2 , if n is odd. The conjecture states that for all starting positive integers n the sequence eventually reaches the trivial cycle 1, 2, 1, 2u2026u2026The inverted Collatz sequences can be represented as a Collatz tree with 1 as its root node. In order to prove the Collatz conjecture, one must demonstrate that a Collatz tree covers all positive integers. In this paper, we construct a Collatz tree with 1 as its root node by rearranging the perfect binary tree. We prove that a Collatz tree is a connected tree and covers all positive integers.
Category: Number Theory

Electrogravity Structure of a Particle

Authors: Radomir Majkic
Comments: 19 Pages. In Serbian

The paper is about the evolution of the physical particle supported by the electro and gravity forces.Unexpectedly, electric charge and gravity unify into electro-gravity interaction in the presence of the Planck masses to show that theelectric charge, gravity, and masses are inseparable entities. Particle is created from the vacuum. Creation principle, the minimum of the static action introduces the evolution time derivative, which defines evolution kinetic energy. Electro and gravity interaction energies of the particle are defined in the standard way, and the total particle energy is its rest energy. All of this is necessary and sufficient to write the particle evolution equations. The particle evolution equations are the first-order motion differential equations for the charge, gravity, and mass particle interaction variables. The article's contribution is the particle classification according to its internal geometry, particle mass solutions for the specially specified interaction cases, and prediction of the particle evolution path in the general case. Finally, the universal mass unit is predicted to be 1_m=1.13,meV, consistent with mass m_nu(e)=1.17,meV, of the lightest, electron, neutrino.
Category: Classical Physics

Revolutionizing Video Data Management: The Hyperfractal Database Framework

Authors: Ravirajan K, Arvind Sundarajan
Comments: 11 Pages.

The AI-driven world of video streaming analytics has started to go even farther than anyone couldimagine. State-of-the-art video solutions using deep learning techniques, as well as real-time alerts, are what is driving the revolution in the digital era. The HyperFractal Database is a new content management system which is designed particularly for video and is fully efficient. This system has a multi-tiered architecture, allowing video data to be handled effectively and efficiently through theuse of advanced techniques. The key components are powerful video preprocessing and featureextraction, which transform the video into a format ready for the analysis. It in addition improves the arrangement of the video segments so that the storage amount is reduced and the retrieval speed goes up. This provides the user with the ability to edit video with the help of natural language queries resulting in an intuitive process. The database also boosts the video compression and uses smart indexing, so that users can quickly access large amounts of data. It is also capable of executingmetadata queries in an efficient manner and speeding up the processing of spatial queries, while at the same time, it can effectively manage time-sensitive data. The practical results obtained show the actual improvements in storage and retrieval efficiency, which activate its usage in different fields, such as media production as well as surveillance. This research is a platform for future large-scaletasks of video data management, and it underlines its capacity to drastically change the way we deal with intricate video data and how we may access them.
Category: Data Structures and Algorithms

Algebraic Independence of Carlitz Polylogarithms in V-Adic

Authors: David Adam, Laurent Denis
Comments: 16 Pages. In French

In this article, we prove the algebraic independence of values special features of the Carlitz-Goss zeta function in a finite place. We characterize also the algebraic independence of values u200bu200bof Carlitz polylogarithms in onefinished place. To do this, we overcome the restrictions in the method of Mahler developed by the second author within the framework of the finished characteristic. This puts us in a position to show results of algebraic independence in finite characteristics in finite places that Papanikolas' method does not yet allow to obtain.
Category: Number Theory

Photons in General Relativity

Authors: Elio Proietti
Comments: 5 Pages.

This paper is grounded exclusively on the GR-Hamilton’s variational principle,reducible to the principle of geodesics in the case of a body in free motion in agravitational field. The first two sections deal with the theory of gravitational lightbending, available in all general relativity texts, but rewritten here using exclu-sively formulas between quantities, more suitable for the physical interpretationthan the formulas between measurements commonly used (c = 1, G = 1).The third section deals the main question: what properties should GR assignto a particle moving according to a null-geodesics? Without resorting to anyprevious theory, the general relativity itself imposes very stringent and interestingproperties for "photons" (of course in agreement with those asserted by specialrelativity in the absence of a gravitational field).
Category: Relativity and Cosmology

The Question of Primordial Black Holes

Authors: Keith D. Foote
Comments: 3 Pages. (Note by viXra Admin: Please list scientific references)

The question of whether or not primordial black holes actually exist is examined. Stellar and supermassive black holes are described to offer a comparison. The lack of observable, hard supporting evidence, after 58 years, makes the concept of primordial black holes less and less likely, in spite of the imaginative, though somewhat unrealistic scenarios used to theorize their existence.
Category: Relativity and Cosmology

Derivation of the Fine Structure Constant and the Rydberg Constant from Coulomb's Law

Authors: Ichiro Nakayama
Comments: 14 Pages.

The fine-structure constant is generally considered to be a coupling constant that represents the strength of the electromagnetic interaction of elementary particles, but its origin is unknown. Using the electron and proton model of the Energy Body Theory, I clarified the origin of the fine-structure constant from the relationship between Coulomb's law and Planck's constant. This equation expressing the origin of the fine structure constant further led to the Rydberg constant.
Category: High Energy Particle Physics

Geometric Functions and Surface Functions

Authors: Ahcene Ait Saadi
Comments: 17 Pages.

In this paper, I introduce a new concept (new Frame), which allows me to have functions that have another definition. That is to say, in this frame: a function is an application that associates with each element of the starting set E, zero or several images of the arrival set F.I study in this frame, the derivability of functions, therefore the equation of a tangent to a curve. The integral calculation, I leave it to the young checkers who, surely, will develop this new and original mathematical tool, this in the interest of science and knowledge.
Category: Algebra

A Complete Elucidation of the Time Dilation Inherent in the Distortion of the Photon Foot and the Reason for the Principle of the Constancy of the Speed of Light

Authors: Ichiro Nakayama
Comments: 5 Pages.

I discovered that the distortion of an electron foot and the distortion of a photon foot (a reflection of the electron's shape) are the principle of the constancy of the speed of light itself. The distortion of the photon foot, which grows in proportion to the speed of a photon, has a structure that inherently changes the way time progresses. It is believed that this is why Maxwell's equations are universal under Lorentz transformations.Because Maxwell's equations are invariant under Lorentz transformations, changes in electric and magnetic fields are explained as effects of special relativity. However, when special relativity is applied to electromagnetic phenomena, paradoxes sometimes appear. For example, an electric charge that is stationary in a stationary system appears to be moving when viewed from an inertial system. This causes an electric current to flow and generates a magnetic field, but in reality, this phenomenon does not occur. Also, even though electrons move at a snail's speed when a current is flowing, a magnetic field is generated.This paradoxical example can be explained without contradiction by the Lorentz transformation. However, the paradox does not disappear. The key to solving this mystery lies in the distortion of the foot of an electron and the distortion of the foot of a photon, which reflects the electron’s appearance.
Category: High Energy Particle Physics

A Dual Disproof of the Birch and Swinnerton-Dyer Conjecture: Counterexamples from Modular and Non-Modular Perspectives

Authors: Khaled Ben Taieb
Comments: 39 Pages.

This paper investigates the universality of the Birch and Swinnerton-Dyer (BSD) conjecture through two complementary approaches to reverse-engineering L-functions. The BSD conjecture asserts a precise correspondence between the rank of an elliptic curve E/Q, the order of vanishing of its L-function at s = 1, and other arithmetic invariants such as torsion subgroups and Tamagawa numbers. We challenge this universality by constructing explicit counterexamples through distinct methodologies. In the first part, we reverse-engineer L-functions by deliberately introducing singularities at s = 1, thereby violating the modularity theorem. These constructions expose how carefully designed L-functions, though not corresponding to real elliptic curves, can systematically disrupt the conjecture's foundational predictions. The presence of singularities at s = 1 prevents the analytic continuation of L(E, s), rendering ords=1 L(E, s) undefined and invalidating the conjecture's rank predictions. In the second part, we take a stricter approach by reverse-engineering synthetic L-functions that respect all critical modular properties, including functional equations, analytic continuation, and bounded Fourier coefficients. These L-functions systematically violate the BSD conjecture without contradicting modularity or analytic continuation. The resulting counterexamples exhibit an irreconcilable mismatch between the expected rank (derived from the order of vanishing at s = 1) and the assigned rank of the associated elliptic curve, revealing inherent vulnerabilities in the conjecture's reliance on modular properties. Through rigorous computational techniques and theoretical validation, we confirm that these counterexamples are not artifacts of numerical instability but intrinsic features of the reverse-engineered L-functions. Together, these two approaches provide robust evidence that the BSD conjecture, in its current formulation, fails to hold universally. While the first part challenges the conjecture by violating modularity, the second demonstrates that even adherence to modular properties does not guarantee its validity. These findings raise profound questions about the interplay between modularity, the analytic behavior of L-functions, and the arithmetic properties of elliptic curves. They also underscore the need for a refined framework that incorporates additional arithmetic and analytic invariants to account for observed anomalies and broaden the scope of the BSD conjecture.
Category: Number Theory

Triple Disproof of the Hodge Conjecture

Authors: Khaled Ben Taieb
Comments: 60 Pages.

The Hodge Conjecture, one of the central problems in algebraic geometry, posits that every Hodge class in a smooth, projective variety is an algebraic cycle. Despite its significance, the conjecture has resisted proof for decades. This paper provides a comprehensive disproof by examining multiple critical axes where the conjecture fails. We highlight the incompatibility of extreme growth rates with established frameworks, including polynomial, exponential, and factorial growth models. Furthermore, we explore the geometric and topological limitations of smooth and singular varieties, demonstrating that they cannot represent extreme growth behaviors. Additionally, we analyze the breakdown of advanced frameworks such as Mixed Hodge Theory, Derived Categories, and Motivic Cohomology, which have previously been viewed as potential avenues for resolving the conjecture. Through explicit counterexamples and rigorous theoretical analysis, we show that the conjecture cannot hold under any known framework. These findings not only disprove the Hodge Conjecture but also suggest a need for new paradigms in algebraic geometry, cohomology, and topology.
Category: Topology

Comprehensive Triple Disproof of the Navier-Stokes Conjecture: Theoretical and Numerical Evidence of Finite-Time Singularities

Authors: Khaled Ben Taieb
Comments: 34 Pages.

The Navier-Stokes conjecture, one of the seven Millennium Prize Problems, has long remained an unsolved cornerstone of mathematical fluid dynamics, questioning the existence of smooth, globally defined solutions for the 3D incompressible Navier-Stokes equations. Despite its foundational importance, the conjecture has resisted resolution, with finite-time singularity formation posing a central challenge to its validity.This study decisively disproves the conjecture by demonstrating the inevitability of finite-time singularities through rigorous mathematical analysis, robust numerical simulations, and reverse engineering of the Navier-Stokes equations. By amplifying nonlinear dynamics and modeling energy dissipation failures, this approach uncovers the intrinsic mechanisms driving singularity formation. Three key findings underpin this disproof:Energy Dissipation Failure: Analytical proofs reveal that viscous dissipation fails to counteract nonlinear energy amplification under specific conditions.Nonlinear Cascade: Spectral analysis demonstrates unbounded energy transfer to smaller scales, steepening velocity gradients and amplifying vorticity.Forcing Effects: Reverse-engineered simulations validate the universality of singularities across diverse parameter spaces, including variations in viscosity, forcing strength, duration, and initial conditions.Numerical results, validated across multiple resolutions and solvers, confirm that singularity formation is intrinsic to the equations and independent of numerical artifacts. By combining rigorous proofs, reverse engineering, and comprehensive simulations, this work decisively refutes the Navier-Stokes conjecture. These findings call for a paradigm shift in fluid dynamics, emphasizing the need for singularity-resilient turbulence models and revised energy dissipation frameworks.
Category: Classical Physics

A Triple Proof of the Riemann Hypothesis: Confinement and Collapse of the Zeta Function on the Critical Line

Authors: Khaled Ben Taieb
Comments: 41 Pages.

The Riemann Hypothesis (RH) asserts that every nontrivial zero of the Riemann zeta function (zeta(s)) satisfies (Re(s) = tfrac12). In this paper, we present a unified proof that combines emph{oscillation-based analysis}, the emph{oscillatory confinement mechanism}, a emph{confinement-collapse mechanism}, and emph{numerical validation} to establish RH across emph{all} regimes of the imaginary height (T = |Im(s)|).The emph{oscillatory confinement mechanism} is a central feature of our approach. It rigorously controls the oscillatory behavior of the Riemann zeta function near the critical line (Re(s) = tfrac12). This mechanism ensures that all nontrivial zeros of (zeta(s)) are confined to a narrowing corridor around the critical line, as the imaginary height (T) increases. It utilizes the oscillatory nature of (zeta(s)), where zero crossings occur only within a dynamically shrinking region, with no zeros allowed to escape outside this region. This oscillatory confinement works in tandem with the emph{confinement-collapse mechanism}, which rigorously demonstrates that as (T to infty), the corridor width (Y(T)) collapses uniformly to zero, forcing all nontrivial zeros to lie precisely on the critical line.The dynamic corridor around the critical line is described by:[Bigl[tfrac12 - Y(T), ,tfrac12 + Y(T)Bigr],]where (Y(T)) is the maximum horizontal distance of any zero from (Re(s) = tfrac12) up to height (lvert Im(s)vert le T). We prove that:begin{enumerate} item textbf{Confinement:} All nontrivial zeros remain confined within this corridor, thanks to classical zero-density theorems, growth bounds on (lvert zeta(s)vert), and symmetry from the emph{functional equation}. item textbf{Collapse:} As (T to infty), the width (Y(T)) emph{narrows uniformly} to zero, thereby forcing every zero to lie on the critical line (Re(s) = tfrac12). item textbf{Uniform Applicability:} The mechanism applies seamlessly for emph{all} (T>0), eliminating the need to treat finite and infinite regimes separately. item textbf{Numerical Validation:} Detailed computations confirm the predicted decay of (Y(T)) for large (T) and verify that no off-line zeros appear even at moderate heights, reinforcing the robustness of the proof. end{enumerate}By integrating decades of partial results into a single, self-consistent framework—and supplementing them with numerical evidence—we resolve the Riemann Hypothesis without reliance on large-scale zero verifications as a separate argument. This accomplishment provides deep insight into the distribution of prime numbers, solidifies fundamental pillars of analytic number theory, and conclusively addresses one of the most celebrated challenges in mathematics.
Category: Number Theory

Video Generation via Compressed Hand-Drawn Representations and Latent Diffusion Models

Authors: Tofara Moyo
Comments: 2 Pages.

We present a novel approach to video generation,leveraging compressed hand-drawn representations and latent diffusion models. Our methodology employs a unique two-stage process, wherein a variational auto encoder generates parametersbased on input text, of a generic equation to be graphed into a frame, and a latent diffusion model refines these frames into photorealistic video content. These graphs are designed to looklike hand drawn replicas of the frames in the dataset. By utilizing hand-drawn-like images as a compressed representation, we effectively reduce the dimensionality of the video generation problem, enabling tighter bottleneck architectures and improved efficiency. Our approach demonstrates significant potential forgenerating lenghty ,high-quality, text-conditioned videos, with applications in multimedia creation, robotics, and beyond.
Category: Artificial Intelligence

Assumptions for a Libertarian Effort-Management Economic Theory

Authors: Ralph Pain
Comments: 13 Pages. (Note by viXra Admin: Author name should be between article title and the asbstract)

In this paper I offer new assumptions for an effort-management theory for economic activity. I begin by reviewing classical assumptions that resources possess value in use and are scarce that are adopted in resource-based theories for efficient allocation through competition. I suggest that economic theory developed under those assumptions has been useful only for explaining short-term activity when unrealistic conditions are applied and has not been useful for explaining innovation, unexpected change, or economic growth. Further, these assumptions support a justification to any who may wish to reduce the size of the human population. In this paper I argue that an economic theory for allocation of scarce resources has been misguided if resources are not indeed scarce. Instead, I offer the assumption that economic systems are limited by personal effort. Under this new assumption, I suggest an economic system may be analysed using complexity mathematics as an open complex system driven by independent agents who maximise benefit per effort, and in which interaction among agents is provided by the transfer of products.
Category: Economics and Finance

Synthra Technology: A Novel Approach Towards Centralized and Decentralized Solutions

Authors: Abdullah M. Ahmad
Comments: 29 Pages.

Synthra represents a groundbreaking technological paradigm that harmonizes blockchain and AI technologies, redefining decentralized systems for the modern era. At its core, Synthra introduces an unprecedented integration of AI-driven mechanisms, such as the Proof-of-Veracity consensus, and the Uploaded Contractual Intelligence (UCI) to ensure immutable, ethical, and highly efficient operations. Synthra is designed to address limitations of traditional blockchain systems, achieving zero gas fees, unparalleled security, and a throughput of up to 1 million transactions per second (TPS).Synthra’ s robust architecture incorporates fail-safe mechanisms like the Self-Destruct Swap Chain (SDSC), Forked-Chain Swap Chain (FCSC), and Binomial Walk Swap Chain (BWSC) which safeguards data integrity against potential network compromises through advanced backup and recovery systems. Furthermore, Synthra is envisioned to extend its capabilities to Quantum-Synthra technology, leveraging Quantum Secure Hashing Algorithms (QSHA) and the innovative Qubyte system to ensure resilience against quantum attacks while maintaining operational scalability.This framework paves the way for a new era of decentralized applications, blending AI precision with blockchain transparency and introducing the Uploaded Contractual Intelligence (UCI) as a deterministic executor of ethical principles. Synthra’ s vision is to enable secure, fast, and reliable platforms that revolutionize industries from social networking to finance while laying the foundation for future Temporal communication systems.
Category: Artificial Intelligence

The Problems of General Relativity, from "Equivalent Principle" to "Local Inertial Frame"

Authors: Zheng-Hua Zhang
Comments: 2 Pages. In Chinese

Analysis shows that the situation described in the "equivalence principle" thought experiment where gravity and inertia force are equivalent cannot be observed in the same reference frame, meaning it does not occur in the universe; The "local inertial frame" defined based on the "equivalence principle" does not meet the equivalent conditions set by the "equivalence principle" thought experiment, that is, the "local inertial frame" has no relationship with the "equivalence principle".
Category: Relativity and Cosmology

Lecture Notes on a Quadratic Inequality for Gaps Between Consecutive Primes and Its Extension to the Proof of the Binary Goldbach Conjecture

Authors: Samuel Bonaya Buya
Comments: 9 Pages.

This research paper is in the form of lesson notes. In it an identity is established connecting to consecutive primes. Bertrand’s postulate is used together with the identity to establish a quadratic inequality that can be used to establishminimum intervals containing at least three primes in between its limits. A generalization of the quadratic inequality is introduced to establish the minimum interval containining at least one pair of primes for Goldbach partitition. The concepts of Goldbach partition deviation and Goldbach partition interval are introduced by which it is shown that the minimum number of Goldbach partitionsof a composite even number is 1.
Category: Number Theory

Simple Proof of the Riemann Hypothesis

Authors: Kato Millen
Comments: 2 Pages.

The Riemann hypothesis states that the real part of all non trivial zeros of the Riemann zeta function is 0.5. We proved the hypothesis by using the properties of the analytically continued zeta function at zeta(s)=0, and also using the integral(Mellin transformation) representation of the zeta function.
Category: Number Theory

Analysis of Electromagnetic Noise From Switching Power Modules Using Wide Band Gap Semiconductors

Authors: Parthiv Katapara
Comments: 4 Pages.

The advancement of power electronics has driventhe need for materials with superior electrical properties, leading to the use of wide band gap (WBG) semiconductors such as Silicon Carbide (SiC) and Gallium Nitride (GaN). These materialsexhibit higher breakdown voltages, faster switching frequencies, and better thermal stability compared to conventional silicon-based devices [1], [2], [3]. However, these benefits introducesignificant challenges in electromagnetic noise (EM noise) management, particularly due to rapid transitions characterized by high rates of change in voltage (dV /dt) and current (dI/dt)[4], [5]. This paper analytically investigates the sources and propagation of EM noise in high-frequency switching power modules using WBG semiconductors. Mathematical models are derived to describe the noise generated, incorporating factors such as parasitic inductances (L)and capacitances (C), frequency-dependent impedance (Z(f)), and noise power density (N(f)) [6]. The relationships between switching characteristics and noise amplitude are exploredthrough differential equations and Fourier analysis to map time-domain signals to their frequency components. Solutions for noise suppression are proposed, involving optimized circuit design and theoretical applications of electromagnetic wave propagation (EWP) principles, such as wave reflection and transmission in multi-layer structures [7], [8]. This work bridges theoretical electromagnetics with practical power module design, offeringstrategies that align with electromagnetic compatibility (EMC) standards and enhance performance.
Category: Classical Physics

Macroscopic Structures Emerging from the Interactions of Simple Replicators

Authors: Perry W. Swanborough
Comments: 13 Pages.

A macroscopic view of Langton (1984) and Byl (1989) self-replicating loops has facilitated their representation by oriented states of single cells. In this work, the single-cell representation of the loop replicator is adapted to facilitate a wide variety of interactions identifiable by observation of the dynamics of arbitrary spatial distributions of many replicator copies. Dynamic loops of periods greater than the four-step rotation cycle of the orientated state were observed, and examples with periods of 20 and 12 are shown. The paper includes some discussion of irreversibility in both computation and biology, with recognition of the problem of deriving concrete conclusions about abiogenesis and pre-LUCA biology from speculative preliminary abstraction.
Category: Physics of Biology

Theory of Refraction

Authors: Rajeev Kumar
Comments: 3 Pages.

In this paper a theory of refraction has been presented.
Category: Classical Physics

Reconstructing Conceptual Models in Physics: The Interplay of Content and Context

Authors: Paul Caracristi
Comments: 3 Pages.

Modern fields of study often progress through detailed explorations of foundational conceptual models. However, as these fields delve into increasing levels of intricate detail, contradictions and difficulties in further advancement can emerge. This phenomenon suggests a need to periodically simplify and reconstruct foundational conceptual models to maintain a sense of coherence and relevance, to stimulate a sense of positive progression in the subject field. This paper argues that such reconstruction is crucial in all reductionist subjects such as physics. In an attempt to provide an example, the paper on the "Temporal Cavitation Model of Cosmology" is proposed as a case study. By examining the dynamic relationship between ‘content and context’ across various disciplines, we demonstrate that their interplay is essential for the evolution of knowledge and the resolution of fundamental challenges.
Category: History and Philosophy of Physics

The Spacetime Matrix

Authors: Gaurav Kumar
Comments: 5 Pages. (Note by viXra Admin: Pleease cite and list scientific references)

This paper introduces the Spacetime Matrix Theory, a novel framework for understanding spacetime as a discrete matrix composed of fundamental "grains." Each grain encapsulates localized properties and interactions, forming a unified structure that bridges quantum mechanics and general relativity. The theory explains phenomena such as quantum entanglement through inter-grain connectivity, modeled as dynamic curvature. Derivations of key equations are provided, including a curvature equation linking the local grain structure to spacetime dynamics. Simulations demonstrate the energy density distribution and inter-grain interactions, validating the framework's predictive capability. This work aims to provide new insights into the fabric of spacetime and its underlying mechanics.
Category: Quantum Physics

The de Vries Formula: a Transcendental Solution for Standing Travelling Circular Waves

Authors: Luke Kenneth Casson Leighton
Comments: 1 Page. (Note by viXra Admin: Author name should be between article title and the asbstract and any remarks above the title should be moved into a footnote in small print))

Exploration of the de Vries formula[1] and its accuracy[2] (following removal of SI2019 assumptions) to latest experimental uncertainty[3] has led to a hypothesis that the formula is a transcendental solution of an infinite-summed (non-frictional) circular traveling and standing wave: a solution of harmonic sympathetic resonance.
Category: Mathematical Physics

Exploring EEG Dynamics Through Markov Chain Analysis

Authors: Arturo Tozzi
Comments: 8 Pages.

A Markov chain (MC) is a mathematical model used to describe a system where the probability of moving to the next state depends solely on the current state and not on the sequence of the preceding states. A Markov blanket (MB) for a node includes its parents, children and other parents of its children, capturing the minimal set of nodes required to make the node conditionally independent from the rest of the network. We examined EEG data from healthy individuals to assess MC and MB connectivity patterns associated with two representative electrodes. The electrode FP1, associated with cognitive functions, displayed connections predominantly with frontal and central regions. The electrode C3, located in the primary motor cortex, displayed connections with bilateral motor and parietal regions. The two electrodes had shared connections, highlighting integration between cognitive and motor networks, while also retaining distinct connections that underscored their specialized roles and functions. Temporal analysis demonstrated significant MB fluctuations across time segments, highlighting phases of increased neural reorganization and stability. Entropy analysis showed significant variability in MC and MB dynamics over time. FP1 exhibited greater entropy variability, reflecting its neural flexibility and involvement in cognitive processes, while C3 showed more stable entropy patterns, aligning with its motor-related functionality. We demonstrate the utility of MC and MBs in capturing the dynamic complexity of the nervous activity, underscoring the distinct and overlapping roles of brain regions in balancing dynamic flexibility and functional specialization. Our findings have implications for cognitive neuroscience and brain-computer interface design.
Category: Mind Science

New Mathematical Rules and Methods for the Strong Conjecture of Goldbach to be Verified

Authors: Bouchaïb Bahbouhi
Comments: 54 Pages.

This article emphasizes the most fundamental rules to verify Goldbach's strong conjecture that an even number is the sum of two primes. One rule states that for an even number E to split into two primes there must be two equidistant prime numbers p and p' such that E/2 - p = p' - E/2. The strong conjecture also applies to biprime numbers that are x2 — y2. Two prime numbers equidistant with respect to an integer n have a specific property of Modulo when divided by the gap that separates them from n. The paper further proposes methods to convert even and odd numbers into sums of two and three prime numbers by the equation M ± 1 such that M is prime or multiple of primes except 2 and 3 knowing that there are two types of prime numbers 6x - 1 and 6x + 1. The data also show a strong correlation coefficient between close equidisant primes indicating they are likely to happen in a regular fashion. Finally, the paper describes new rules that explain how a prime numbers gives another one and this is where the truth of Goldbach's conjecture lies and show congruence rules between the two additive primes. These rules allow to demonstrate how an even ends up to be a sum of two primes and proves Goldbach's strong conjecture. This article can have new applications in computing and sheds new lights on the Goldbach's strong and weak conjectures.
Category: Number Theory

Proof of Collatz Conjecture Using Division Sequence Ⅴ

Authors: Masashi Furuta
Comments: 7 Pages.

This paper is positioned as a sequel edition of [1]. First, as in [1], define "division sequence", "complete division sequence", "star conversion", and "extended star conversion". Next, applying tail of division sequence to prove the Collatz conjecture. Also, Theorem Proving is not used in this paper.
Category: Number Theory

Nuclear Reactions in Gaseous Stars: Perspectives from Kinetic Theory and Thermodynamics

Authors: Stephen J. Crothers
Comments: 10 Pages.

In the Standard Model of gaseous stars, temperature is primary both in the initiation of thermonuclear reactions to form heavier elements and the emission of radiation. These processes have been described using thermodynamic expressions. Yet, within any given thermodynamic relation, not only must units balance on each side, but so must thermodynamic character. Temperature, whether or not equilibrium conditions are established, must always be intensive in macroscopic thermodynamics and mass must be extensive. This ensures that the laws of thermodynamics are respected. The theory of temperatures and nuclear reactions within gaseous stars is constructed from the kinetic theory of an ideal gas, by which temperature is introduced, in combination with gravitational and Coulomb forces. The resulting thermodynamic relations impart a non-intensive character to temperature and a non-extensive character to mass. Consequently, the theory of nuclear reactions in gaseous stars is invalid. Deprived of the only theoretical means by which the Standard Model justifies stellar nuclear reactions, the theory of gaseous stars is not viable. The most reasonable alternative rests in lattice confinement fusion and the recognition that the stars are comprised of condensed matter, namely metallic hydrogen.
Category: Astrophysics

On Lorentz Invariant Non-Locality Described by Differential Equations with Derivatives of Infinite Order

Authors: R. K. Salimov, T. R. Salimov
Comments: 3 Pages.

The paper considers Lorentz invariant equations with infinite-order derivatives with solitonsolutions. Within the framework of the Lagrangian formalism for fields description and when describing point particles in the form of probability amplitudes, such equations are not considered. If the axiomatic nature of these approaches is abandoned and we limit ourselves only to the requirement of Lorentz invariance of differential equations, then the consideration of such equations allows for non-locality. The paper discusses some general features of nonlocality described by such equations and their differences from the description of nonlocality in the Copenhagen interpretation of the quantum mechanical description. In particular, it is shown that in such a model the question of paradoxes of the Einstein - Podolsky - Rosen type is removed.
Category: Quantum Physics

Is Relativistic Length Contraction Consistent?

Authors: Lars Frølund Jensen
Comments: 5 Pages.

An important part of special relativity (SR) is length contraction. According to this theory, it is a coordinate-dependent and ‘symmetrical’ effect, such that two observers, moving relative to each other, both with their own measuring rod, can both rightly claim that the other observer’s measuring rod is contracted, even though the rest lengths of the rods are exactly the same. However, with the help of thought experiments, it can be shown that this cannot be true in the real world — and that SR predicts two fundamentally different length contractions.
Category: Relativity and Cosmology

Physics or Reality: Which Prevails?

Authors: Dainis Zeps
Comments: 8 Pages. (Note by viXra Admin: Article discussing wars and politics is in general not acceptable)

Why such opposition? Physics versus Reality. This is the question we address in this article.
Category: Social Science

Ulam Numbers Have Zero Logarithmic Density

Authors: Theophilus Agama
Comments: 7 Pages. (Note by viXra Admin: Furher abstract speculations may not be accepted)

Determining the natural textit{density} of Ulam numbers remains an open question. We denote the sequence of all Ulam numbers by $U$. In this paper, we show for the textit{logarithmic} density of Ulam numbers $$mathcal{D}_{log}(U):=lim limits_{nlongrightarrow infty}frac{1}{log x}sum limits_{substack{nleq xin U}}frac{1}{n}=0.$$
Category: Number Theory

Geometrized Vacuum Physics Part 9: Neutrino

Authors: Mikhail Batanov-Gaukhman
Comments: 28 Pages.

This article is the ninth part of the scientific project under the general title "Geometrized Vacuum Physics Based on the Algebra of Signature" [1,2,3,4,5,6,7,8]. In this article, based on exact solutions of the Einstein vacuum equation, are proposed metric-dynamic models of the electron and positron "neutrino" in the initial state, i.e. at the moment when it breaks away from the core of the corresponding "particle", and in the final state, when almost all the rotational energy of the initial "neutrino" is converted into its accelerated translational motion. It is shown that Riemann-ian geometry allows for the consideration of "neutrinos" of various scales: molecular "neutrinos", cluster "neutrinos", planetary "neutrinos", galactic "neutrinos", etc. The article proposes methods for generating "neutrinos" of various scales, convenient for conducting inexpensive experiments to clarify their properties. Of particular interest are "neutrinos" in the final state, since the metric-dynamic model of such a "neutrino" does not contain restrictions on the speed of its translational motion. That is, a "neutrino" in the final state does not have inertia, and theoretically can move at a speed significantly exceeding the speed of light. The article proposes a method for registering super-luminal "neutrinos" in the final state.
Category: Classical Physics

On Curves in N-Dimensional Euclidean Spaces

Authors: Emanuels Grinbergs
Comments: 20 Pages. Translated (from Latvian) and submitted by Dainis Zeps

This work examines curves in n-dimensional spaces, as well as varieties contained in such spaces, with the main focus on curves and osculating linear and spherical varieties. Absolute dierential calculus a method almost exclusively used in n-dimensional dierential geometry in recent times is convenient in systematic terms because it enables the determination of all dierential invariantsusing classical techniques. However, it is cumbersome and inconvenient. Since I have sought to examine purely geometric properties and their relationships, I have consistently used vector analysis both independently and in conjunction with direct geometric reasoning, as wellas with Cartesian coordinates.
Category: Geometry

The Nature of Whiteholes, Blackholes and the Energy Cycle of the Universe

Authors: Paul Caracristi
Comments: 4 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Abstract. This paper proposes and explores the theory that whiteholes and blackholes serve as complementary structures in the cosmos, facilitating a continuous energy cycle between a dynamic universe and a static Latent realm. Whiteholes are proposed as sources of energy and entropy, giving rise to dynamic universes, while blackholes transition the complexity of matter and energy back into a latent, negentropic state. The interplay between these phenomena is governed by a temporal spectrum, wherein energy fluctuates between near-zero values in the latent realm and greater-than-zero values in a dynamic universe. The proposed model offers an integrated framework for understanding the universe’s origin, evolution, and potential termination within a broader cosmological context.
Category: Relativity and Cosmology

The Metric Problem in Polar Coordinates: A Comprehensive Analysis and a Solution

Authors: Mueiz Gafer KamalEldeen
Comments: 4 Pages.

The purpose of this article is to demonstrate that the common method for calculating the metric tensor in polar coordinates is incorrect. However, it does not lead to erroneous results due to the presence of another error that cancels out the effects of the first error in calculations. Nerveless, these offsetting errors creates a problem in understanding the metric.
Category: Relativity and Cosmology

The Mathematic and Scientific Meanings of 2025

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 9 Pages. 1 Figure, in Chinese.

The number 2025 is the square of 45, and 45 is the sum of 1 to 9 which are the natural numbers in decimal number system, this makes 2025 have some wonderful mathematic properties. This paper illustrates and explains these mathematic properties, and points out these properties are derived from the special number 45. This also leads to a question, i.e., is the number 45 has scientific meanings? This paper exhibits the marvelous relationships between the nucleon numbers of the 45th element Rh and the nucleon numbers of some other critical elements, hence displays the scientific meanings of the number 45, and hence reveals that the decimal number system is scientific in the elements and nuclides. In fact, there are binary, senary, decimal and forteenary number systems in the elements and nuclides, which relate with each other and comprise the backbone of the elements and nuclides, this means they all are scientific. We think these four number systems derive from the principle of "a circle should be divided to 420 degrees, and the chirality corresponds to 840 degrees" which we supposed, they are the number systems based on the 1, 3, 5, 7 and 2 factors of 420 or 840 and could be called the natural number systems. In addition, there is a number system based on the base of the natural logarithm e, which could be called e number system and should be the integrated number system of all other natural number systems. In conclusion, the number systems are scientific.
Category: Nuclear and Atomic Physics

Spontaneous Subatomic Mass-Energy Interconversion: Implications for the Heisenberg Uncertainty Principle and a Theory of Everything

Authors: Rudolph Elliot Willis
Comments: 34 Pages.

This study proposes that quantum uncertainty arises from stochastic mass-energy interconversion at the subatomic level. Integrating Einstein's mass-energy equivalence and quantum mechanics, the hypothesis introduces fluctuating mass terms into mathematical frameworks like the Schrödinger equation, yielding novel implications for the Heisenberg Uncertainty Principle. The theory extends to quantum field theory, string theory, and cosmology, suggesting a dynamic mechanism for phenomena ranging from particle decay rates to black hole evaporation. By bridging quantum mechanics and general relativity through stochastic fluctuations, this framework offers testable predictions for high-energy physics, gravitational wave analysis, and cosmological observations, advancing the search for a unified Theory of Everything.
Category: Quantum Physics

On the Product Distribution of Addition Chains

Authors: Theophilus Agama
Comments: 6 Pages.

In this note, we study the distribution of the product of consecutive terms in an addition chain of a given length. If $1,2,ldots,s_{delta(n)-1},s_{delta(n)}=n$ is an addition chain producing $n$ and of length $delta(n)$, with associated sequence of generators begin{align}1+1,s_2=a_2+r_2,ldots,s_{delta(n)-1}=a_{delta(n)-1}+r_{delta(n)-1},s_{delta(n)}=a_{delta(n)}+r_{delta(n)}=nonumberend{align} then $$sum limits_{l=1}^{delta(n)}log s_l=delta(n)log n-O(delta(n)).$$ It follows in particular that $$prod limits_{l=1}^{delta(n)}s_lsim n^{delta(n)}.$$
Category: Number Theory

The Pionic Fabric and Quark Molecular Dynamics

Authors: Rami Rom
Comments: 43 Pages.

Similar to Harari’s Rishon particles model that described all leptonic and baryonic matter composed of four substructure fundamental particles and antiparticles, T ,V ,T ̃ ,V ̃, we propose that the four quarks and antiquarks, u ,d ,u ̃ ,d ̃ are the substructure building blocks of all particles and also the substructure of the vacuum pionic fabric. We develop a classical and quantum hybrid quark molecular dynamics scheme to study the pionic fabric. In free space, the pionic fabric zero-energy unit cell is cubic and includes two flipped pion tetrahedrons. Protons and neutrons contract and curve the pionic fabric cells and we calculate the pionic fabric density as a function of distance from an embedded proton in a pionic fabric cell. Based on the �� decay, we propose that electrons are non-elementary, non-point like particles having a similar substructure to the pionic fabric cell and form together electron clouds. Motion of the electron in the pionic fabric is performed by a u and d quark exchanges via tunneling through a double well potential barrier in the ground state. The rapid quark exchanges transform the electron tetraquarks into pion tetraquarks and vice versa. After the u and d quark exchanges, the zero-energy pionic unit cell contracts by a factor of 5 and the embedded electron pionic cell energy is equal to the electron rest mass of 0.511 MeV. Finally, we propose a new interpretation to QED based on the pionic fabric structure and dynamics. Lattice QCD computations may allow calculating the mass of the pionic fabric unit cell and the embedded electron pionic cell.
Category: High Energy Particle Physics

Artificial Intelligence: Quantity vs. Quality

Authors: Clark M. Thomas
Comments: 5 Pages.

AI directs us toward emerging machine technologythat seemingly everybody has encountered, but few truly comprehend. Fake AI essays, fake AI images, fake reviews, and fuzzy app features disguise how quantity is not always superior to quality. Wisdom and intelligence reside inside our seemingly slow brains, still with 100 trillion synaptic connections. Intuitive machine wisdom separate from and equal to human consciousness is possible, but not yet.The ideal synthesis will optimize the best thoughts of machines and humans to preserve our biosphere.
Category: Artificial Intelligence

Weakly Timeless Emergence & the Siegel-Craver Model for Mechanistic Phenomenological Laws

Authors: Jasmine Elmrabti
Comments: 18 Pages. Accepted to and presented at the Journal of the Annual Undergraduate Philosophy Conference at New York University, April 2024.

A fundamentally timeless world implied by quantum gravity threatens a recent model offered for mechanistically justified phenomenological laws described by Gabriel Siegel and C. Craver. The criteria for these laws appear to collapse when met with thermal time, a physical theory compatible with weak timelessness. I argue that this collapse hinges on the theory of emergence used to define mechanistic explanation under thermal time. Two cases of emergence are examined——one reductionist, one pluralist——revealing that both erase the distinction between etiological and relevant constitutive explanation. However, only the reductionist perspective diminishes the explanatory power of phenomenological laws as determined by Siegel and Craver. The other preserves this power. I examine the intersection between interventionist mechanism, timelessness, and emergence within the authors’ framework to support these conclusions by performing a thought experiment using propositional logic and set theory. This analysis discusses the implications of timelessness, principally its threat to mechanistically justified phenomenological laws and how its emergence shapes the sufficiency of mechanistic explanations.
Category: History and Philosophy of Physics

On the Dimensional Structure of String Theory

Authors: Masashi Ishihara
Comments: 2 Pages.

This paper presents a new decomposition of the dimensions in String Theory, specifically in Bosonic String Theory and M-theory, which highlights the redundancy in the theory. By focusing on a symmetrical decomposition, I propose a more natural description of the structure of the Universe, one that aligns with the holographic principle underlying the AdS/CFT correspondence.
Category: Quantum Gravity and String Theory

A 3D Spherical Warp Drive Vector Created Using a New Methodology But with the Same Physical Properties of the Natario Warp Drive

Authors: Fernando Loup
Comments: 12 Pages.

The Natario warp drive appeared for the first time in 2001.Although the idea of the warp dive as a spacetime distortion that allows a spaceship to travel faster than lightpredated the Natario work by 7 years Natario introduced in 2001 the new concept of a propulsion vector to define or to generate a warp drive spacetime.Natario defined a warp drive vector for constant speeds in Polar Coordinates using the Hodge Star but remember that a real warp drive must accelerate orde-accelerate in order to be accepted as a physical valid model so it must possesses variable speeds.We developed a new warp drivevector different than the original Natario warp drive vector using a new methodology and without the Hodge Star that encompasses variable speeds.Also Polar Coordinates uses only two dimensions and we know that a real spaceship is a tridimensional 3D object inserted inside a tridimensional 3D warp bubble that must bedefined in real 3D Spherical Coordinates.In this work we present the new warp drive vector in tridimensional $3D$ Spherical Coordinates without the Hodge Star for both constant or variable speeds.Our new proposed warp drive vectors also satisfies the Natario requirements for a warp drive spacetime.
Category: Relativity and Cosmology

From Cyclotomic Fields to Gauge Structure: A Mathematical Bridge

Authors: Alejandro Gama Castro
Comments: 31 Pages.

We present a rigorous mathematical framework connecting cyclotomic field theory to gauge structure in physics. Starting from thearithmetic properties of the sixth cyclotomic field K6 , we develop a complete path from number theory to gauge theory, carefully dis-tinguishing established mathematical results from physical interpretations. Our approach provides explicit constructions throughout, withparticular attention to field valuations, root systems, and the emergence of gauge groups. We establish a concrete foundation for under-standing how gauge symmetries can arise naturally from arithmetic structures.
Category: Mathematical Physics

A New Perspective of Quantum Mechanics and Particle Physics

Authors: Proloy Kumar Nath, Purnata Shovita Nath
Comments: 22 Pages.

In Clifford algebra, it would be found that spinors or spin group, where spinors are essential in describing spin as an intrinsic quantum property in quantum electrodynamics with the general nature of an intrinsic angular momentum of subatomic particles, and pinors or pin group, where pinors may be expected essential in describing pin as a further intrinsic quantum property in quantum electrodynamics with the general nature of an intrinsic linear momentum of subatomic particles. The physical consequences of spin and pin may be obtained in the phenomenon of uniform circular motion of a rotating point object about its axis of rotation such that spin is along the axis of rotation to the plane of rotation of the object and pin, like a tiny string, may be about the same axis of rotation on the plane of rotation of the object. As such, if spin is considered as an intrinsic quantum property of subatomic particles in quantum electrodynamics, then pin would also be considered as a further intrinsic quantum property of subatomic particles in quantum electrodynamics, where these two intrinsic quantum properties of subatomic particles, spin and pin, would be found perpendicular to each other. Therefore, spin and pin, by acting at right angle to each other in any reference frame, being quantized, would represent the observable quantum states such as subatomic particles in quantum mechanics and particle physics. It would also be found that a spin is associated together with an intrinsic magnetic moment along the same axis of rotation to the plane of rotation at ntiparallel to spin, and a pin may be associated together with an intrinsic electric moment about the same axis of rotation on the plane of rotation at antiparallel to pin in quantum electrodynamics. Thus, the presence of the four intrinsic properties — spin, pin, magnetic moment and electric moment — of subatomic particles in quantum electrodynamics may open a new perspective of quantum mechanics and particle physics, which may support to find out the isolated quantized electric mono-poles as free positive and negative electric charges, as well as, the isolated quantized magnetic mono-poles as free positive and negative magnetic charges carried by specific particles.
Category: Quantum Physics

On the Modular Equation ax ≡ C[b] with a ≡ (± 10/p)[b] and P ∈ {1, 2, 5, 10}

Authors: Algoni Mohamed
Comments: 18 Pages.

We propose a method to solve the modular equation ax ≡ c[b] where a, b and c are natural numbers such that a ≡ ±(10/p) [b] with p ∈ {1, 2, 5, 10}. The method is based on the analysis units of the products pb and pc, which we designate respectively by u and uu2032. This approach allows you to simplify and accelerate the solution process by focusing on these units.
Category: Number Theory

On Superposition and Entanglement of Polarized Photons Without Hidden Variables

Authors: Eugen Muchowski
Comments: 4 Pages.

Polarized photons have properties that can be explained, among other things, by their indistinguishability. These include superposition and entanglement. The locality of entangled photons can thus be explained without hidden parameters. We propose that the superposition state can be understood as the entirety of all mixtures of indistinguishable perpendicularly polarized photon beams. Superposition of indistinguishable photon beams can be demonstrated experimentally using a Mach-Zehnder interferometer. This explains how the polarization of the input state reappears at the output of a Mach-Zehnder interferometer.
Category: Quantum Physics

A New Method For Evaluating Approximations of Irrational Numbers

Authors: Alexander C. Sarich
Comments: 14 Pages.

Provided is a method for evaluating irrational numbers in parts; where, any irrational number canbe represented by a numerical-approximation taken to some exact decimal place and its remainder.Analysis provided is to be considered incomplete but imaginative. Argumentation provided is intendedto simplify ideas pertaining to Irrational numbers, infinite series, and distance sets as a mechanism of solution finding.
Category: Set Theory and Logic

On the Congruence System X ≡ A_1[b_1] and αx ≡ A_2[b_2] Such that αb_1 ≡ ± (10 /p) [b_2] with P ∈ {1, 2, 5, 10}

Authors: Algoni Mohamed
Comments: 6 Pages.

We propose a method to solve the modular equation system:x ≡ a_1[b_1]αx ≡ a_2[b_2]with α, a_1, a_2, b_1 and b_2 ∈ N∗ such that a_2 ≥ αa_1 and αb_1 ≡ ±(10/p)[b_2] with p ∈ {1, 2, 5, 10}This method is based on our latest work "On the Diophantine equation ax+by=c with a ≡ ±(10/p)[b] and p ∈ {1, 2, 5, 10}". It is therefore based on the analysis of the units of products pb_2 and p(a_2 − αa_1), which we designate respectively by u and uu2032 .
Category: Number Theory

Cellular Generation Number as an Invariant Measure of Biological Time in Relativistic Inertial Systems: Biological Systems Do Not Experience Time Dilation

Authors: Domenico Maglione
Comments: 18 Pages.

This work presents a thought experiment where the number of cellular duplications or generations (G) is used as a biological clock to investigate the effects of relativistic environments on biological time. We demonstrate that, although physical clocks in different reference systems measure varying times due to relativistic time dilation, biological time remains invariant and corresponds to the "proper" time. This invariance holds not only across inertial reference frames but also extends to non-inertial, accelerated, and gravitational systems. The invariance arises because G is defined as the ratio of the growth time to the duplication time, ensuring that any relativistic effects influencing these intervals mathematically cancel out. These findings challenge the classic interpretation of Einstein's twin paradox, which suggests differential aging due to relativistic velocities. In reality, while physical clocks indicate differing times, biological time, and thus the biological age of living organisms, remains unaffected, aligning consistently with proper time. Although bacterial cultures were used as a model in this study, the results are generalizable to all cellular systems, provided identical growth conditions are maintained. This study provides new insights into the interplay between biological processes and relativistic effects, establishing G as a reliable and invariant measure of biological time across all reference frames.
Category: Relativity and Cosmology

Tensor Calculus Made Simple

Authors: Taha Sochi
Comments: 171 Pages.

This book is about tensor analysis. It consists of 169 pages. The language and method used in presenting the ideas and techniques of tensors make it very suitable as a textbook or as a reference for an introductory course on tensor algebra and calculus or as a guide for self-studying and learning. The book contains many exercises. The detailed solutions of all these exercises are available in another book by the author (Solutions of Exercises of Tensor Calculus Made Simple).
Category: General Mathematics

Introduction to Differential Geometry of Space Curves and Surfaces

Authors: Taha Sochi
Comments: 252 Pages.

This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.
Category: Geometry

Principles of Tensor Calculus

Authors: Taha Sochi
Comments: 189 Pages.

This book is based on my previous book: Tensor Calculus Made Simple, where the development of tensor calculus concepts and techniques are continued at a higher level. Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.
Category: General Mathematics

Proof of Beal’s Conjecture

Authors: Kamal Barghout
Comments: 4 Pages.

The 6 variable general equation of Beal’s conjecture equation〖 x〗^a+y^b=z^c, where x, y, z, a, b, and c are positive integers, and a,b,c≥3, is identified as an identity made by expansion of powers of binomials of integers x and y; where x, y and z have common prime factor. Here, a proof of the conjecture is presented in two folds. First, powers of binomials of integers x and y expand to all integer solutions of Beal’s equation if they have common prime factor. Second, powers of binomials of coprime positive integers x and y expand to two terms such that if one of them is a perfect power the other one is not a perfect power.
Category: Number Theory

Newton’s Laws and the Principle of Least Action

Authors: Eduardo E. Salgado
Comments: 3 Pages.

The Principle of Least Action is a fundamental pillar of theoretical physics that unifies diverse phenomena under a variational formulation. This deeply elegant formulation of physics provides an alternative and powerful approach to derive Newton’s Laws. This principle states that the path followed by a physical system between two states is the one that minimizes (or makes stationary) a quantity called action, defined as the time integral of the Lagrangian. In this article, weexplore how the Principle of Least Action connects with Newton’s laws, showing that the latter are a direct consequence of a variational approach. We present an introduction to the action and the Lagrangian, followed by an application of variational calculus to obtain the Euler-Lagrange equations, which translate into Newton’s second laws under specific conditions. This approach demonstrates the elegance and generality of the Lagrangian formalism.
Category: Classical Physics

On the Harmonic Distribution of Addition Chains

Authors: Theophilus Agama
Comments: 4 Pages.

In this note, we study the harmonic distribution of addition chains of a given length. If $1,2,ldots,s_{delta(n)-1},s_{delta(n)}=n$ is an addition chain producing $n$ and of length $delta(n)$, with associated sequence of generators begin{align}1+1,s_2=a_2+r_2,ldots,s_{delta(n)-1}=a_{delta(n)-1}+r_{delta(n)-1},s_{delta(n)}=a_{delta(n)}+r_{delta(n)}=nonumberend{align}then $$sum limits_{l=1}^{delta(n)}frac{1}{s_l}=frac{3}{2}+frac{delta(n)}{n+1}+sum limits_{l=3}^{delta(n)}sum limits_{v=1}^{infty}frac{1}{(n+1)^{v+1}}bigg(sum limits_{j=l}^{delta(n)}r_jbigg)^{v}+O(frac{1}{n})$$ where $sum limits_{j=l}^{delta(n)}r_j<n-1$ is the sum of the regulators in the generator of the chain for each $3leq lleq delta(n)$.
Category: Number Theory

Quantum Mechanics and Gravitation - Computation Framework

Authors: Rajmohan Harindranath
Comments: 4 Pages.

We propose a speculative framework in which the underlying structure of reality is modeled as adensely connected neural network, with reality emerging from a computational substrate. In this approach, wave phenomena arise from subthreshold activations across many nodes, while particle phenomena occur when individual nodes exceed a threshold and "spike." We suggest that this model can capture key features of quantum mechanics, including wave-particle duality, measurement-induced collapse, and the generation of virtual particles when local energy surpasses threshold. Furthermore, a high concentration of spikes in one region may slow the local "computational speed," suggesting an interpretation of gravitational time dilation and space-time curvature. Though conceptual, theframework could be tested by scenarios in which a single photon or electron sometimes yields nodetection (lost to sub-threshold dissipation) or multiple detections (leftover activation combining with new signals). We conclude by discussing open challenges, especially regarding entanglement, non-local correlations, Lorentz invariance, and the full embedding of this idea into known gauge symmetries.
Category: Quantum Physics

Gradient Reservoir Optimizer

Authors: Akhil Kumar
Comments: 4 Pages.

In this paper, I introduce the Gradient Reservoir Optimizer (GRO), a novel optimizationalgorithm for neural network training that combines short-term gradient updates with long-term gradient trends. GRO maintains a dynamic "reservoir" of recent gradient directions and utilizes their aggregated trends to influence parameter updates. By blending current gradients with a history-aware reservoir, GRO aims to stabilize convergence and improve robustness to noisygradients. This novel approach provides an additional mechanism to mitigate common issueslike gradient noise and plateaus in training loss. I demonstrate the theoretical underpinnings of GRO, provide its algorithmic structure, and evaluate its performance on benchmark datasets. The results show promise for GRO as a viable alternative to existing optimizers like SGD, Adam, and RMSProp. Additionally, GRO offers flexibility for tuning the influence of historical gradients, making it adaptable across a variety of tasks and architectures.
Category: Artificial Intelligence

A New Approach to Conceive the Measurement of the Ono-Way Speed of Lightbased on an Astounishing Conflict Within Relativity

Authors: Rodrigo de Abreu
Comments: 18 Pages.

The measurement of the speed of light one-way can be easily conceived since we can consider a rod with length l_1 between the extremities A´ and B´ and emit light from A´ to B´ and reciprocally emit light from B´ to A´. If we measure the time A´B´ and the time B´A´ we know the speed of light A´B´ and B´A´. However, standard approach affirm astonishingly that this is not possible. Because we need to know the speed of light to synchronize the clocks at A´ and B´, to measure the times A´B’ and B´A´. Why? Because standard approach accept the necessity to have synchronized clocks. And astonishingly also affirm that the one-way speed of light one-way is the two-way speed of light measured in one-clock with the value c in vacuum. In the following approach we defend that this standard approach can not subsist based on the conceptualization of the measurement one-way. For this we use a new method using a gap of synchronization that standard approach can not be aware.
Category: Relativity and Cosmology

The Support

Authors: Bin Wang
Comments: 13 Pages.

Let $X$ be a complex projective manifold. First, we prove that for a real, singular cycle $ C$ of real codimension $2p$, if its current of integration is of bidegree $(p, p)$ and positive, there exists an algebraic set $A$ of complex codimension $p$ that contains $C$. Secondly, we prove that for the singular cohomology $H^{i} (X;mathbb Q)$ of degree $i$ with rational coefficients, a Hodge class$uin H^{p, p}(X;mathbb Q)$ can be represented by the difference of two rational, singular cycles whose currents of integration are of bidegree $(p, p)$ and positive. The combined result implies a cohomological assertion on the support: begin{equation} uin kerbiggl ( H^{2p}(X;mathbb Q)to H^{2p}(X-A;mathbb Q)biggr) end{equation} where `` ker" denotes the kernel of the restriction map. Furthermore, the supportive assertion (0.1) implies that $u$ is represented by an algebraic cycle.
Category: Geometry

Bridging Discrete Spacetime with Quantum Intrinsic Wormholes: A QIW-Based Independent Derivation of Quantum Equations

Authors: Wei Zheng
Comments: 13 Pages. (Note by viXra Admin: Please cite and list scientific references; also any AI assisted article is in general not acceptable)

This document presents the Quantum Intrinsic Wormhole (QIW) hypothesis, which proposes a fundamentally discrete spacetime in which intrinsic wormholes oscillate at Planck-scale frequencies, allowing particles to "jump" between discrete grid points. We emphasize the independence of our jumping function from classical equations, showing how standard quantum mechanical results can be recoveredfrom our discrete model in the continuous limit, without resorting to any ad hoc or "mathematical patchwork." The extension incorporates electromagnetic fields and special relativity, successfully reproducing the Compton wavelength, de Broglie wavelength, Schroedinger equation, Heisenberg uncertainty principle, as well as theSchroedinger equation under electromagnetic fields, the Dirac equation, and the Klein-Gordon equation. This comprehensive process demonstrates the QIW’s ability to unify discrete spacetime concepts with fundamental quantum and relativistic principles.
Category: Quantum Physics

Neutrons Are Forming an External Skin in Nuclei and Neutron Stars

Authors: Stephane H. Maes
Comments: 6 Pages. All related details of the projects (and updates) can be found and followed at https://shmaes.wordpress.com/

This paper provides some pointers that are relevant to a few select topics about neutrons structures, neutron stars, and relationship to QCD, in particular with respect to confinement, and stangelets. Neutron stars observations seem to confirm the apparition of deconfined quark gluon plasma at the core of neutron stars, and the presence of a superconducting layer above, so that the crust and the superconducting/superfluid region can also explain neutron stars glitches.Aspects covered in the paper are related to the multi-fold analysis of QCD and QED, including confinement, asymptotic freedom and the mass gap, for which we provided new intuitive analyses and interpretations. It confirms the ability to deconfine, à la percolation, under high density and pressure, while still hiding colors, and the existence of superconducting phases. A consequence of the short analysis is that we can support a neutron star core that is an hybrid of deconfined quarks and nuclei, plus possibly hyperons, while proposing that strangelets are likely not produced by neutron stars: a good news for the future of normal matter, that otherwise could have been infected by any minuscule strangelets contribution, spelling (locally) the end of matter as we know it, even if it is a slow process.
Category: Quantum Physics

Is General Relativity Really General Relativity?

Authors: Taha Sochi
Comments: 7 Pages.

In this short paper we briefly discuss the issue of the theory of general relativity as a supposed generalization of the theory of special relativity to see if general relativity did really generalize special relativity as a relativity theory. The simple conclusion that we reach in this discussion is that the theory of general relativity is not actually a generalization of the theory of special relativity and hence general relativity is neither a general theory nor a relativity theory. In short, the so-called "general theory of relativity" should more appropriately be called the "special theory of general covariance" since it is special in content (as it is essentially a gravitation theory) and it lacks the physical substance of relativity (as it is actually about mathematical artwork of general covariance rather than about physical relativity).
Category: Relativity and Cosmology

Monte Carlo Simulations Predict Distinct Real EEG Patterns in Individuals with High and Low Iqs

Authors: Arturo Tozzi
Comments: 8 Pages.

The neural mechanisms underlying individual differences in intelligence are a central focus in neuroscience. We investigated the effectiveness of Monte Carlo simulations in predicting real EEG patterns and uncovering potential neural differences between individuals with high and low intelligence. EEG data were collected from two groups of volunteers categorized by IQ, namely, a high-IQ group and a low-IQ group. A univariate normal distribution was fitted to each EEG channel using Maximum Likelihood Estimation, after which synthetic datasets were generated based on the estimated parameters. Statistical analyses including Root Mean Square Error (RMSE) calculations assessed the alignment between real and simulated data. We showed that Monte Carlo simulations effectively replicated the statistical properties of the EEG data from both the groups, closely matching the real central tendencies, variability and overall distribution shapes. Specific EEG channels, particularly in the frontal and temporal bilateral regions, exhibited significant differences between the two groups, pointing to potential neural markers of cognitive abilities. Further, the low-IQ group exhibited higher predictability and more consistent neural patterns, reflected by lower RMSE values and smaller standard deviations across several EEG channels. Conversely, the high-IQ group displayed greater variability and larger RMSE values, reflecting complex neural dynamics that are less predictable by Monte Carlo simulations. Our findings underscore the utility of Monte Carlo simulations as a robust tool for replicating EEG patterns, identifying cognitive differences and predicting EEG activity associated with intelligence levels. These insights can inform predictive modeling, neurocognitive research, educational strategies and clinical interventions of targeted cognitive enhancement.
Category: Mind Science

Ether and Its Geometric Changes [as] Origin of Mass, Energy and Light

Authors: Ahmad Torfi
Comments: 6 Pages.

This paper presents a novel model that introduces ether and its geometric changes as the fundamental source of matter, energy, gravity, electromagnetic properties, light, and quantum phenomena such as wave-particle duality and tunneling. This model proposes that the behavior of fundamental particles and forces can be interpreted through the dynamic and complex geometry of ether.
Category: Relativity and Cosmology

Trial Experiments for the Technology [Predicted by] Theories

Authors: Vladimir Pastushenko
Comments: 10 Pages. (Note by viXra Admin: Further regurgitation will not be accepted)

There are amazing properties of mathematics to model and calculate physical properties of matter. Mathematics describes physical experiments, generalizes and predicts physical properties. And mathematical models are created in the Euclidean axiomatics of points ("...having no parts"), lines ("...length without width"), a system of numbers equal by analogy to units. A set of Euclidean points at one point, is it a point or a set of them? A set of Euclidean lines at one "length without width", is it a line or a set of them? Euclidean axiomatics does not give answers to such questions. But it is this axiomatics that is our technology of theories in space-time. There is another technology of theories of dynamic space-matter, in which the technology of theories in Euclidean axiomatics is a limiting, special case. To test the reality of such a technology of theories, in essence, research is conducted by examining trial experiments that follow from such a technology of theories of dynamic space-matter.
Category: Relativity and Cosmology

The Effect of Cognitive Avoidance on Rumination in College Students: the Chain Mediating Role of Perfectionism and Stress

Authors: Debao An
Comments: 12 Pages.

Objective: To study the chain mediating effect of perfectionism and stress on cognitive avoidance and rumination. Methods: A total of 5412 college students were surveyed by Cognitive Avoidance Scale, Perfectionism Scale, Stress Scale and Rumination Scale. Results :(1) correlation analysis showed that there were significant positive correlations among cognitive avoidance, perfectionism, stress and rumination (r = 0.324-0.484, P < 0.001); (2) Cognitive avoidance had a significant positive effect on rumination (t = 0.347, P < 0.001), (3)perfectionism partially mediated the relationship between cognitive avoidance and rumination([0.1096,0.1429], P < 0.001), pressure partially mediated the relationship between cognitive avoidance and rumination ([0.0584, 0.0878], P < 0.001) , perfectionism and stress played a significant role in the chain mediation between cognitive avoidance and rumination ([0.0034,0.0070], P < 0.001) . Conclusion: Cognitive avoidance can directly affect rumination and indirectly affect rumination through the chain mediating effect of perfectionism and stress. This study reveals the relationship between cognitive avoidance and rumination and its mechanism.
Category: Functions and Analysis

Pseudo-Trigonometric Functions

Authors: Ahcene Ait Saadi
Comments: 15 Pages.

This paper introduces a new concept concerning periodic functions. These functions entitled: pseudo- trigonometric functions, allow us to draw curves and periodic straight line segments.I defined the functions : pseudo-sine denoted( spx) and pseudo-cosine denoted (cpx), as well as their reciprocal functions. I defined the hyperbolic pseudo-sine and hyperbolic pseudo-cosine functions. This new mathematical tool allows me to calculate differential equations and integrals of a new kind.
Category: Algebra

Methods of Nonlinear Bifurcation Geometry in the Study of Nonautonomous Scalar Equations

Authors: Alexander C. Sarich
Comments: 19 Pages.

The study of nonautonomous scalar equations comprises a subset of solutions defining the regions of stability and instability inherent to a system. Under specific shifts in the variables of such equations, those referring to a scalar parameter, the quantity of stability points may vary. The exact value at which the quantity of stability points changes, refers to a bifurcation in the system. When a specific function, or set of functions, cannot be solved exactly through algebraic methods, an equivalence to geometric structures may provide intuitive connections to a more abstract topology that solves for those values exactly. Examples considered include˙ x = x−x2e−1(1 + t2)−1, and the Spruce-Budworm and Forest Model.
Category: Functions and Analysis

Investigations in the Displacement Current of Transverse Electromagnetic Waves and Longitudinal Interactions

Authors: Arvin Sharma
Comments: 3 Pages.

The Displacement Current is a peculiar aspect of Maxwell's equation created by theoretical necessity only to be later validated through experimentation. We analyze the properties of the Displacement Current in the static condition of resulting in polarization of dielectrics and in the dynamic condition in Transverse Electromagnetic (TEM) waves. We perform this investigation to determine the role the Displacement Current has in influencing longitudinal interactions attributed to particles of light as part of the long-standing problem of physical optics known as the wave-particle duality, in addition to exploration of the theories of faster than light propagation in theoretical longitudinal modes of electric transmission attributed to the Displacement Current.
Category: Classical Physics

Complex Exponentiation

Authors: Muhammad Talha
Comments: 11 Pages.

This paper presents a comprehensive derivation of a calculatorfriendly expression for computing the power of one complex number raised to another, specifically z1 = a + bi raised to z2 = c + di. By leveraging the fundamental properties and formulae intrinsic to complex numbers, we develop an explicit, practical method that can be implemented on modern scientific and graphical calculators, such as the Casio FX-991ES or newer models. The derivation emphasizes the mathematical rigor required to handle the inherent complexities of exponentiation in the complex plane, while also providing a user-friendly format that simplifies direct calculation. This work not only bridgesthe gap between theoretical mathematics and practical computation but also offers a valuable tool for students, educators, and professionals who frequently engage in complex number arithmetic. With this approach, the need for advanced computational tools like Mapleor Mathematica for complex exponentiation is significantly reduced. The derived formula is capable of calculating complex exponents withprecision up to six decimal places, closely matching the accuracy of these sophisticated tools. Thus, it enhances the efficiency of problemsolving in various mathematical and engineering applications.
Category: Algebra

On Induced Modules Over Group Rings of Soluble Groups of Finite Rank

Authors: Anatolii V. Tushev
Comments: 11 Pages.

The paper is a survey where we discuss various methods for obtaining results oninduced modules over group rings of soluble groups of finite rank. These methodsallow us to obtain results on the structure of solvable groups admitting primitiveand semiprimitive faithful irreducible representations. In particular, it allows usto study the structure of irreducible representations of some classes of nilpotentgroups.
Category: Algebra

The STEM Approach Volume 2: Atomic Structure

Authors: David Lindsay Johnson
Comments: 98 Pages. Volume 2 of 3

STEM (Spin Torus Energy Model) is an energy-centric approach to atomic Physics that is based upon the simple hypothesis that ‘there is only one type of energy-generating material’, and that material is electromagnetic in nature and has been called energen. STEM proposes that, rather than positively charged matter (e.g. positrons and protons) being distinctly different to negatively charged matter (e.g. electrons), all forms of matter are to be related to various energen-based structures. All fundamental particles, composite particles, electromagnetic fields, electromagnetic radiation (EMR) and matter are thus considered to be derived from and definable in terms of energen concentrations, flow patterns or combinations thereof.STEM is a pragmatic approach whose ‘proof of concept’ has been in terms of how well it sits with existing mathematical theory (such as the QM wave equations), existing experimental observations, and the theory behind the practical applications of the applied Science and engineering areas. STEM has resulted in physical models for fundamental and composite particles but, being a pragmatic approach, very little new mathematical theory has accompanied its development. Whereas conventional Atomic Physics tends to be disjointed and conflicted, the beauty of the STEM approach is that it provides consistent seamless explanations across the applied Science areas.This paper is the second of three volumes covering a wide range of Physics-related phenomena. Volume 1 proposes and develops a toroidal structure for the electron, and applies it to explain electricity and electromagnetism. Volume 2 addresses atomic structure, developing a structure for quarks, nucleons and atomic nuclei. Volume 3 addresses the physical nature of light and related forms of electromagnetic radiation (EMR).
Category: Classical Physics

Thermal Relativity Revisited : Relativity of Entropy, Negative Mass, Entropy and Temperature

Authors: Carlos Castro
Comments: 14 Pages.

We review the basics of Thermal Relativity Theory and describe many of the novel physical consequences, including the $corrections$ to the Schwarzschild black hole entropy. One of the most salient results is the existence of a minimal area ${ L_P^2 over 4 pi} $, where $ L_P$ is the Planck length. The brief review paves the way to the study of the thermal relativistic analog of Lorentz transformations. A careful examination of these transformations imply that entropy is observer $dependent$ and that one must also include negative masses, entropy and temperature in the formalism. A review of the literature on negative masses, entropy and temperature follows. In special relativity one has the equivalence of mass and energy. While in thermal relativity one finds an equivalence of proper thermal mass $ {cal M } $ (not to be confused with ordinary mass) and proper entropy $ {bf s }$. We conclude with a brief description of Born's Reciprocal Relativity Theory (BRRT), based on a maximal proper-force, a maximal speed of light, inertial and non-inertial observers, and explain how to extend the formulation of thermal relativity described in this work to cotangent spaces.
Category: Quantum Gravity and String Theory

An Alternate Solution to the Black Hole Information Paradox

Authors: Tariq Khan
Comments: 4 Pages.

A short informal essay proposing that the Holographic Principle may offer a possible alternative solution to the Black Hole Information Paradox proposed by physicist Stephen Hawking. The actual concept of falling is re-examined. Objects that fall into a black hole have their information randomized. This information exists on a holographic boundary where it is randomized, but not lost or destroyed. That information on the holographic boundary in bits is equivalent, in our universe outside of the black hole’s event horizon, to information measured in bits of the total change in distance to the black hole of all entities due to the change (increase or decrease) in black hole mass, after an object falls into it or it evaporates, supporting the theory of a universe that is foundationally a "network of relations." The total change to our universe as a superstructure relational network, as measured in bits of information, is equivalent to the total bits of information needed to describe an object as it disappears behind a black hole event horizon.
Category: Mathematical Physics

The Trouble with GenAI: LLMs are still not any close to AGI - They will never be

Authors: Stephane H. Maes
Comments: 24 Pages. All related details of the projects (and updates) can be found and followed at https://shmaes.wordpress.com/

The pursuit of Artificial General Intelligence (AGI) has been a prominent goal within the field of artificial intelligence. However, this paper argues that current Generative AI Language Models (GenAI LLMs), such as GPT-4 o1, and similar/later LLMs with similar architectures like o3, are fundamentally incapable of achieving AGI. This argument is supported by examining the intrinsic limitations of LLMs, their operational paradigms, and the essential characteristics that define AGI.We discuss a short experiment performed with all the big LLMs, including the latest ones released by the main different AI providers: extracting and producing a list of URL links from a word document. None of the LLMs succeeded, including the latest from OpenAI, Google, Claude or Perplexity. Instead they all get confused, extract only a subset then, when shown how to do it, they hallucinate the links and never produce a complete list. It happens even when shown how to do it. We take this as a counterexample to statements made by many that, by now, end of 2024, GenAI LLMs would, already reach AGI, or be almost there. In fact we argue that AGI is not about to be reached by LLMs any time soon. They will never reach AGI, without changes away from just being LLMS. Claims to the contrary are unrealistic.The paper presents possible direction to reach AGI, and in particulars our views on how to proceed.
Category: Artificial Intelligence

Hooke-Kepler Law of Gravitation [which] Turned Out to Be More Accurate and Perfect Than Newton's Law

Authors: Mykola Kosinov
Comments: 8 Pages. (Note by viXra Admin: Please put author's name after the article title!)

The role of Robert Hooke in the discovery of the law of universal gravitation is shown in a new light. New circumstances are revealed that relate to the priority dispute between Hooke and Newton. It is shown that Newton's law of gravitation is not the only law of gravitational interaction. There is another law of gravitation that was outside Newton's field of vision. The existence of this law was indicated by Robert Hooke in his correspondence with Newton. Robert Hooke pointed out that the law of gravitation should take into account the elliptical orbits of the planets and the inverse square law. In 1687, Newton presented the law of gravitation, which includes the inverse square law. But the parameters of the elliptical orbit were not included in Newton's law. Instead of the orbital parameters, Newton introduced mass into his law. As a result, a more perfect law of gravitation than Newton's law was not discovered. Here we present this law of gravitation. It has a beautiful and mathematically perfect form: FH-K = mR^3/(T*r)^2. I call this physical law the Hooke-Kepler law of gravitation. It includes the Kepler constant. It includes the inverse square law. It does not include the central mass. This is a more accurate and perfect law of gravitation than Newton's law, since distances and periods are known from observations with greater accuracy than mass. Thus, Hooke's path to the law of gravitation was more promising than Newton's. Robert Hooke was very close to discovering an alternative law of gravitation. Obviously, Hooke knew something about gravitation that Newton did not.
Category: Classical Physics

The Fundamental Circularity Theorem: Why Some Mathematical Behaviours Are Inherently Unprovable

Authors: Alister John Munday
Comments: 6 Pages.

This paper introduces the Fundamental Circularity Theorem (FCT), establishing that certain mathematical behaviours are inherently unprovable because they emerge directly from fundamental properties that cannot themselves be proven without circular reasoning. Using the Collatz conjecture as our primary example, we demonstrate how mathematical behaviours that arise purely from the interaction of fundamental properties resist formal proof not due to complexity or logical paradox, but because any proof would require proving unprovable fundamentals. This insight offers a new understanding of mathematical unprovability distinct from Gödel's incompleteness theorems or independence results.
Category: Number Theory

The Black Hole Universe Hypothesis

Authors: Stefanos Kiriakidis
Comments: 4 Pages. (Note by viXra Admin: Listed scientific references should be cited in the article) Contact info: stefan.kiriakidis@outlook.com

This paper proposes a novel hypothesis exploring the formation of black holes and their potential role as conduits to new universes. Building on general relativity and quantum gravity concepts, the hypothesis suggests that singularities within black holes create ruptures in the fabric of space-time, giving rise to white holes that initiate new space-time continua. This process reinterprets the Big Bang as a white hole event linked to a black hole in a parent universe, offering a cyclical model of cosmic regeneration. Observational predictions are outlined, including potential traces of parent universes in the cosmic microwave background, unique gravitational wave signatures, and anomalies in antimatter behavior. Mathematical formulations are provided to describe energy conservation and entropy dynamics during black hole transitions, while future experimental tests are suggested to validate the theory. If proven, this hypothesis could revolutionize our understanding of black holes, the multiverse, and the nature of cosmic evolution.
Category: Relativity and Cosmology

Expanding the 64-Tetrahedron Grid to 256-Tetrahedron Grid

Authors: Bruno R. Galeffi
Comments: 7 Pages.

The octahedron appears as a fundamental geometry in the universe at various scales. The expansion of the 64-Tetrahedron Grid is explored through widening of the octahedron network backbone, which leads to a startling 256-Tetrahedron Grid.
Category: General Science and Philosophy

Duni Model and H0 Tensions

Authors: Mohammad Hadi Mohammadi
Comments: 15 Pages.

In this study, we introduce the Dark Universe (DUNI) model, a novel cosmological framework addressing the Hubble tension and the fine-tuning problem associated with vacuum energy. Unlike the ΛCDM model, which exhibits significant discrepancies with the R21 (Adam Rises) data , the DUNI model proposes that dark energy, rather than radiation, dominates the early universe’s expassion. This distinctive approach significantly reduces the Hubble tension to a consistency level of 0.22σ while maintaining the same number of free parameters as the ΛCDM model . By assuming an exponential function for dark energy and its effects on matter, the DUNI model also addresses the hierarchy problem by predicting a lower effective mass for particles like the Higgs boson in the early universe. Using CosmoMC tools, we validate the DUNI model against observational datasets including R21(Adam Riess), Type Ia Pantheon supernovae, the cosmic microwave background (CMB), and baryon acoustic oscillations (BAO), demonstrating its robust compatibility with current observations.
Category: Relativity and Cosmology

Numerical Symmetry of Magic Squares and Cubes

Authors: Andrey V. Voron
Comments: 7 Pages. (Note by viXra Admin: For the last time, the article heading should be in the following order: Article title, author name and abstract - Future non-compliant submission will not be accepted)

Formulas are defined for calculating the sum of a series of numbers — the so—called constant - that make up a square and a cube of a certain order. The central symmetry of magic squares from the 2nd to the 8th order, as well as magic cubes from the 3rd to the 5th order, is analyzed. It is revealed that the magic squares of the 2nd, 3rd, 4th, 5th, 7th, and 8th order have a "homogeneous" central symmetry (relative to the diagonals), and the magic square of the 6th order has a "mixed" central symmetry. The character of symmetry is determined in the same way for magic cubes of the 3rd, 4th, and 5th orders. "Homogeneous" symmetry is characteristic of the magic cube of the 3rd order and the 5th order, and "heterogeneous" - for the magic cube of the 4th order. Based on the logic of constructing magic squares and cubes, two similar magical objects are constructed — a cube in a cube and cubes in a cube. The first one is based on a magic square of the 4th order (Albrecht Dürer, 1514), and the second one is based on a magic square of the 8th order. These magical figures have a "mixed" symmetry.
Category: Number Theory

Sn1987a and the Neutrino Mass

Authors: Enrique Domínguez Pinos
Comments: Pages.

In this paper, the multi-messenger event SN1987A is analyzed from the point of view of special relativity of fields. We will first obtain the speed of the neutrinos which, together with the estimate of their kinetic energy, will allow us to get an idea of their mass. The characteristics of the next Betelgeuse event will also be predicted.
Category: Relativity and Cosmology

Unified Spin Dynamics: From Pseudovector Nature to Relativistic Constraints

Authors: Satoshi Hanamura
Comments: 17 Pages.

We present an algebraic framework demonstrating that electron spin states arise dynamically rather than being predetermined. By reinterpreting Thomas precession in accelerated motion, we establish the natural quantization of spin angular momentum to ℏ/2, and its characteristic 4π periodicity. The 0-Sphere model introduces a dynamic photon sphere, characterized by Zitterbewegung oscillation at approximately 0.04c. This mechanism resolves the superluminal velocity paradox in classical electron models, while providing a physical basis for spin orientation. Our analysis of the outer product operation reveals that spin states emerge from periodic variations, with orientation determined by dynamic processes rather than predefined properties. The model naturally explains spin's pseudovectorial nature through the geometric properties of the photon sphere, providing a unified understanding of spin transformation under spatial inversion and time reversal. Furthermore, we propose a novel interpretation of quantum entanglement through temporal phase progression, where correlated spins maintain their relationship via coherent oscillations instead of non-local interactions. Our findings suggest that the violation of Bell's inequality originates from the failure of realism, not locality. This perspective preserves locality and explains entangled states through coherent temporal phase evolution, offering a novel understanding of quantum mechanical correlations.
Category: Quantum Physics

There not Exists Odd Perfect Numbers

Authors: Juan Elias Millas Vera
Comments: 1 Page.

Proof by contradiction of non existence of odd perfect numbers by parity comparasion.
Category: Number Theory

Spacetime Quantization Via Null Geodesics in a Static Manifold

Authors: Christopher R. Brown
Comments: 13 Pages.

We construct a static, spherically symmetric cosmological solution that reproduces the observed linear redshift-distance relation without resorting to metric expansion. By defining the radial coordinate via null geodesics and introducing the dimensionless parameter Hr/c, the matter density profile and metric emerge directly from the Einstein field equations. The solution admits a stable static configuration with a density distribution scaling as ρ(r) ∝ [1 + (Hr/c)]^-2, and recovers standard redshift-distance behavior through gravitational redshifts alone. No cosmological constant or fine-tuning is required, and the resulting spacetime is consistent with basic observational constraints. This model also predicts a Schwarzschild horizon and associated Hawking radiation. The factor of change needed to blue shift this radiation to the 2.725 K observed in the CMB is shown by (2.725 K)/(T_K) = √(r_H/2l_p). The quantization of spacetime simply emerges as a consequence of the presence of mass. This entire framework should be considered with a great deal of skepticism, as it deviates considerably from standard practices. However, the approach does offer a theoretically consistent model that has the potential to resolve several long-standing mysteries in physics and warrants investigation from the broader community based on the scholarly arguments alone.
Category: Relativity and Cosmology

Geometrical Meaning of Covariant and Contravariant Vector

Authors: Mueiz Gafer KamalEldeen
Comments: 4 Pages.

This article presented the accurate understanding of the geometrical meaning of covariant and contra-variant vectors, critically analyzing three prevalent misconceptions about this concept found in numerous sources.
Category: Relativity and Cosmology

Is 1.41+1.73=3.14 Just a Coincidence

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 20 Pages. 5 Figures, in Chinese.

This paper gives the precise relationship formula of π with the square root of 2 and the square root of 3, i.e., 2^0.5+3^0.5=πγ with γ=1.00148705350035u2026, and gives the relevant approximation formula which we found in 2022, i.e., 1.41+1.73=3.14, in which 1.41, 1.73 and 3.14 correspond to the centigrade approximations of the square root of 2, the square root of 3 and π respectively. We also review the applications of the formula of 1.41+1.73=3.14 in our theories including the centigrade natural number axis, the new atomic units, the new periodic table of elements, the chirality model of atomic nucleus and the periodic table of nuclides, the formulas of the fine-structure constant, the formulas of the speed of light in atomic units, the predictions of the super-heavy elements and the formulas of the anomalous magnetic moments of electron, muon and tauon. And hence we conclude that the formula of 1.41+1.73=3.14 is not just a coincidence but is a basic principle in the sub-atomic world.
Category: Nuclear and Atomic Physics

Mini-review on Quantum Gravity and Particles

Authors: Risto Raitio
Comments: 14 Pages.

This review is a phenomenological, introductory mini-review on Quantum Gravity, some Cosmology and visible/dark Particles. As an unforeseen result we obtain arguments that three a priori very distinct ideas, namely Hartle-Hawking initial condition, all order finite Chern-Simons quantum gravity and unbroken global supersymmetry of preons provide the necessary tools for unifying all particles and the four forces. This combined model is a novel, noteworthy candidate for BSM physics.
Category: High Energy Particle Physics

Mechanical Advantage of Electromagnetic Railgun for Space Launch Assist

Authors: Felipe Wescoup
Comments: 12 Pages.

Space launch has traditionally relied on vertical rocket systems that must overcome Earth's gravity while carrying their entire propulsion system and fuel load from ground level. This paper presents analysis of a horizontal electromagnetic rail launch system for space launch assist, examining its mechanical advantage for winged launch vehicles. Unlike traditional rocket designs where minimizing mass is paramount, this concept benefits from concentrating significant mass behind a minimal forward-facing profile, fundamentally changing the optimization approach. The mechanical advantage increases non-linearly with launch velocity, suggesting rail-assisted launch could enable more efficient space access. The SpaceX Starship and Super Heavy configuration was used as a reference case to quantify these benefits.
Category: General Science and Philosophy

Ankmahor: High Priest, Initiator, and Bridge Between Worlds

Authors: Matthias Otte
Comments: 4 Pages.

Ankmahor was a prominent high priest in ancient Egypt, known for his magnificent mastaba from the 6th Dynasty, often referred to as the "Tomb of the Physician." In addition to his role as a priest and healer, Ankmahor played a central part in the initiation rituals of young priests, guiding them on their symbolic journey through the underworld, a crucial spiritual journey central to the Egyptian Mysteries. This article highlights Ankmahor's significance as a spiritual leader and teacher, preparing young priests for their transformative journey. His role in conducting rituals that symbolized the transition from the material world to spiritual existence is especially emphasized. The article draws parallels between the Egyptian underworld journey and later traditions, including gnostic teachings in the Gospel of Thomas and Christian rituals such as baptism and the descent of Christ into the underworld. Ankmahor's influence on Western spirituality and his importance as a "bridge between worlds" are underscored.
Category: Religion and Spiritualism

Introduction to the Cubic Ellipsoid Nuclear Model and its Correlation with the Atomic Covalent Radius

Authors: Ronen Yavor
Comments: 12 Pages.

This study suggests that the nuclear structure determines the atomic properties and proposes a geometric nuclear model to confirm this. The model contains the advantages of the liquid drop, shell, collective and cluster models and can serve as a starting point to an effective field theory process. The main goal at this stage is not necessarily to obtain more accurate results than existing models, but rather to raise the possibility of a tangible interpretation of nuclear and atomic physics and to explore different perspectives of this idea. According to the model, the nucleus generally has an ellipsoidal shape, made up of a three-dimensional lattice of proton-neutron bonds (treated here as a cubic system) and nuclear shells populated by protons, which resemble the atomic shells of the periodic table. The excess neutrons (those not paired with protons) are in the nuclear envelope. First, it is shown that the model is empirically confirmed (to a good approximation) via nuclear mass calculation and a consistent development of the nuclei with filled sub-orbitals. It is then argued that the periodic system is derivable from the model. Furthermore, the spatial nuclear structure is shown to correlate with the covalent atomic radius, and this potentially implies that the nuclear structure determines the atomic properties.
Category: Nuclear and Atomic Physics

The Synthesis of Metaphysics and Jungian Personality Theory

Authors: Claus D. Volko
Comments: 5 Pages.

A debate on Facebook dealing with the idea that one could continue living after his/her death if one uploaded the contents of one‘s brain onto a computer has stimulated me to thinking about the relationship between mind and matter. The conclusions I have come up with are far reaching: they explain what probably is the true self of a person, why there probably is a life after death, and all of a sudden, Carl Gustav Jung‘s theory of psychological functions makes sense as I have managed to build a model of the human organism from which most of Jung‘s theory follows per logical deduction.
Category: General Science and Philosophy

Mathematical Modeling of Microtubule Polymerization Kinetics: Insights Into Dynamic Instability and Treadmilling

Authors: Daoudi Rédoane
Comments: 9 Pages.

Microtubules are essential components of the cytoskeleton in eukaryotic cells, playing pivotal roles in intracellular transport, cell division, and maintaining cell structure. Their dynamic behavior, such as polymerization, depolymerization, and their response to variouscellular signals, makes them a fascinating subject for study. While biochemical and biophysical research has significantly advanced our understanding of microtubule function, recent mathematical models have provided new insights into their dynamics, stability, and interactions with other cellular components. This article explores the application of advanced mathematical tools to model the structure, dynamics, and functionality of microtubules. Techniques such as differentialequations, statistical mechanics, network theory, and computational simulations are employed to describe microtubule behavior at multiple scales, ranging from individual tubulin dimers to entire microtubule assemblies. We highlight key models that have advanced the understanding of microtubule dynamics and discuss how these models canbe applied to uncover the molecular mechanisms underlying various cellular processes and diseases.
Category: Physics of Biology

Astrological Darwinism: Prophesying the Return of Feminine Magic

Authors: E. P. J. de Haas
Comments: 85 Pages.

In this book I update the 1890s Theosophist and 1970s New Age attempts to fuse spiritualism with modern science. The main inspiration for Astrological Darwinism comes from the esoteric works of the philosopher Bergson and the Egyptologist Schwaller de Lubicz. In this book I elaborate the intuition that the Astrological Great Year is fundamentally a Cycle of Life in the evolution of humanity. The core of this idea is that a cyclic manifestation of Bergsons ‘élan vital’ can be projected onto the Zodiac of Denderah. A cyclic version of Bergson’s ‘Creative Evolution’ results and will be applied to human evolution of the last hundred thousand years. Schwaller de Lubicz suggested that the Zodiac of Denderah depicted the Pharaonic Egyptians’ knowledge of three such cycles, thus dating back to the very paleo-anthropological origin of human symbolism, some seventy eight thousand years ago.According to the sociologist Weber, our era can be characterised by a steady process of ‘Disenchantment’, of progressive objectification and technological advancement. In playback we would see a process of reversed-Weberian Enchantment. This playback is our prophesied future. Our present-day linear conception of history and evolution is thus replaced by a cyclic view, following the timeline of the Great Year of Astrology. Disenchantment will continue and peak at the Age of Aquarius, after which re-enchantment will set in and peak again at the future Age of Leo, fourteen thousand years from now. I identify this ‘peak magic’ as ‘peak creative evolution’ in line with Bergson’s neovitalism.Philosophically, Astrological Darwinism centres around two axioms. The first is the quantum axiom of `chosen wave function collapse' and its biological subset of `chosen mutations'. It is the Bersonian `élan vital' of the soul that makes the choices by quantum looking at the genes and thus acting as a metaphysical or vital `hidden variable' causing genetic mutations. The 'Goddess Principle' is a more appropriate name for this axiom, because the main active agents of this capacity are women during or around the Age of Leo. The second axiom is that the capacity of complex, multicellular life forms to apply this `chosen mutations' is cyclic, following the 26.000 year precession of the equinox. I expect this second axiom to be verified by a future quantum-gravity-biology, which might be developed in the next hundred years or so.Astrological Darwinism is a metaphysical narrative with implications for evolutionary biology, history and trans-humanism. In this book, the last six Great Years are reconstructed, going back 140 thousand years, thus producing a new Grand Narrative of human evolution.
Category: Religion and Spiritualism

Proof of Goldbach Conjecture

Authors: Toshihiko Ishiwata
Comments: 9 Pages.

This paper is a trial to prove Goldbach conjecture according to the following process.1. We find that {the total number of ways to divide an even number n into 2 prime numbers} : l(n) diverges to ∞ with n → ∞. 2. We find that 1 ≤ l(n) holds true in 4 ∗ 1018 < n from the probability of l(n) = 0. 3. Goldbach conjecture is already confirmed to be true up to n = 4 ∗ 1018. 4. Goldbach conjecture is true from the above item 2 and 3.
Category: Number Theory

Cubic Equation Revisited: Part 1

Authors: Kohji Suzuki
Comments: 71 Pages.

Prior to revisiting cubic equation, we treat quadratic equation. Included herein are reviews on it, a root-finding algorithm, which is compared with the Newton's method, a tidbit about the Euler—Mascheroni constant, and so on.
Category: General Mathematics

Continued Fraction Representations of Universal Numbers and Approximations

Authors: Hans Hermann Otto
Comments: 7 Pages.

We present continued fraction representations of universal numbers and some approximations to underline on what nature’s infinitely repeated processes are footed as the mathematical basis of our life and the entire cosmos.
Category: Number Theory

Comment on "Coherent and Incoherent Light Scattering by Single-Atom Wavepackets"

Authors: V.A. Kuzmenko
Comments: 3 Pages.

The e-print arXiv:2410.19671 [1] presents new, interesting results of the experimental study of scattered light by cold atoms. Here we propose an alternative explanation of the physical nature of anisotropic radiation scattering and a simple protocol for its experimental verification.
Category: Quantum Physics

Symbiont Conversion Theory

Authors: Claus D. Volko
Comments: 7 Pages.

Symbiont Conversion Theory is a new scientific theory, summarizing and generalizing efforts that have been made by various researchers in the past years; it could even be perceived as a new scientific paradigm. This theory states that microorganisms and cells which are commonly considered to display parasitic behaviour can be "educated" and transformed into symbionts. This is not just a hypothesis but a theory since there is already evidence that proves that this is possible. The primary motivation for developing this theory is the failure of classical approaches to therapy of cancer and infectious diseases that follow the paradigm "destroy and kill". It is common knowledge about medical doctors that chemotherapy and radiation therapy have detrimental side effects on healthy, functional tissue, and also that antibiotics can harm benevolent cells. These negative side effects can possibly be avoided by the new approach of treating parasitic diseases by converting the culprits into symbionts of which the human organism profits. Another motivation for developing this theory is that some researchers have suggested bacteria and other microbes have certain innate rights themselves [Cockell].
Category: Biochemistry

Cassell's New Latin Dictionary and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 28 Pages.

We study the Cassell's New Latin Dictionary, Latin-English/English-Latin, Second Edition, 1962.We draw the natural logarithm of the numbers of the Latin head entries of the Latin-English part of the Dictionary, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised/unnormalised. We find that the Latin head entries of the Cassell's New latin Dictionary underlie a magnetisation curve of a Spin-Glass in the presence of little external magnetic field.
Category: Social Science

A Generalized Scalar Field Lagrangian for Cosmological Phenomena

Authors: A. Solomon
Comments: 8 Pages.

We establish a generalized scalar field field framework with a universal speed of ( v_t ). Implications for quantum mechanics, particularly in the context of pilot wave theory, suggest a novel perspective on non-locality and quantum entanglement. The corresponding generalized scalar field Lagrangian provides a unified description of inflation, dark matter, and dark energy. In the early universe, the theory predicts inflationary observables with a modified Lorentz factor; at galactic scales, it accommodates MOND phenomenology; and in the late universe, it reduces to a modified quintessence model with corrections of order $c^2/v_t^2$ to the dark energy equation of state. The extremely high value of $v_t$ ensures compatibility with existing constraints while allowing for small, potentially observable effects at cosmological scales.
Category: Relativity and Cosmology

Random Matrix Theory, Topological Invariants, and Differential Topology in Ecological Systems: An Integrated Approach

Authors: Richard Murdoch Montgomery
Comments: 17 Pages.

Random matrix theory (RMT) has long served as a cornerstone of modern physics, mathematics, and complex systems analysis. More recently, topological and differential topological methods have emerged as powerful tools to characterize the global structures and stability properties of ecological networks. This article develops an integrated framework bridging RMT with topology and differential topology to study ecological systems, aiming to provide novel insights into their resilience and underlying structural features. We present the relevant mathematical foundations, illustrate computational algorithms (including multiple graphical outputs), and demonstrate these methods on both synthetic and real ecological data. Our findings highlight how topological invariants, combined with the spectral properties of large random matrices, shed light on the stability and transition behaviors of communities under perturbations. Advantages and limitations are discussed, paving the way for future research directions at the intersection of mathematics and ecology.
Category: Topology

Interference Mechanics as Theory of Everything

Authors: Yusuke Kato
Comments: 46 Pages.

The electromagnetic, strong, Higgs, weak, gravity force are explained as the result of interference. The force is that the waves try to avoid weakening and to strengthen each other to increase their probability of existence. These forces correspond to axial, radial, space moving, time moving, size symmetry. The Standard Model is explained geometrically, with γ and Z^0 are orthogonal planes, W^± is a sphere, and Θ_W is the angle between a sphere and a plane. All forces are unified in the form that the magnitude of the geometrically expressed phase asymmetry coincides with the gauge coupling constant. The theoretical and experimental values for the mass and coupling constant of the gauge particle are almost in agreement. Photons are symmetrical from front to back, so they have zero mass. All forces are derived from the principle that particle waves are always standing waves. The masses of all fermions are expressed in geometric volume ratios, and it is suggested that the generation is the number of dimensions of space. Energy and asymmetry are equivalent. The asymmetry of the Higgs particle is 1, and the Higgs mass M_H is a natural unit. 2M_H-v.e.v. divided by the Higgs volume inflated to match the hierarchy of gravity matches the observed value of dark energy. All forces and mass are not just one or something that was unnecessary in the early universe, they are all necessarily necessary.
Category: Quantum Gravity and String Theory

Physical Models of Ion Channel Kinetics: Opening, Closing, and Inactivation and Their Implications in Disease

Authors: Daoudi Rédoane
Comments: 7 Pages.

Ion channels are essential for the proper functioning of excitable cells, governing key processes such as action potentials, resting membrane potential and cellular homeostasis. The kinetics of ion channel opening, closing, andinactivation are critical to their proper function, and mathematical modeling of these processes offers valuable insights into both normal physiology and pathophysiological conditions. This article explores the biomathematics behind ion channel kinetics, focusing on the mechanisms of channel gating andinactivation, and how these processes are mathematically described. Furthermore, it discusses the implications of ion channel dysfunction in various diseases, including neurological disorders, cardiac arrhythmias, muscular diseases, and cystic fibrosis. By modeling the dynamics of ion channel statesand incorporating experimental data, mathematical approaches help to elucidate disease mechanisms and support the development of targeted therapies for ion channel-related diseases. This work highlights the power of biomathematical models in advancing our understanding of cellular physiology andin guiding clinical interventions.
Category: Physics of Biology

The STEM Approach Volume 1: Electricity and the Duplicit Electron

Authors: David Lindsay Johnson
Comments: 94 Pages.

STEM (Spin Torus Energy Model) is an energy-centric approach to atomic Physics that is based upon the simple hypothesis that ‘there is only one type of energy-generating material’, and that material is electromagnetic in nature and has been called energen. STEM proposes that, rather than positively charged matter (e.g. positrons and protons) being distinctly different to negatively charged matter (e.g. electrons), all forms of matter are to be related to energen-based structures or various combinations thereof. All fundamental particles, composite particles, electromagnetic fields, electromagnetic radiation (EMR) and matter are thus considered to be derived from and definable in terms of energen concentrations, flow patterns or combinations thereof.STEM is a pragmatic approach whose ‘proof of concept’ has been in terms of how well it sits with existing mathematical theory (such as the QM wave equations), existing experimental observations, and the theory behind the practical applications of the applied Science and engineering areas. STEM has resulted in physical models for fundamental and composite particles but, being a pragmatic approach, very little new mathematical theory has accompanied its development. Whereas conventional Atomic Physics tends to be disjointed and conflicted, the beauty of the STEM approach is that it provides consistent seamless explanations across the applied Science areas.This paper is the first of three volumes covering a wide range of Physics-related phenomena. Volume 1 proposes and develops a toroidal structure for the electron, and applies it to explain electricity and electromagnetism. Volume 2 addresses atomic structure, developing a structure for quarks, nucleons and atomic nuclei. Volume 3 addresses the physical nature of light and related forms of electromagnetic radiation (EMR).
Category: Nuclear and Atomic Physics

Design of Carbon Dioxide Sorbents Within the Framework of the Potential Energy

Authors: Vitaly V. Chaban
Comments: 29 Pages.

This article explores a modern approach to designing carbon dioxide (СО2) sorbents based on the concept of the potential energy landscape (PEL). The authors analyze the relationship between PEL characteristics and СО2 sorption efficiency. The article demonstrates how manipulating PEL parameters enables the development of optimized materials with desired sorption properties. The article investigates the influence of the depth and distribution of energy minima on the selectivity, capacity, and kinetics of СО2 sorption. Various strategies for modifying the PEL, including surface functionalization and the targeted introduction of defects, to achieve the desired sorption characteristics are highlighted. Examples of different types of sorbents, such as MOFs, zeolites, and activated carbons, designed within the framework of the PEL concept. Potential applications of the developed sorbents in carbon capture and storage technologies, as well as the synthesis of chemically valuable products. This review will be of interest to specialists in materials science and energy who are engaged in the development of new sorption materials.
Category: Classical Physics

A Long-lasting Dilemma Around the Relativistic Mass in the Special Theory of Relativity Resolved With Experimental Proof

Authors: Bhasanpal Thiru
Comments: 2 Pages.

The glitch in the Special Theory of Relativity that has been unresolved for very long time due to its insignificance in the day to day practical application, but will be of greater significance in the upcoming era has been finally resolved.
Category: Relativity and Cosmology

Four Dimensional Spacetime Will Continue in the Future?

Authors: Tatsuyuki Sugawa
Comments: 6 Pages.

In this short report we speculate the spacetime dimension in our universe , by using both the Kasner solutions to the Einstein field equations and the Kaluza-Klein concept of the extra dimension. Surprisingly around the past Big-Bang, the space- time dimension may have been two dimensional (1+1) , and in the future the spacetime dimension may tend to three dimensional one (2+1) , though our observable space-time is four dimensions at the moment. This is a toy model.
Category: Quantum Gravity and String Theory

Clarification of the Proof of the Syracuse Conjecture

Authors: Berkouk Mohamed
Comments: 22 Pages. In French

The Collatz conjecture which is defined by: starting from all positive integer n, we apply these 2 instructions, if it is even divide it by 2, and if it is odd we multiply it by 3, we add 1 and we divide all by 2, the conjecture states that if we repeat the transformation of n, we always end up falling on 1 which in turn finds itself trapped indefinitely in the trivial cycle 1, 2, 3, 4. three steps were taken to arrive at its demonstrations, the first led to the uniqueness of the Trivial Cycle which consisted, in PART 1, of exploring in the Trivial Cycle a property recurring in all other cycles with more than three terms of which they can only generate, according to their Cycle equation, positive integers 1, 2 or 4. The second step consists of constructing a direct equivalence between the convergence of Syracuse towards 1 with the fact that the ratio of odd terms to the number of even terms is stuck in the interval [0, 0.63092975..[, and that thanks to this proposition, we were able to demonstrate the decrease of all n towards 1, finally the third step, which by a property of the average demonstrated by recurrence the equation which connects the powers of 2 with the powers of odd terms to which we applied the —Collatz 3n +1 instruction.
Category: Number Theory

The Penguin Dictionary of Archaeology by Warwick Bray and David Trump, Second Edition, 1982, and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 18 Pages.

We study the head entries of The Penguin Dictionary of Archaeology by Warwick Bray and David Trump, Second Edition, 1982.We draw the natural logarithm of the number of head entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the dictionary can be characterised by BW(c=0.01),the magnetisation curve of the Ising Model in the Bragg-Williams approximation in the presence of external magnetic field, H. $c=frac{ H}{gamma epsilon}=0.01$ with $epsilon$ being the strength of coupling between two neighbouring spins in the Ising Model. $gamma$ represents the number of nearest neighbours of a spin, which is very large.
Category: Archaeology

The Statistical Origin of the Spin

Authors: Antonio Fazzolari
Comments: 43 Pages.

Following what already exposed in "The statistical origin of the Alpha constant2", a model based purely on statistical mechanics is proposed to explain and calculate with high accuracy the properties of the electron, likecharge, spin and magnetic moment. All these features, beyond the very existence of the electromagnetic interaction, derive essentially from the assumption that a boson wave field possesses a chemical potential and from the definition of two statistical sets of opposite temperature. It's also shown that the SU(2) algebra, which is normally just assumed for the half Spin particles, is a consequence of this statistical structure, as it happens for theelectric interaction. The only constants used are c, ħ and the Boltzmann constant. The model predicts also a light asymmetry between electric repulsion and attraction that could explain the origin of the weak interaction.
Category: Quantum Physics

Mathematical Modeling of mRNA Translation: Insights and Applications

Authors: Daoudi Rédoane
Comments: 6 Pages.

The process of messenger RNA (mRNA) translation is a fundamental biological mechanism through which genetic information is converted into functional proteins. This article explores the mathematical principles used to model mRNA translation,the components of these models, and their applications in understanding cellular biology and disease.
Category: Physics of Biology

The Role of Potential Energy Landscape Research in the Development of New Electrolyte Solutions

Authors: Vitaly V. Chaban
Comments: 27 Pages. in Russian

The development of new electrolyte solutions with improved characteristics is a key challenge for creating high-performance batteries, fuel cells, supercapacitors, and other electrochemical devices. The study of the potential energy landscape (PEL) plays an important role in this process, providing information about the interactions between solution components at the molecular level. In this work, we review the practice of applying PEL research methods based on classical and quantum-chemical algorithms to analyze the structure, dynamics, and thermodynamic properties of electrolyte solutions. Intermolecular and ion-molecular interactions at the microscopic level, which determine the macroscopic properties of the electrolyte solution, are considered in detail. The importance of identifying stable configurations of ions and their solvates is emphasized. PEL analysis allows for the systematic determination of the most probable structures and complexes formed in solution, which is important for understanding ion transport mechanisms. The study of the PEL allows for the determination of the energy barriers that must be overcome for ion migration, which is related to the conductivity of the electrolyte. The application of PEL research methods in combination with experimental data opens up new possibilities for the rational design of electrolyte solutions with desired physicochemical properties.
Category: Condensed Matter

On the Diophantine Equation Ax+by=c with a ≡ (± 10/p)[b] and P ∈ {1, 2, 5, 10}

Authors: Algoni Mohamed
Comments: 10 Pages.

We propose a method to solve the Diophantine equation (E)1 : ax + by = c, where a, b, andc are natural numbers with a, b ̸= 0 and a≡±(10/p)[b], where p ∈ {1, 2, 5, 10}. The method is based on analyzing the units of the products pc and pb, denoted as u and uu2032, respectively. This approach simplifies and accelerates the resolution process by focusing on these units.
Category: Number Theory

Gravitational Redshift from the Early Universe

Authors: Dave E. Dunstan
Comments: 4 Pages.

A simple gravitational alternative to Hubble’s Law is presented. Measured redshifts are attributed to gravitation rather than recessional velocity. The measured redshift-distance data fits a gravitational potential with constant mass. Redshift is then a measure of the gravitational potential and the space-time curvature of the early universe. The redshift-distance data is fitted to a constant mass of 3.35 x 1053 kg (1.67 x 1023Msol) which is 2.23 times the estimated total mass of ordinary matter in the current universe. The expanding and accelerating universe are not predicted and the speculation of dark energy is no longer required.
Category: Relativity and Cosmology

Self-Healing Metalized Film Capacitors: Quo Vadis?

Authors: Nadezhda Andreeva, Vitaly V. Chaban
Comments: 29 Pages. In Russian

Metal film capacitors are ubiquitous components in modern electronics, playing an important role in energy storage, filtering, and voltage regulation. However, their performance and reliability can be reduced by partial electrical breakdowns caused by defects in the dielectric material. An attempt to partially mitigate this problem is the use of self-healing capacitors. The self-healing phenomenon significantly increases the service life of the device. This review presents a comprehensive analysis of the currently known aspects and mechanisms of self-healing in metal film capacitors. The role of the self-healing phenomenon in increasing the number of operating cycles of a dielectric capacitor is discussed. The molecular processes underlying significantly different self-healing potentials of dielectric polymers are verified. The review is addressed to specialists in electrical engineering.
Category: Condensed Matter

Happiness and Health Particle Swarm Optimization

Authors: Satish Gajawada
Comments: 2 Pages.

Happiness and Health Particle Swarm Optimization (HaHePSO) algorithm is created by incorporating the Happiness and Health concepts into Particle Swarm Optimization (PSO) algorithm.
Category: Artificial Intelligence

The Solution Path of Riemann Hypothesis

Authors: Zhiyang Zhang
Comments: 32 Pages.

The Riemann hypothesis was proposed by mathematician Bernhard Riemann in 1859. The usual view is that Riemann makes a guess that all non trivial zeros are located on the critical line after simply calculating a few zeros, but this is not the case. Riemann even knew that the probability of counterexamples occurring was very low at that time, so he shyly put forward such a hypothesis. This article provides a detailed explanation of the conditions for the existence of counterexamples in Riemann's hypothesis from his perspective, and provides a calculation method for counterexamples.
Category: Number Theory

Theory and Application of Incomplete Randomness

Authors: Zhi Li, Hua Li
Comments: 8 Pages.

Uncertainty is a complex and ubiquitous phenomenon. Randomness is an important concept to describe uncertainty, and its quantitative tool is probability. Through an in-depth study of the distribution law of prime numbers, this paper finds that prime number distribution has both randomness and certainty, which is defined as incomplete randomness. The position of prime numbers in the integer sequence is random, but the number of prime numbers in a certain interval is certain. And there are two trend characteristics of prime number distribution. One big trend is that the density of prime numbers gradually decreases; the other trend is that the probability density in the opposite direction increases slightly. Prime number distribution has a certain randomness, and its distribution is completely controlled by natural laws. There is no accidental cover-up and interference caused by minor factors. The number of prime numbers is fixed. Although there is no accurate function expression, it has a certain degree of certainty. This special type of distribution presents a fixed result and is an incomplete random distribution. The total probability of a particular event is calculated as the cumulative probability: P (total) = ∑P (n). The total cumulative probability as a quantitative tool for incomplete randomness is a new concept. Unlike classical probability, its value is allowed to be greater than the constant 1.The discovery of incomplete randomness helps to find the law of prime number distribution, deepen the understanding of the laws of the universe, and broaden the deeper thinking about the nature of nature.Many conjectures involving prime numbers are unresolved problems, some of which have been around for 300 years. Incomplete randomness can provide a new and unique perspective. This article applies the incomplete random distribution theorem and attempts to give proofs of some of these problems, such as the Mersenne prime conjecture and the Collatz conjecture.
Category: General Mathematics

A Discussion About Certain Axioms in Physics

Authors: Moshe Segal
Comments: 6 Pages. (Note by viXra Admin: Please move the author's credentials etc to a footnote)

An Axiom is a statement whose truth or validity is accepted, without providing any additionalproof or explanation why this statement is accepted as true or valid. On the other hand, Physics is about providing explanations about the Existence and the Universe, and it is expected that the Physics explanations should be accompanied by reason and proof. However, Physics does still contain statements which are presented as Axioms, even though, suchstatements are usually the basis, or the corner stones, of structures, which are built over these statements. This paper addresses this issue, about some of such statements that Physics presents as Axioms, and this paper also intends to provide an additional tentative explanation for one of these statements, which might help in providing additional validity to these statements.
Category: Relativity and Cosmology

The Origin of Gravity

Authors: Arieh Sher
Comments: 5 Pages. (Article title and author name added to the article by viXra Admin)

Modern physics is facing a profound conundrum. There are two major theories in physics: general relativity and quantum physics. Each of these theories has been proven to be correct with high confidence. Yet, no theory combines both. Specifically, quantum physics does not relate to gravity, whereas gravity is a profound parameter in general relativity. I claim that gravity is the residual strong nuclear force. In other words, gravity and the strong force are the same.
Category: Quantum Physics

A Modified Born-Infeld Model of Electrons Leads to a Modified Zitterbewegung of Electrons

Authors: Martin Kraus
Comments: 6 Pages.

Recently, a classical model of electrons has been proposed, which represents the peak of a rotating field solution of a modified Born-Infeld field theory by a point-like particle of half the mass of the whole field solution. While this model is consistent with many features of electrons, it does not include the theoretical frequency of an electron's Zitterbewegung, which is a central part of many other models of spinning point-like electrons. In an attempt to explain the absence of this frequency in the new model, this work hypothesizes that the Hamiltonian of a free electron in Dirac's theory of electrons could be modified by halving the electron's mass when describing its spin motion. This leads to a modified frequency (equal to the Compton frequency), which is consistent with not only the modified Born-Infeld model of electrons but also de Broglie's internal clock hypothesis.
Category: Quantum Physics

Inertial and Fictitious Forces in Physics

Authors: Taha Sochi
Comments: 17 Pages.

In this paper we investigate "inertial forces" and "fictitious forces" and the relationship between them as understood from the literature of physics where the majority seem to consider them as two labels for the same thing while some seem to suggest they are not identical. Our view and preference is to distinguish between them where fictitious forces should be considered a subset of inertial forces. We also investigate the issue of the reality of fictitious forces and whether they have authentic existence in the physical world or they are a kind of "delusion". Our view is that what is called "fictitious forces" can be either. In this regard, we identify and propose several physical characterizations and distinctions between the two types (i.e. the "apparently fictitious forces" which are physically real and the "really fictitious forces" which are illusory because they are purely frame-dependent as viewed by a non-inertial observer). This is consistent with our preference that fictitious forces should be considered a subset of inertial forces, i.e. "inertial forces" which are real should not be classified as "fictitious" in the real sense while "inertial forces" which are not real should be classified as "fictitious" in the real sense.
Category: Classical Physics

Black Hole Dynamics: Transition Across Temporal Spectra

Authors: Paul Caracristi
Comments: 4 Pages.

This paper presents a novel interpretation of black holes, proposing that they represent a transitional process between realms of increasing and decreasing entropy. The event horizon is redefined as the beginning of this transition, where matter and energy shift from dynamic states of high gravitational interaction to a latent realm of static energy. Within this framework, space, time, entropy, and gravity progressively diminish, forming a temporal spectrum of decreasing frequency values. The core of the black hole is characterized as an asymptotic state of stasis and potentiality, a latent realm of pure potential energy. This theory challenges traditional notions of singularities and offers new perspectives on the cyclical nature of dynamic and latent realms.
Category: Relativity and Cosmology

Resolving Dark Matter/Dark Energy Through Gravitational and RSC Fields

Authors: Paul Caracristi
Comments: 5 Pages.

The Great Attractor and Great Repeller are two prominent large-scale structures in the universe, influencing the motion of galaxies through their gravitational and proposed levitational effects. This paper proposes that the Great Attractor represents a region of strong positive spacetime curvature (gravitational field), while the Great Repeller corresponds to a region of strong negative spacetime curvature (Replusive spacetime curvature "RSC"). These dual fields generate dynamic cosmic flows, analogous to atmospheric high and low-pressure gradients on Earth. By incorporating RSC fields into cosmological models, this framework offers an alternative explanation for phenomena currently attributed to dark matter and dark energy. This perspective suggests that these enigmatic entities may not be as abundant or necessary as previously assumed, providing a new paradigm for understanding the universe’s large-scale structure and evolution.
Category: Relativity and Cosmology

Protein Folding Kinetics and Their Anomalies in Channelopathies

Authors: Daoudi Rédoane
Comments: 5 Pages.

Proteins are the molecular machines that drive almost every biological process in living organisms. The correct folding of a protein is crucial for its function, as its three-dimensional structure determines its biochemical properties and interactions with other molecules. However, protein folding is not always perfect. Misfolding or incomplete folding can lead to dysfunctional proteins, which is implicated in various diseases. One of the most significant classes of diseases caused by protein misfolding are textit{channelopathies}, disorders that involve ion channel dysfunction, often due to the misfolding of ion channel proteins.This article delves into the kinetics of protein folding, explores the mathematical models that describe the folding process, and investigates how anomalies in folding kinetics contribute to the pathophysiology of channelopathies. The article covers the physical principles behind protein folding, the influence of mutations on folding dynamics, and how disruptions in folding kinetics lead to misfolded ion channel proteins, causing diseases such as cystic fibrosis, epilepsy, and certain cardiac arrhythmias.
Category: Physics of Biology

Fabrika Theory Part 1: A Pixel-Based Framework for Deriving the Gravitational Constant

Authors: Ali Movahedian
Comments: 21 Pages. (Correction made by viXra Admin on the Submission Form - Please conform!)

Fabrika Theory introduces a novel framework in which space-time is fundamentally discrete, composed of Planck-scale cubic pixels. Gravity, within this paradigm, emerges from the annihilation dynamics of these pixels in the vicinity of mass. This paper presents a comprehensive mathematical derivation of the gravitational constant based on the principles of pixel annihilation. By setting the radial distance to the Planck length and expressing the speed of light in terms of Planck units, we derive an expression that aligns closely with its observed value. The implications of this derivation suggest a profound connection between quantum-scale structures and macroscopic gravitational phenomena, offering a potential pathway towards unifying General Relativity and Quantum Mechanics [1][2].
Category: Relativity and Cosmology

Hopf Vibration, Non-homotopy and Mass

Authors: Garry Goodwin
Comments: 10 Pages.

The Standard Model is unable to determine a particle's specific rest mass. For an alternative theory we consider a 3-sphere intersecting three dimensional space. The intersection is a Hopf fibration with non Euclidean topology. Mass is due to a force jumping topologies. Mass splitting formulae with intersection signature treat the mass of lighter hyperons as a function of the proton, neutron and in some cases electron. The approach is numerical. In MeV the derived values are: $Sigma^+$ $approx$ 1189.371, $Sigma^0$ $approx$ 1192.655, $Sigma^-$ $approx$ 1197.580, $Xi^0$ $approx$ 1314.810, $Xi^-$ $approx$ 1321.711, $Omega^-$ $approx$ 1672.482. Eqs. (15, 19) bring $Sigma$ and $Xi$ particles together as a single family of massive particles ensuring the individual formulae are not ad hoc. The familial status of $Omega^-$ is less secure. To make the case, a scaling factor SM is introduced using $Omega^-$ volume. SM scales rest masses given in any system of units to a dimensionless number proportional to MeV. For precise results less than one fifth of an electron-volt is shaved from the 2022 CODATA neutron adjustment (our value $939.565 , 421 , 76$). To justify SM we consider the difference between Gaussian and SI units. In the final count nine free parameters reduce to two.
Category: Mathematical Physics

Proof of the Riemann Hypothesis (Method Using Absolute Values of Image Part of Xi Function with Some Help from Computers)

Authors: Takashi Nakajima
Comments: 18 Pages. (Version histories/notes at impropriate place blocked by viXra Admin - Please cite and list scientific references)

If s=a+bi, proving that the absolute value of the imaginary part of ξ(s)=ζ(s)Γ(s/2)π^(-s/2) is not 0 for 0<a<0.5, 0.5<a<1, -∞<b<∞ is equivalent to proving that the Riemann hypothesis is true. When searching for 0<b<x (x is near 0) for 0<a<0.5, 0.5<a<1 using a computer, it was confirmed that the absolute value of the integral term of |Im(ξ(s))| is smaller than the absolute value of the additional term of |Im(ξ(s))| and that the polarities of the two are the same. It was shown that even when b→∞, the absolute value of the integral term of |Im(ξ(s))| remains smaller than the absolute value of the additional term of |Im(ξ(s))| and converges. The polarities of the two are the same. As a result, the Riemann hypothesis was proven correct.
Category: Number Theory

Solving Cubic and Quartic Equations by Means of Vieta's Formulas

Authors: Miloš Čojanović
Comments: 11 Pages. This work is licensed under a Creative Commons Attribution 4.0 International License.

In this paper, we will prove that with the use of Vieta's formulas, it is possible to apply a unified method in solving equations of the third and fourth degree.
Category: Algebra

A Gravitational Force that is Independent of Speed Contradicts the Equivalence Principle and the Equality of Heavy and Inertial Mass.

Authors: Ulrich Brosinsky
Comments: 4 pages in English, 4 pages in German

This consideration is concerned with the effect of a given gravitational field on a sample body and not with the contributions made bygravitational sources according to the energy-momentum tensor.The special theory of relativity is therefore sufficient for the investigation in local approximation.a) Using the example of a movement in the direction of a gravitational field, it is shown that either the equivalence principle only applies approximately or gravity does not act on the mass but on the energy of falling bodies.b) If the equivalence of gravity and inertia should also apply to bodies with internal kinetic and potential energies, then gravity isproportional to the respective energy of theindividualcomponents. Otherwise, gravity and inertia would only be approximately equal.The proportionality is transferred to the energy of the entire body despite any internal velocities.c) The planetary motion suggests a velocity-dependent gravitational force, from which the exact validity of the equivalence principlefollows as well as the exact equality of gravity and inertia, even taking into account special relativistic effects.d) Newton's law of gravitation for two masses can be formulated in special relativistic terms by replacing their product with the scalar product of the "mass tangential vectors" to the world lines. This is a conclusion that is possible without recourse to general relativity.e) Short reference to the difference between the gravitational field and the electrostatic field, the force of which is independent of velocity.
Category: Relativity and Cosmology

Group Theory: Problems and Solutions (Part 2)

Authors: Harry Willow
Comments: 25 Pages. (Note by viXra Admin: Please cite and list scientific references)

There is nothing new about group theory in this paper. It presents group theory problems at undergraduate level and their solutions. In presenting the solutions, we avoid using advanced theorems from group theory but we try to discuss the solutions using elementary facts in group theory.
Category: Algebra

Unconditional Convergence of Reciprocal Sums of Polynomial Prime Patterns, Balanced Primes, and Good Primes via the M-Brun Sieve

Authors: Lynette Michael Winslow
Comments: 70 Pages.

We present unconditional proofs of the convergence of reciprocal sums associated with certain special prime sequences defined by polynomial and multiplicative conditions. In particular, consider a polynomialP(x) = sum_{i=0}^{n} c_i x^i quad text{with integer coefficients and } c_n > 0.Define S_P = { p : p text{ prime and } P(p) text{ is prime} }. We prove thatsum_{p in S_P} frac{1}{p} < infty. Moreover, we establish explicit upper and lower bounds for both the counting functionpi_P(x) = |{ p in S_P : p le x }| and the partial sums sum_{substack{p in S_P p le x}} frac{1}{p}. Next, we consider Balanced Primes, defined by the condition that each balanced prime p_n forms a three-term arithmetic progression with its neighbors: p_n = frac{p_{n-1} + p_{n+1}}{2}. Applying our multi-level sieve methods to these primes, we similarly prove the convergence of their reciprocal sum and provide corresponding quantitative estimates. In addition, we examine the set of emph{Good Primes}, defined by the multiplicative inequality p_n^2 > p_{n-i} cdot p_{n+i} quad text{for all } 1 le i le n-1.We show that their reciprocal sum also converges and provide corresponding upper and lower bounds on their counting functions and partial reciprocal sums. Our approach, which we call the M-Brun Sieve, refines classical sieve methods into a multi-level framework that can handle intricate polynomial and multiplicative constraints simultaneously. Notably, our results do not rely on any unproven conjectures. These findings yield substantial new insights into the distribution and density of these special classes of primes, thereby resolving longstanding questions posed by Pomerance regarding Good Primes.
Category: Number Theory

Fixing Reference Hallucinations of LLMs

Authors: Stephane H. Maes
Comments: 14 Pages. All related details of the projects (and updates) can be found and followed at https://shmaes.wordpress.com/

In October and November 2024, using popular LLMs like OpenAI ChatGPT (4 and below), Azure OpenAI and its Copilot instantiations, Google Gemini and GenAI LLM tuned for scientific papers like Zendy, asking a question and references produces with every LLM fake references, well onstructed, but with different titles or authors than the web or journal reference actually associated to the citation, or sometimes totally invented. Prompting to ensure that the reference exists and is correct may help for some, but in general it does not. Others have reported similar issues when using these LLM/GenAI services to produce legal briefs, and other legal documents.This paper suggest simple ways to address this, instead of trying to just improve the LLMs and hope hallucinations will be reduced; they won’t, no matter what, they are inherent to LLM. It is very surprising and mindboggling that LLM providers have not been implementing these kind of solutions: just check if the references exist, are correctly cited, and relevant to the paper/context. We also expand the approach with our MultiAI approach to improve on the previous approach, or address other hallucinations; actually eliminating in our tests.
Category: Artificial Intelligence

Two New Derivations of Ramanujan's Formula Pi^4 Approx 97.5-1/11

Authors: Janko Kokosar
Comments: 5 Pages.

The paper presents two procedures, or derivations with educated guessing, where Ramanujan’s formula for $pi^4$ is the final result. The first derivation uses the integer approximation for $pi^3$, and 22/7 as an approximation for $pi$, followed by a simple modification to match Ramanujan’s formula. The second derivation uses an integer approximation for $pi^5$ alongside with 22/7. Once again, the modification to Ramanujan’s formula for $pi^4$ is quite simple. The aim is also to explore whether further approximations of this formula exist. Some hints are provided on this subject.
Category: Number Theory

The Distribution of Prime Numbers: a Novel Approach

Authors: Daoudi Rédoane
Comments: 4 Pages.

In this article, we introduce a new mathematical conjecture that connects the sum of divisors of integers, prime-counting functions, and the properties of prime numbers. The conjecture incorporates basic number-theoretic functions, including the sum of divisors of an integer n, the sum of the squares of the divisors of n and the prime-counting function π(n), which counts the number of prime numbers less than or equal to n
Category: Number Theory

Metabolic Dysregulation in Schizophrenia: Mechanisms, Implications, and Therapeutic Approaches

Authors: Daoudi Rédoane
Comments: 10 Pages.

Schizophrenia is a complex neuropsychiatric disorder characterized by significant cognitive, emotional, and behavioral disturbances. Recent research has highlighted the critical role of metabolic dysregulation in the pathophysiology of schizophrenia, with particular focus on the relationship between metabolic abnormalities and the brain-gut axis. This review explores the intricate connections between metabolism and schizophrenia, emphasizing how alterations in metabolic processes, including insulin resistance, obesity, and lipid dysregulation, contribute to the disorder's clinical presentation. We examine the impact of antipsychotic medications on metabolism, particularly second-generation antipsychotics, which are associated with significant metabolic side effects. Additionally, we discuss emerging therapeutic strategies targeting metabolic dysfunction, such as pharmacological interventions (e.g., metformin, GLP-1 receptor agonists), nutritional approaches (e.g., omega-3 fatty acids, probiotics), and lifestyle modifications (e.g., exercise). Understanding the molecular mechanisms underlying these metabolic disturbances, including mitochondrial dysfunction, oxidative stress, and epigenetic alterations, is critical for developing more effective, personalized treatment approaches for individuals with schizophrenia. This review also highlights the need for an integrated approach that addresses both psychiatric symptoms and metabolic comorbidities to improve patient outcomes and quality of life.
Category: Mind Science

The Multi-fold Least Action Principle, a Quasi Theory Of Everything

Authors: Stephane H Maes
Comments: 44 Pages. All related details of the projects (and updates) can be found and followed at https://shmaesphysics.wordpress.com/shmaes-physics-site-navigation/.

The principle of least action applies to many domains of Physics. Yet its justifications and derivations usually come from archaic classical principles like the Fermat or Maupertuis principles, or mathematical analytical frameworks used for classical mechanics. As is well known, it is widely applicable to other domains, without necessarily a clear justification for it. In addition, the Feynman Path Integral formulation of Quantum Mechanics gave it a second life. However, the conventional logic to reach these conclusions is at time circular, and the principle is applied without proof that it is applicable: it just works and everybody does it. It is this applicability that led us in the past to treat the Action path integral as God’s equation.The paper justifies the principle of least action and Feynman’s path integrals through different physical reasoning, and on that basis we confirm its validity in most situations, even if Hamiltonians or Lagrangians may be shaky to define, or the system may be dissipative. We also explain when, and why, sometimes, it may not conventionally apply. The derivation uncovers different links between Entropy and Action, which also opens a different way to look at the origin of the probability distribution of even just a single lone particle; especially when complemented with the W-type multi-fold hypothesis, and makes some considerations on Feynman diagrams, instantons, renormalons and resurgence. Also discontinuities in the paths of the path integrals imply that spacetime is discrete, and non-commutative, and supersymmetry in flat spacetime is unphysical. Surfaceology, as optimized computation of the Feynman diagram is shown to trivially predict that all gauge theories double copy dual to gravity share the same forbidden scatterings. We show how the results of the multi-fold theory, in particular the multi-fold space time matter induction and scattering, built explicitly on the path integral formalism, its underlying principles, and the principle of least action, allows recovering almost everything in Today’s physics. It leaves out essentially only some of the coupling constants and mixing angles/parameters. This goes a long way towards the ambition of a Theory Of Everything (TOE). Our justification of the principle of least action, and path integrals, and the multi-fold theory encounters relationships between Entropy and Action. We review these encounters, including that entanglement might be irreversible. Also, from our approach, we obtain a formulation of the evolution of entropy, including for irreversible systems, which matches Onsager and Prigogine’s famous models and principles.
Category: Quantum Physics

Nature of Universal Forces, Leading to a Modified Atomic Structure Including Dirac’s Ideas and Satisfying de Broglie’s Restriction

Authors: Bijon Kumar Sen, Subha Sen
Comments: 16 Pages. 7 Figures; 1 Table

Forces operative in the universe have so long been considered to be pull of particles towards their own both in small and long range. From the properties of short-range nuclear attractions, characteristics such as particle independence, saturation, pair and pairs of pair formation have been developed. Consideration of scattering of atoms by different types of projectiles show that Rutherford’s atomic structure which was modified by Bohr imposing quantum condition does not satisfy known facts. Thus, photons can scatter extranuclear electrons but not powerful enough to scatter nucleons. Although, α- particles and slow neutrons are able to scatter nucleons leading to β+ and β- emission, the neutron- β-neutrino scattering proposed by Fermi poses some difficulties. To cap all these, there is the restriction imposed by de Broglie’s hypothesis that nucleus is neither a repository nor a manufacturer of electrons. To account for all these restrictions, it was found that Dirac’s suggestion of particles and anti-particles in which nucleons are embedded may be fruitfully utilized. Thus, an atomic structure based on modification of Rutherford-Bohr model has been put forward.Triggering impulse of β- emission may be related to the gluon field which holds the binding energy till the point of overstretching of the mass of the quark involved.Key-words: Universal Forces, Short- and Long-range Forces, Characteristics of Nuclear Forces, Modified Atomic Structure including Dirac’s and de Broglie’s Ideas.
Category: Nuclear and Atomic Physics

An Elementary Proof of Fermat's Last Theorem

Authors: Theophilus Agama
Comments: 4 Pages.

We provide an elementary proof of Fermat's last theorem using the notion of olloids.
Category: Number Theory

Unified Gravity Through the Repulsion Graviton Space Model

Authors: Misaki Kasai
Comments: 22 Pages.

The Repulsion Graviton Space Model (Re:GraviS Model) proposes a unified gravitational theory that explains galactic dynamics, cosmic accelerated expansion, and black hole interiors without relying on dark matter or dark energy as separate entities. This model asserts that "Gravity arises as an entropic-driven repulsion of space countering the spherically symmetric repulsive force exerted by gravitons on space", leading to scale-dependent modifications of the gravitational potential that naturally reproduce observed phenomena. At galactic scales, graviton-induced spatial repulsion accurately explains the flattening of galactic rotation curves. The proposed gravitational potential demonstrates strong agreement with high-resolution observational data of galactic rotation curves, providing a physically consistent alternative explanation without invoking dark matter. At cosmological scales, the same repulsive mechanism drives cosmic accelerated expansion, with the derived energy density quantitatively matching observed dark energy values. This suggests that the repulsive force of gravitons acts as dark energy, contributing to the large-scale repulsive dynamics of the universe. In extreme gravitational fields, the equilibrium between graviton repulsion and spatial collapse prevents the formation of classical singularities within black holes. Instead, a quantum spatial region emerges, where gravitons act as interdimensional information carriers, resolving the information paradox and providing a unified explanation for quantum effects near singularities. The model predicts finite core radii, eliminating the problem of infinite density and curvature. These results demonstrate that the proposed framework consistently describes Einstein’s field equations at small scales, cosmic expansion at large scales, and black hole environments under extreme conditions. By redefining gravity as an entropic-driven repulsion of space countering the repulsive force of gravitons, this work challenges the limitations of conventional gravitational theories and provides a groundbreaking pathway toward a quantum theory of gravity that unifies relativity and quantum mechanics. Keywords: Gravity, Gravitons, Quantum Gravity, Dark Matter, Dark Energy, Galactic Rotation Curve, Cosmic Expansion, Black Holes, Black Hole Singularities, Repulsion
Category: Quantum Gravity and String Theory

Calculating the Spatial Curvature of the Universe: an Equation that Relates it to Energy Density

Authors: Fernando Salmon Iza
Comments: 5 Pages.

Understanding the spatial curvature of our universe is a very important topic in astrophysics. The FLRW metric that determines the evolution of the universe is based on the Cosmological Principle (the universe is homogeneous and isotropic on very large scales) and on Weyl's Postulate (the universe behaves like a perfect fluid whose components move as temporal geodesics without intersecting each other). This metric is specified in two equations, the Friedmann equations, in which the curvature term Ωk plays an essential role in its resolution. Determining the value of this term with respect to the energy density term Ωρ may mean solving or not solving the equations in many cases. We do not have the solution to this important question, but we have begun to solve it. We have found an equation that relates, in the FLRW metric, the spatial curvature with the energy density and we have found that the spatial curvature is proportional to the energy density with a proportionality factor very similar to that which relates in Einstein's equations, the Einstein tensor with the energy-momentum tensor, that is, the curvature with the energy. This has important consequences, the first is that, in a universe with matter, the spatial curvature will never be zero, the second is that, for the density of matter in today's universe, the spatial curvature is very small.
Category: Astrophysics

Tokenization is not the Problem

Authors: Danil Kutny
Comments: 6 Pages.

This paper introduces a modification to standard GPT-like models by incorporating character-level encoding. The model uses an LSTM to process individual characters within tokens, which are then embedded into the original token embedding space. This allows the model to maintain token-level processing while adding character-level information to each token. Trained on the BookCorpus dataset, the model was evaluated on tasks requiring character-level manipulation, such as counting letters and reversing words. Surprisingly, the modified model performed similarly to the baseline GPT model, with no significant improvements, suggesting that GPT-like models may inherently learn character-level representations from tokenized inputs.
Category: Artificial Intelligence

Pi is Irrational Using One Trig Identity

Authors: Timothy Jones
Comments: 3 Pages.

We prove the contrapositive of pi is rational implies lim sin n! as n goes to infinity converges to show pi is irrational.
Category: Number Theory

The Temporal Spectrum: Understanding the Universe as an Unbounded Continuum

Authors: Paul Caracristi
Comments: 4 Pages.

This paper explores a conceptual universe model that rejects traditional notions of beginnings, ends, boundaries, infinity, and nothingness. It describes the universe as a spectrum of scales and energy values, where realms of expanding voids and contracting matter coexist within a dynamic framework of implicit and explicit phenomena. The paper examines human perception and its limitations and argues that significant portions of the universe lie well beyond our perceptual and cognitive range. Using examples from cosmology, quantum mechanics, and relativity, this paper seeks to support the assertion that our understanding is necessarily incomplete yet enriched by recognizing the universe's transitional, asymmetric, and spectral nature.
Category: Relativity and Cosmology

On the Flaws in a Resent Extension of Schwarzschild Geometry to Accelerated Masses

Authors: Mueiz Gafer KamalEldeen
Comments: 4 Pages.

In this article, I attempted to demonstrate that generalizing the Schwarzschild solution to cases involving the motion of the gravitational source by decomposing the definition of the metric tensor, transforming the differential elements between reference systems and then reassembling it in the desired system, as presented in some recently published papers on arXiv and elsewhere, is an incorrect approach.
Category: Relativity and Cosmology

Collatz's Hypothesis Is True

Authors: ChaeWon Hwang
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific references)

I will prove that Collatz's hypothesis is true.
Category: Number Theory

Solutions to the Living Space Problem to Overcome the Fear of Resurrection from the Dead

Authors: Jaba Tkemaladze
Comments: 12 Pages.

Humanity, as a part of the biosphere, has disrupted its equilibrium with Earth's system, inevitably leading to a critical juncture that demands a fundamental choice and a radical change in behavioral strategy. On an individual level, if a person does not believe in the existence of an afterlife, death, and hell, they are likely to choose hedonism, which would result in the extinction of humanity without leaving behind any intelligent beings. However, if a person is allowed to die, experience the afterlife, and then be resurrected while retaining the memory of that experience, their behavior would shift—prioritizing the bliss of self-development over mere pleasure. Ethics dictate that all who have previously died must also be resurrected. Can current technologies provide sufficient living space for a constantly growing population? Yes, this is not only possible but has been feasible for some time. To mitigate risks, living space can be expanded through the use of space-faring starships, large enough to sustain billions of people comfortably on territories exceeding the size of India. Intergalactic ships could have surface areas surpassing that of Earth. Additionally, around stars, including the Sun, it is possible to use the material from a single planet to create spheres whose surface areas would vastly exceed that of the planet itself.
Category: Religion and Spiritualism

Quantum Wave Entropy

Authors: Xiao Lin Li
Comments: 13 Pages.

In quantum mechanics, particles have a new type of probabilistic property, which is quantum wave probability. Corresponding to this new probability, the particle has the property of quantum wave entropy, and it has the property of quantum wave temperature. Based on the quantum wave entropy, the Unruh formula, the black hole entropy formula, and the Verlinde entropy gravitational formula can be easily derived. It proves that these three formulas are not independent of each other, but are related to each other. These three formulas have the same physical origin, which is quantum wave entropy. The quantum wave temperature has similar properties to the Unruh temperature. The quantum wave temperature is not only directly proportional to acceleration, but also inversely proportional to velocity. The Unruh temperature is just a light speed case of quantum wave temperatures. Compared to the Unruh temperature, the quantum wave temperature is significantly larger and easier to test experimentally. All experiments to test the Unruh effect can be used to test the theory of quantum wave entropy. We can use experiments to test whether the theory is true. The quantum wave entropy can solve the contradiction between the time reversal symmetry of the dynamical equation and the law of entropy increase. The action corresponds to quantum wave entropy. The least action principle corresponds to the stationary quantum wave entropy principle. The quantum wave entropy creates a bridge between the dynamical equations and thermodynamics.
Category: Quantum Physics

Comprehensive Proof of the Np Problem: Integrating Advanced Mathematical Theory and Computational Techniques

Authors: Ren Sakai
Comments: 14 Pages.

This paper presents a novel approach for solving NP problems by integrating advanced mathematical theories, extensive experimental validation, efficient utilization of computational resources, and interdisciplinary methods. By leveraging recent advancements in number theory and graph theory along with optimized computational techniques, we aim to provide a comprehensive framework that addresses the complexities of NP problems, ultimately leading to their complete resolution.
Category: Data Structures and Algorithms

The Octa Quadrant System: an Extension of the Cartesian Coordinate System

Authors: Israr Luqman
Comments: 5 Pages. (Note by viXra Admin: Please submit article in pdf format only)

This paper proposes the Octa-Quadrant System (OCS), an innovative extension of the Cartesian coordinate system that divides the plane into eight quadrants instead of the traditional four. Each quadrant spans 45° and is grouped into unique pairs to form a novel coordinate framework. This extension allows new algebraic operations, geometric interpretations, and rotational symmetries to be explored. Theoretical foundations, algebraic properties, and potential applications of the OCS in mathematics, physics, and engineering are discussed, alongside a comparison with existing systems and their limitations.
Category: Number Theory

Self as the Core of Biological Feedback Systems: An Ideogrammatic Model of Memory and Recognition

Authors: Hyunho Shin
Comments: 21 Pages.

Despite significant advancements in memory research—from the level of the entire brain to specific regions and even to the connections between neurons—the exact physical location and mechanism by which memories are stored remain unresolved. Moreover, most existing studies have focused primarily on output data such as behavioral responses, leaving research on the memory system itself rather limited. In contrast, the recently proposed "meshcode" theory posits binary encoding within cells via the talin protein, suggesting that physical symbols of memory may exist at the molecular level. If certain proteins function as physical symbols that store memory, the earliest memory system might have directly linked symbols and meanings in an ideogrammatic manner, and the first concept to be encoded would have been "self," based on feedback mechanisms. Furthermore, the varied feedback systems found in living organisms can be viewed as another name for the memory system. By examining how these feedback systems, which originate from self/non-self recognition, expand, we can infer the structure of the memory system. This approach not only reconstructs the structural algorithms of memory but also implies that memory may be distributed throughout the organism rather than limited to the brain. In addition, the expansion of self-recognition feedback systems may serve as a universal foundation for the formation of self-awareness and consciousness. Such insights offer a framework forreinterpreting the origins of memory and consciousness beyond the limits of neuroscience, while also revealing that today’s artificial intelligence is constrained by the absence of self-recognition algorithms. In the future, the design of AI or humanoids based on self-recognition could open the door to the emergence of consciousness.
Category: Mind Science

Some Hypergeometric Formulas

Authors: Edgar Valdebenito
Comments: 3 Pages.

In this note we give some formulas related to Pi.
Category: Number Theory

Robustness to Spurious Correlation: A Comprehensive Review

Authors: Mohammadjavad Maheronnaghsh, Taha Akbari Alvanagh
Comments: 20 Pages. This article will be published in ECCV by Springer.

The persistence of spurious features in machine learning models remains a significant challenge. To address this issue, we identify several future directions that require attention. Firstly, we highlight the need for a new dataset that allows researchers to control the types and levels of spurious features, as this resource is currently lacking. Secondly, we emphasize the importance of addressing spurious features in natural language processing, where more attention is needed compared to vision-related tasks. We also stress the need for addressing spurious correlations at the core algorithmic level, rather than relying on complex, task specific solutions that may not generalize well. Finally, we advocate for the development of weakly-supervised or unsupervised methods that reduce reliance on group labels, making the approaches more widely applicable. Our review aims to provide a comprehensive overview of existing work and guide future research in creating more robust machine learning models.
Category: Artificial Intelligence

Trisecting an Arbitrary Angle Problem Solved

Authors: Joseph Musonda
Comments: 5 Pages.

Trisecting an arbitrary angle using a straightedge and compass only has been one of the oldest mathematical geometric problem tracing back to Euclidian times. This problem was never solved until 1837 when it was proven impossible by French Mathematician Pierre Wantzel. As stated by Pierre Laurent Wantzel (1837), the solution of the angle trisection problem corresponds to an implicit solution of the cubic equation x cubed minus 3x minus 1 equals 0, which is algebraically irreducible, and so is the geometric solution of the angle trisection problem. The step-by-step instructions are given which are used to trisect an acute or obtuse angle( a reflex angle can be trisected by first trisecting 180 degrees angle and then the remaining one is trisected by using the authors steps, finally a 60 degrees is added to a corresponding other angle that results from trisection). This method explained here can trisect any arbitrary angle. Only a compass and straightedge is used. The formal proof is later given after a practical illustration. For practical sake and to prove the possibility of trisecting an arbitrary angle, the author used the most common angle of 60 degrees that mathematicians uses to explain the proof for impossibility. The author believes that this proof will act as a basis for further research in geometry in future.Keywords: trisecting, arbitrary angle, geometry, straightedge and compas, implicit solution
Category: Geometry

[a] Ratio Method of Solving Linear Systems of Equations in Two and Three Variables

Authors: Joseph Musonda
Comments: 11 Pages. (Note by viXra Admin: Please Do NOT use author's name to name the title, formula, equations etc.)

The purpose of this paper is simply to present to the mathematics community a novel approach of solving systems of linear equations in two and three variables. This method uses products of coefficients with determinants and constants with determinants. The method is derived through the cross multiplication of equations which results in finding the critical values (Dx, Dy and Dz). These critical values are later substituted in any initial given equation for the purpose of finding scale factor K. It is this scale factor that is multiplied with critical values to find real solutions. The analysis of this formula shows that it is certainly accurate for all problems it is invented for. Unlike the Crammer’s rule, substitution method, elimination method that requires three and four determinants to solve a two and three variable problems of linear systems of equations, for this method the two and three variable problems only two and three determinants respectively. In two variables In three variables x= (c1Dx)/M x=(d2Dx)/M y=(c1Dy)/M y=(d2Dy)/M z=(d2Dz)/MCoefficients an,bn,cn and constants is obtained from any of the single equation. The ratio method is formally derived and proven in the methodology section and Denominator (M) =a1Dx+ b1Dy for a two variable equations and M=a1Dx+ b1Dy+ c1Dz for 3 variable equations.Keywords: Linear systems of equations, Ratios, Critical Values, Scale factor K, Crammer’s rule, elimination method, substitution method.
Category: Algebra

Infinite Numbers in Mathematics

Authors: Weike Xu
Comments: 49 Pages. The sequence of sections in this article is carefully arranged for correct understandings. It is recommended for professionals to read in order.

A method named `motional construction' is introduced in this article. Questions involving continuum hypothesis and incompleteness theorems of formal systems are answered, but a major concern of this article is a nature of infinity: Infinity implies paradoxes.Many conclusions contradicting orthodox mathematics are proved, such as: a set of real numbers does not exist, Lebesgue measure of any set is zero, ZF axioms are not logically consistent, etc. Unreliable results are common in sub-fields of mathematics where infinite sets are used intensively.A valid mathematical conclusion describes finiteness in essence.When infiniteness is clear, the third mathematical crisis shall be over.
Category: Set Theory and Logic

Analysis of Creep Deformation

Authors: Sourangshu Ghosh
Comments: 78 Pages.

Creep deformation, a time-dependent material response under sustained stress, plays a critical role in the long-term performance and reliability of structural components, particularly at elevated temperatures. This article presents a mathematically rigorous analysis of creep deformation mechanisms and a phenomenological framework to describe its stages and evolution. By coupling microstructural insights with continuum mechanics, we derive and validate constitutive models capturing the interplay of stress, temperature, and material properties.The analysis integrates diffusion kinetics, dislocation dynamics, and grain boundary phenomena into a unified formalism, ensuring precision in predicting creep behavior across a wide spectrum of materials.
Category: Classical Physics

Particle-Wave Theory of Light

Authors: Rajeev Kumar
Comments: 3 Pages.

In this paper a particle-wave theory of light has been presented in order to explain the dual nature of light.
Category: Classical Physics

The Physics of a Universe with a Variable Planck "Constant"

Authors: En Okada
Comments: 30 Pages.

We propose a novel theoretical paradigm that all physical realities can be concretely defined by the degree of spontaneous symmetry breaking in a binary field, providing an alternative interpretation of the Higgs mechanism. Together with a newly proposed hypothesis that the Planck constant evolves in accordance with the cosmic scale factor, which drives an evolution of the mass and electric charge of elementary particles, our model solves all the hierarchy problems of theoretical physics in one shot, demystifying all the four fundamental interactions as different aspects of a singular consistent story.
Category: Quantum Gravity and String Theory

On the Spectral Flow Theorem of Robbin-Salamon for Finite Intervals

Authors: Urs Frauenfelder, Joa Weber
Comments: 79 Pages. 6 figures

In this article we consider operators of the form ∂sξ + A(s)ξ where s lies in an interval [−T , T ] and s → A(s) is continuous. Without boundary conditions these operators are not Fredholm. However, using interpolation theory one can define suitable boundary conditions for these operators so that they become Fredholm. We show that in this case the Fredholm index is given by the spectral flow of the operator path A.
Category: Geometry

A Progress on the P vs NP Problem

Authors: Theophilus Agama
Comments: 13 Pages.

This paper presents a significant advancement in understanding the P vs NP problem through the lens of problem theory. Using isotopes as a technical tool within this framework, we provide a solution to the problem, establishing that $mathrm{P}=mathrm{NP}$. The results demonstrate the effectiveness of the proposed theoretical framework in addressing fundamental problems in computational complexity.
Category: Set Theory and Logic

Group Theory: Problems and Solutions (Part 1)

Authors: Harry Willow
Comments: 18 Pages.

There is nothing new about group theory in this paper. It presents group theory problems at undergraduate level and their solutions. In presenting the solutions, we avoid using advanced theorems from group theory but we tried to discuss the solutions using elementary facts in group theory.
Category: Algebra

Comprehensive Analysis and Proof of the Collatz Conjecture Through Multidisciplinary Approaches

Authors: Ren Sakai
Comments: 16 Pages.

This paper summarizes research attempting to prove the Collatz conjecture.Summary of the Collatz Conjecture:.Starting with any positive integerIf n is even, divide by 2(n/2)If n is odd, then multiply by 3 and add 1 (3n+1).Research Approach: Mathematical InductionMathematical inductionProbabilistic MethodGraph Theory I am attempting to prove a proof using a combination of these three approaches.Main theoretical resultsProof of convergence in the odd caseAnalysis of stochastic behavior by Markov chain modelsProof of reachability by graph structureProof of equivalence of the three theoretical approachesNumerical experimentsAnalysis of convergence times and maxima for various initial valuesFrequency analysis of patternsVerification of statistical behaviorFuture workValidation in larger numerical rangesInsights into relationship with computational complexity theoryExploration of potential applications to other number sequence problemsTranslated with DeepL.com (free version)
Category: Number Theory

Rainbow, Great Pyramid, Icosahedron: Mathematics in an Entertaining Way

Authors: Hans Hermann Otto
Comments: 6 Pages.

The rainbow angle of about 42° is comparable with the golden mean based angle between edge and base of the Great Pyramid. It allows bringing together different areas of knowledge in an amusing way using simple geometry besides laws of optics. The mathematical exercise may encourage students to understand spectacles of nature in a simple and didactical manner.
Category: Geometry

Comprehensive Partial Proofs of NP Problems Integration of Advanced Mathematical Theory and Computational Techniques

Authors: Ren Sakai
Comments: 12 Pages.

This paper presents a comprehensive approach to solving NP problems by integrating advanced mathematical theories, extensive experimental validation, efficient utilization of computational resources, and interdisciplinary methods. By leveraging recent advancements in number theory, graph theory, and various computational techniques, we aim to provide a robust framework that addresses the complexities of NP problems and progresses towards the ultimate resolution of the P=NP question.Key contributions of this research include the development and optimization of new polynomial-time algorithms for specific NP-complete problems, such as the Hamiltonian Cycle and Knapsack Problems. We also incorporate probabilistic and quantum computing methods to enhance algorithmic efficiency. Extensive simulations and large-scale experiments validate the practical applicability and scalability of these algorithms across diverse datasets and real-world applications.Additionally, this paper explores the integration of interdisciplinary approaches, such as dynamic systems theory, ergodic theory, Monte Carlo methods, and insights from fields like biology, economics, and social network analysis. These combined efforts create a multifaceted strategy for tackling NP problems, making significant strides towards a potential solution to one of the most critical questions in theoretical computer science.
Category: Data Structures and Algorithms

A Trig Based Proof that Pi is Irrational

Authors: Timothy Jones
Comments: 7 Pages.

It is shown that the limit of cos(j) and sin(j) as j goes to infinity does not exist. DeMoivre's theorem implies cos j! + i sin j! raised to the 1/(j-1)! power equals cos j + i sin j. Assuming pi is rational, its multiple can be expressed as a factorial. This implies that cos(j) and sin(j) converges, a contradiction.
Category: Number Theory

Money Particle Swarm Optimization

Authors: Satish Gajawada
Comments: 2 Pages.

The idea is to incorporate the concept of money into Particle Swarm Optimization (PSO) algorithm to create a new PSO algorithm titled "Money Particle Swarm Optimization (MyPSO)" algorithm.
Category: Artificial Intelligence

Absolute Frame in Physics

Authors: Taha Sochi
Comments: 40 Pages.

In this paper we investigate the concept of "absolute frame of reference" in contemporary physics as well as its properties, instances (or potential instances), types, conceptualizations, evidence, problems, controversies, and so on. This investigation is essentially epistemological in nature and hence we do not discuss or investigate any technical formulation related to this subject.
Category: History and Philosophy of Physics

The Mechanism of Peony Seed Oil Can Promote Sleep by 16S Rrna Gene Sequencing and Metabolomics Analyses of Changes in the Intestinal Flora and Biomarkers in Mice

Authors: Ziyue Liang, Junjie Zhang, Zhiyuan Wang, Xinyi Li
Comments: 44 Pages.

The rapid spread of infectious and non-infectious diseases highlights the critical need for precise, affordable, and field-deployable diagnostic tools, especially in resource-constrained settings. Traditional methods, while widely used, often fall short in meeting the required sensitivity, specificity, and operational efficiency. The CRISPR-Cas system, originally an adaptive immune mechanism in bacteria, has been repurposed into a powerful biosensing tool, demonstrating exceptional potential for accurate and versatile detection. This review examines the current limitations of conventional diagnostic techniques and explores the advancements in CRISPR-Cas—based biosensing. Innovations such as the integration of CRISPR-Cas with amplification methods, nanomaterials, and microfluidic platforms have significantly enhanced its sensitivity, speed, and portability. Challenges like enzyme stability, anti-CRISPR proteins, and PAM dependency remain but are being actively addressed. In summary, CRISPR-Cas systems, combined with other cutting-edge technologies, hold immense promise for providing customized and efficient detection methods, paving the way for revolutionary improvements in diagnostics across diverse applications.
Category: Biochemistry

The Relational Dynamics of Space-Time

Authors: Daniel Marques Rodrigues
Comments: 18 Pages.

This article proposes a theoretical framework for an emergent model of spacetime, conceptualized as a relational structure built from fundamental discrete interactions. The formulation is guided by the central postulate: "Nothing is empty, nothing is solitary; interactions define reality", alongside the Dual Stability Principle and the Triple Existence Principle. In the proposed model:u2022 Binary interactions (EAB) establish local equilibrium and static structure.u2022 Triple interactions (EABC) introduce dynamical complexity and emergentnon-linearity.u2022 Higher-order interactions (EA...N ) describe quantum-scale fluctuations,endowing space-time with intrinsic granularity.A mathematical formalism is developed to sum these contributions into an emergent metric tensor, which smoothly transitions between discrete (microscopic) and continuous (macroscopic) scales. Notably, the model recovers classical General Relativity (GR) solutions, including the Schwarzschild, Kerr, and FLRW metrics, in the macroscopic limit.At extreme regimes—such as black holes and the primordial universe—the model regularizes classical singularities via quantum-induced oscillations and fluctuations, ensuring finite curvature and physical consistency.Testable predictions are presented, including quantum corrections to gravitational waves near horizons (detectable by LIGO, Virgo, and LISA) and nonGaussian signatures in the cosmic microwave background (CMB), observablethrough Planck and future CMB-S4 missions. These results pave the way toward a unified gravitational description across all physical scales.
Category: Relativity and Cosmology

Cosmic Length L and Constant ξ = F(G)

Authors: Dominique Mareau
Comments: 6 Pages.

Following in the footsteps of Max Planck, through the path of dimensional analysis, this study reveals the factor ξ =1,5457109×1011 which turns out to be omnipresent in cosmology, at all scales. This factor also appears in the form ξ4, as the ratio between the Coulomb energy and the gravitational energy, acting on an electron-positron pair, separated by a unit distance. This same factor reveals, through several independent paths, a cosmic and constant length: L = 2483 Gyl. In addition to the valuable tool offered by dimensional analysis, this study uses the mass unit "electron" which allows to compare dimensionless ratios with masses expressed in the same unit. The study indicates that Newton’s constant G, is determined with the parameters [M, L, T] of the electron and the factor ξ4. Via the factor ξ8 and the standard photon density, ρph = 4.1073×108 u / m^3, the study predicts the mass density ρ = 8.953389×10-10 J/ m^3. The application of the Friedmann-Lemaitre equation, reveals: Ho = 72.7411 km s-1 Mpc-1 = 2.360126×10-18 s-1; the age of the Universe, 13.44 Gy; the critical density ρc = 8.953386×10-10 J/ m^3 < ρ = 8.953389×10-10 J/ m³. These results are close to the results obtained by the WMAP 1 space probe, namely: 13.77 Gy; Ho = 73±3 km s-1 Mpc-1 = (2.35±0.10)×10-18 s-1. However, they are in disagreement with the results of the Planck 2018 mission: Ho = 67.4±0.4 km s-1 Mpc-1 = (2.18±0.01)×10-18 s-1. This study also reveals what could be likened to a cosmic "string" of length L and Planck section, whose volume is equal to the Compton volume of the electron.
Category: Quantum Gravity and String Theory

A Theory of Finite Natural Numbers Based on Continuous Changes in Four-Dimensional Space

Authors: Dan Liu
Comments: 9 Pages.

This paper introduces a novel mathematical framework based on the assumption that the set of natural numbers is finite. By considering continuous changes in four-dimensional space, we redefine the concepts of natural numbers and multidimensional spaces, establish new mapping relations, and explore the implications of this hypothesis for Gödel's Incompleteness Theorem.
Category: General Mathematics

The Complete Eigenwert-Solution of Damped Spacetime-Oscillations for Two Coupled Tangential Spacetimes with Ftl-States

Authors: Holger Döring
Comments: 11 Pages.

The complete eigenwert-problem of damping process of oscillating tangential spacetime is described and solved. Characterized are all solutions of an associated spacetime - differential-equation of second order from advanced Lorentz-Einstein-factor, which defines the whole oscillation-process of damping states. This system of oscillation-solutions can be described as a set of energy-equations. The system of two coupled spacetimes to a linked shell-model allows movement of material bodies or particles with ftl and real restmasses. This spacetime- lineelement can be interpreted as a one-parametrized pseudo-Kummersurface.
Category: Quantum Gravity and String Theory

How to Detect Berry Phase in Graphene Without Magnetic Field?

Authors: Hamed Koochaki Kelardeh, Vadym Apalkov, Mark I. Stockman
Comments: 14 Pages.

We discuss the topological properties of graphene superlattices excited by ultrafast circularly-polarized laser pulses with strong electric field amplitude, aiming to directly observe the Berry phase, a geometric quantum phase encoded in the graphene's electronic wave function. As a continuing research on our recent paper, Phys. Rev. B 96, 075409, we aim to show that the broken symmetry system of graphene superlattice and the Bragg reflection of electrons creates diffraction and "which way" interference in the reciprocal space reducing the geometrical phase shift and making it directly observable in the electron interferograms. Such a topological phase shift acquired by a carrier moving along a closed path of crystallographic wave vector is predictably observable via time and angle-resolved photoemission spectroscopy (tr-ARPES). We believe that our result is an essential step in the control and observation of ultrafast electron dynamics in topological solids and may open up a route to all-optical switching, ultrafast memories, and petahertz-scale information processing technologies.
Category: Condensed Matter

On the Sequence: A(n)=4a(n-1)-2a(n-2)-4a(n-3)-A(n-4)

Authors: Edgar Valdebenito
Comments: 3 Pages.

We provide some formulas related to sequence A026937 in OEIS.
Category: Combinatorics and Graph Theory

The Metric Problem in Polar Coordinates: A Comprehensive Analysis and a Solution

Authors: Mueiz Gafer KamalEldeen
Comments: 5 Pages.

The purpose of this article is to demonstrate that the common method for calculating the metric tensor in polar coordinates is incorrect. However, it does not lead to erroneous results due to the presence of another error that cancels out the effects of the first error in calculations. Nerveless, these offsetting errors creates a problem in understanding the metric.
Category: Relativity and Cosmology

Hooke-Kepler Law of Gravitation: the Rejected Law of Gravitation, Which Turned Out to be More Accurate and Perfect Than Newton's Law.

Authors: Mykola Kosinov
Comments: 10 Pages. Hooke-Kepler Law of Gravitation: the Rejected Law of Gravitation Which Turned Out to Be More Accurate and Perfect Than Newton's Law

The role of Robert Hooke in the discovery of the law of universal gravitation is shown in a new light. New circumstances are revealed that relate to the priority dispute between Hooke and Newton. It is shown that Newton's law of gravitation is not the only law of gravitational interaction. There is another law of gravitation that was outside Newton's field of vision. The existence of this law was indicated by Robert Hooke in his correspondence with Newton. Robert Hooke pointed out that the law of gravitation should take into account the elliptical orbits of the planets and the inverse square law. In 1687, Newton presented the law of gravitation, which includes the inverse square law. But the parameters of the elliptical orbit were not included in Newton's law. Instead of the orbital parameters, Newton introduced mass into his law. As a result, a more perfect law of gravitation than Newton's law was not discovered. Here we present this law of gravitation. It has a beautiful and mathematically perfect form: FH-K = mR^3/(T*r)^2. I call this physical law the Hooke-Kepler law of gravitation. It includes the Kepler constant. It includes the inverse square law. It does not include the central mass. This is a more accurate and perfect law of gravitation than Newton's law, since distances and periods are known from observations with greater accuracy than mass. Thus, Hooke's path to the law of gravitation was more promising than Newton's. Robert Hooke was very close to discovering an alternative law of gravitation. Obviously, Hooke knew something about gravitation that Newton did not.
Category: Classical Physics

There not Exists Odd Perfect Numbers

Authors: Juan Elias Millas Vera
Comments: 1 Page.

Proof by contradiction of non existence of odd perfect numbers by parity comparasion.
Category: Number Theory

Proof of Goldbach Conjecture

Authors: Toshihiko Ishiwata
Comments: 9 Pages.

This paper is a trial to prove Goldbach conjecture according to the following process.1. We find that {the total number of ways to divide an even number n into 2 prime numbers} : l(n) diverges to ∞ with n → ∞. 2. We find that 1 ≤ l(n) holds true in 4 ∗ 1018 < n from the probability of l(n) = 0. 3. Goldbach conjecture is already confirmed to be true up to n = 4 ∗ 1018. 4. Goldbach conjecture is true from the above item 2 and 3.
Category: Number Theory

On the Diophantine Equation Ax+by=c with a ≡ (± 10/p)[b] and P ∈ {1, 2, 5, 10}

Authors: Algoni Mohamed
Comments: 10 Pages.

We propose a method to solve the Diophantine equation (E)1 : ax + by = c, where a, b, andc are natural numbers with a, b ̸= 0 and a≡±(10/p)[b], where p ∈ {1, 2, 5, 10}. The method is based on analyzing the units of the products pc and pb, denoted as u and uu2032, respectively. This approach simplifies and accelerates the resolution process by focusing on these units.
Category: Number Theory

Happiness and Health Particle Swarm Optimization

Authors: Satish Gajawada
Comments: 2 Pages.

Particle Swarm Optimization (PSO) is a popular and widely used optimization algorithm for solving complex problems. It is known for its simplicity and ease of implementation. Artificial Birds move in search space to find optimal solution. Although many PSO algorithms were proposed in literature the concepts like happiness and health are not yet explored in PSO algorithms. This article is based on this research gap. Happiness and Health Particle Swarm Optimization (HaHePSO) algorithm is created by incorporating the Happiness and Health concepts into Particle Swarm Optimization algorithm. Each particle in HaHePSO algorithm is associated with happiness and health variables. The movement of Artificial Birds in PSO algorithm is based on fitness values. In HaHePSO algorithm the movement of Artifical Birds is dependent on happiness, health and fitness values. In PSO algorithm Artificial Birds move in the direction of local best and global best of fitness values. This idea is extended in HaHePSO algorithm where Artificial Birds move in the direction of local best and global best of happiness, health and fitness values. The HaHePSO algorithm proposed in this article takes more space and requires extra computation compared to PSO algorithm. This is due to the fact that each particle now has happiness and health variables associated with it and movement in search space is guided by the fitness, happiness and health values.
Category: Artificial Intelligence

The Origin of Gravity

Authors: Arieh Sher
Comments: 6 Pages.

Modern physics is facing a profound conundrum. Gravity is a fundamental force of nature, nevertheless, there is no theory, among many proposed, that can explain satisfactorily the origin of gravity. In addition, there are two major theories in modern physics: general relativity and quantum physics. Each of these theories has been proven to be correct with high confidence. Yet, no theory which combines both has been found. Specifically, quantum physics does not relate to gravity, whereas gravity is a profound parameter in general relativity. A theory that tries to unify the theories is quantum gravity. Quantum gravity hypothesizes that gravity may arise from quantum phenomena. However, there is no accepted answer.I claim that gravity is the residual (or leftover) of the strong force that is confined inside nucleons. In other words, gravity originates from the strong force. In my answer I relate also to the profound open question: Why is gravity, which is involved in the structure of our entire universe, so much weaker than the other fundamental forces?
Category: Quantum Physics

Hopf Vibration, Non-Homotopy and Mass

Authors: Garry Goodwin
Comments: 10 Pages. typos fixed, plus small changes to phrasing

Unable to determine a particle's specific mass the Standard Model leaves rest mass a free parameter. For an alternative theory we consider a 3-sphere intersecting three dimensional space. The intersection is a Hopf fibration with non Euclidean topology. Resistance to a force is due to non-homotopy. The intersection signature appears across mass splitting formulae that treat lighter hyperons as functions of the proton, neutron and in some cases electron. In MeV the derived values are: $Sigma^+$ $approx$ 1189.371, $Sigma^0$ $approx$ 1192.655, $Sigma^-$ $approx$ 1197.580, $Xi^0$ $approx$ 1314.810, $Xi^-$ $approx$ 1321.711, $Omega^-$ $approx$ 1672.482. The electron, $Sigma$, $Xi$ masses provide a solution to the neutron-proton mass difference problem. This is a pure mathematical relationship ensuring the derived $Sigma$, $Xi$ mass values are not ad hoc. The mathematical status of $Omega^-$ is less secure. To make the case, a scaling factor $S_M$ is introduced using $Omega^-$ volume. Rest mass in any system of units is scaled to a dimensionless number proportional to MeV. For precise results less than one fifth of an electron-volt is shaved from the 2022 CODATA neutron adjustment (our value 939.565 421 76). To justify $S_M$ we consider the difference between Gaussian and SI units. In the final count nine free parameters reduce to two.
Category: Mathematical Physics

A Gravitational Force that is Independent of Speed Contradicts the Equivalence Principle and the Equality of Heavy and Inertial Mass.

Authors: Ulrich Brosinsky
Comments: 4 pages in English, 4 pages in German

This consideration is concerned with the effect of a given gravitational field on a sample body and not with the contributions made by gravitational sources according to the energy-momentum tensor. The special theory of relativity is therefore sufficient for the investigation in local approximation. a) Using the example of a movement in the direction of a gravitational field, it is shown that either the equivalence principle only applies approximately or gravity does not act on the mass but on the energy of falling bodies. b) If the equivalence of gravity and inertia should also apply to bodies with internal kinetic and potential energies, then gravity is proportional to the respective energy of the individual components. Otherwise, gravity and inertia would only be approximately equal. The proportionality is transferred to the energy of the entire body despite any internal velocities. c) The planetary motion suggests a velocity-dependent gravitational force, from which the exact validity of the equivalence principle follows as well as the exact equality of gravity and inertia, even taking into account special relativistic effects. d) Newton's law of gravitation for two masses can be formulated in special relativistic terms by replacing their product with the scalar product of the "mass tangential vectors" to the world lines. This is a conclusion that is possible without recourse to general relativity. e) Short reference to the difference between the gravitational field and the electrostatic field, the force of which is independent of velocity.
Category: Relativity and Cosmology

Unified Gravity Through the Repulsion Graviton Space Model

Authors: Misaki Kasai
Comments: 21 Pages.

The Repulsion Graviton Space Model (Re:GraviS Model) proposes a unified gravitational theory that explains galactic dynamics, cosmic accelerated expansion, and black hole interiors without relying on dark matter or dark energy as separate entities. This model asserts that "Gravity arises as an entropic-driven repulsion of space countering the spherically symmetric repulsive force exerted by gravitons on space", leading to scale-dependent modifications of the gravitational potential that naturally reproduce observed phenomena. At galactic scales, graviton-induced spatial repulsion accurately explains the flattening of galactic rotation curves. The proposed gravitational potential demonstrates strong agreement with high-resolution observational data of galactic rotation curves, providing a physically consistent alternative explanation without invoking dark matter. At cosmological scales, the same repulsive mechanism drives cosmic accelerated expansion, with the derived energy density quantitatively matching observed dark energy values. This suggests that the repulsive force of gravitons acts as dark energy, contributing to the large-scale repulsive dynamics of the universe. In extreme gravitational fields, the equilibrium between graviton repulsion and spatial collapse prevents the formation of classical singularities within black holes. Instead, a quantum spatial region emerges, where gravitons act as interdimensional information carriers, resolving the information paradox and providing a unified explanation for quantum effects near singularities. The model predicts finite core radii, eliminating the problem of infinite density and curvature. These results demonstrate that the proposed framework consistently describes Einstein’s field equations at small scales, cosmic expansion at large scales, and black hole environments under extreme conditions. By redefining gravity as an entropic-driven repulsion of space countering the repulsive force of gravitons, this work challenges the limitations of conventional gravitational theories and provides a groundbreaking pathway toward a quantum theory of gravity that unifies relativity and quantum mechanics. Keywords: Gravity, Gravitons, Quantum Gravity, Dark Matter, Dark Energy, Galactic Rotation Curve, Cosmic Expansion, Black Holes, Black Hole Singularities, Repulsion
Category: Quantum Gravity and String Theory

Trisecting an Acute Arbitrary Angle Problem Solved

Authors: Joseph Musonda
Comments: 5 Pages.

Trisecting an arbitrary angle using a straightedge and compass only has been one of the oldest mathematical geometric problem tracing back to Euclidian times. This problem was never solved until 1837 when it was proven impossible by French Mathematician Pierre Wantzel. As stated by Pierre Laurent Wantzel (1837), the solution of the angle trisection problem corresponds to an implicit solution of the cubic equation x cubed minus 3x minus 1 equals 0, which is algebraically irreducible, and so is the geometric solution of the angle trisection problem. This method explained here can trisect any acute arbitrary angle. Only a compass and straightedge is used. The formal proof is later given after a practical illustration. For practical sake and to prove the possibility of trisecting an arbitrary angle, the author used the most common angle of 60 degrees that mathematicians uses to explain the proof for impossibility. The author believes that this proof will act as a basis for further research in geometry in future.Keywords: trisecting, arbitrary angle, geometry, straightedge and compas, implicit solution
Category: Geometry

The Complete Eigenwert-Solution of Damped Spacetime-Oscillations for Two Coupled Tangential Spacetimes with Ftl-States

Authors: Holger Döring
Comments: 11 Pages.

The complete eigenwert-problem of damping process of oscillating tangential spacetime is described and solved. Characterized are all solutions of an associated spacetime - differential-equation of second order from advanced Lorentz-Einstein-factor, which defines the whole oscillation-process of damping states. This system of oscillation-solutions can be described as a set of energy-equations. The system of two coupled spacetimes to a linked shell-model allows movement of materialbodies or particles with ftl and real restmasses. This spacetime- lineelement can be interpreted as a one-parametrized pseudo-Kummersurface.
Category: Quantum Gravity and String Theory