All Submission Categories

Complete Integers: Extending Integers to Allow Real Powers Have Discontinuities in Zero

Authors: Davide Peressoni
Comments: 8 Pages.

We will define a superset of integers (the complete integers), which contains the dual of integers along parity (e.g. the odd zero, the even one, ...). Then we will see how they form a ring and how they can be used as exponents for real numbers powers, in order to write functions which have a discontinuity in zero (the function itself or one of its derivates), as for example |x| and sgn(x).
Category: Functions and Analysis

Universe of Photons and Dark Matter

Authors: Giuseppe Cimino
Comments: 5 Pages.

An alternative hypothesis to the dark matter theory is analysed, using the Photon Universe model to give an explanation to the "missing gap" phenomenon in the rotation curves of some galaxies.
Category: Astrophysics

Modified Alcubierre Warp Drive I: Computation III

Authors: Gianluca Perniciano
Comments: 6 Pages.

A solution of general relativity is presented that describes an Alcubierre propulsion system in which it is possible to travel at superluminal speed while reducing the components of the energy impulse tensor (thus reducing energy density) by an arbitrary value.
Category: Relativity and Cosmology

Multivariate Circle of Partitions and the Squeeze Principle

Authors: Theophilus Agama
Comments: 5 Pages.

The goal of this paper is to extend the squeeze principle to circle of partitions with at least two resident points on their axes.
Category: Number Theory

The Association Between Physical Activity and Cancer Prevention, Recovery, and Recurrence: a Narrative Review

Authors: Shazia Tahira
Comments: 23 Pages. DOI: 10.61838/kman.hn.1.4.7

Cancer is the first most common cause of mortality in the United Kingdom and, after cardiovascular diseases, the second most common cause of mortality globally, accounting for around one in six deaths worldwide. The gravity of this situation highlights the need to find effective ways for prevention and adequate recovery from cancer. Physical activity includes all energy-consuming bodily movements that are produced using skeletal muscles. One in four, or 28%, adults do not engage in adequate physical activity. Physical inactivity is currently the fourth major risk factor for mortality worldwide. Around one-third of deaths from cancer are caused by inadequate physical activity and diet-related factors. Physical activity is associated with both cancer risk and survival for several cancer types; therefore, for controlling cancer, the role of physical activity may be crucial. In this study, a narrative review is presented about physical activity and its association with cancer prevention, recovery, and recurrence. Participation in adequate physical activity is linked to a decreased risk of various cancer types such as breast, endometrial, kidney/renal, colon, rectal, liver, lung, bladder, head and neck cancer, gastric cardia, esophageal adenocarcinoma, myeloma, myeloid leukemia, and non-Hodgkin lymphoma; furthermore, it aids cancer patients of all ages in recovery by reducing the cancer treatment side effects, improving physical fitness, mental health, and quality of life; and additionally, decreases the risk of cancer recurrence after remission. Physical activity impacts cellular processes and tumor growth by controlling body weight and metabolic variables, enhancing mitochondrial and immune function, controlling genomic instability, releasing myokines, and regulating several hormones and circulating biomarkers such as insulin and bile acid. Combining physical activity and therapy is not frequent in real-world settings. Physical symptoms such as pain and fatigue, lack of motivation, lack of time, and lack of exercise information are the major hindrances to physical activity. Therefore, personalized physical activity goals are recommended for all ages, such as active play for children with cancer. In conclusion, an increase in all types of physical activity in all domains of life in the general population and cancer patients according to the recommended guidelines or adapted according to the individual needs of patients can significantly contribute to reducing the burden of cancer and improving overall well-being. Furthermore, there is a need for future studies exploring different domains, various specific types of physical activity, and the association of physical activity with specific cancer sites, with currently limited studies.
Category: Biochemistry

Modified Alcubierre Warp Drive I: Computation II

Authors: Gianluca Perniciano
Comments: 6 Pages.

A solution of general relativity is presented that describes an Alcubierre propulsion system in which it is possible to travel at superluminal speed while reducing the components of the energy impulse tensor (thus reducing energy density) by an arbitrary value.
Category: Relativity and Cosmology

Energy-Momentum Relation in Curved Space-Time

Authors: Jesús Sánchez
Comments: 18 Pages.

In this paper, we will obtain a variation of the energy-momentum relation:E2=m2c4+p2c2To:E2=m2c4+p2c2-Rℏ2c2Where the R corresponds to the Ricci scalar curvature. In very small gravitational fields, the last element (which it can be considered a kind of dark energy) is almost neglectable. Anyhow, we will check the consequences of this in big gravitational fields and in the mass at rest, Klein-Gordon and Dirac equations. In fact, the value of this R has been found to be equal to the cosmological constant (both in the order of 1E-52) making it a perfect candidate for the Dark Energy.
Category: Relativity and Cosmology

Investigation on Brocard-Ramanujan Problem

Authors: Akash Shivaji Pawar
Comments: 7 Pages. 6 Lemma,2 Theorem

Exploring n! + 1 = m^2 for natural number solutions beyond n = 4, 5, 7 confirms no further solutions exist,validated by using GCD Linear Combination Theorem
Category: Number Theory

Understanding the Mathematics of the CMB Power Spectrum

Authors: David Selig
Comments: 14 Pages. (Name added to Article by viXra Admin as required)

The CMB Power Spectrum is one of the most important concepts in Big Bang theory. However, the mathematics of power spectrum analysis are complex and less than intuitive. This paper discusses the mathematics of the power spectrum analysis for CMB, with a focus on bringing clarity to this topic. We discuss the concepts involved and provide examples of the calculations that build towards the CMB power spectrum chart. We examine topics such as the angular power spectrum calculation and associated amplitude calculation. We discuss the spherical harmonic equations and the Legendre functions. We provide example calculations to assist readers in understanding the mathematics behind developing the power spectrum chart. Our audience is those individuals that are interested in cosmology and the Big Bang, and who want to have a better understanding of the mathematics behind the CMB power spectrum analysis.
Category: Relativity and Cosmology

Uk Versus Usa and Ussr Nuclear Warhead Designs History and Its Relevance for Today's Strategic and Tactical Nuclear Weapons in East and West

Authors: Nigel B. Cook
Comments: 26 Pages.

This paper reviews the declassified technical data in the official book "Britain and the H-Bomb". Secrecy-cleared UK thermonuclear warhead historian Lorna Arnold (and her assistant Katherine Pyne) in the UK official history "Britain and the H-Bomb" summarized Atomic Weapons Establishment secret data on UK thermonuclear warhead design tests up to the early interchanges of H-bomb data with America, in 1958-59. The book's information clarifies beyond any doubt the role of plastic foams in dispersing x-rays in the British type of weapon with an isotropically compressed spherical secondary stage, as opposed to the USA use of foam as simply a "radiation mirror" to re-radiate soft x-rays onto the cylindrical Teller Sausage secondary stage requiring only axial compression. Comparing this information to declassified double-primary Russian nuclear warhead design data (see nukegate.org for that) conclusively confirms the different merits of different approaches. This information should be available to inform public debate on not merely whether we have a nuclear deterrent that is efficient and cost effective, but the designs we really need; whether they come from a secrecy-obsessed groupthink culture that drives warhead design into an expensive, inefficient, incredible dead end; or radical, innovative, cheap, credible designs. A summary is given in Fig. 1 of this paper.
Category: Nuclear and Atomic Physics

The Proper Light Speed

Authors: Russell R. Smith
Comments: 15 Pages.

The weak, strong, gravitational, and electromagnetic forces collectively propagate at a rate that is bounded by the speed of light. Since all of the particles within a clock communicate with each other through these forces, when the speed of light dilates, the clock speed changes giving the illusion of time dilation. This can be confusing because the clock slows down, but only due to light speed slowing down, not time itself physically dilating. When you try to measure the speed of light, the clock speed therefore changes proportionally with the change in light speed, so you always measure a value of c no matter what the local speed of light is or how much it changes.Rather than proper time, you have proper light speed, which is how a specified reference frame perceives the speed of light relative to a stationary reference frame in zero-g. The faster an object moves, the slower its proper light speed, which means that all of the fundamental forces slow down causing the moving clock to tick slower than the stationary one. When a muon travels at relativistic speeds, its proper light speed is slow, so all of the forces involved in its decay are slow, causing it to exist for a longer clock-time in the stationary reference frame.The presence of matter changes the local index of refraction, causing light to curve and change velocity. The event horizon of a black hole is where the speed of light is zero. Inside the event horizon, the speed of light is reversed, causing all matter and energy to be forced towards the event horizon, not a singularity.If x is nothing, then by definition, all components of x are also nothing. That is, if a and b are components of x, then [a = x] - [b = x] = x proving that if A - B ≠ x, then A and or B are not components of x. Thus, even in quantum mechanics, something never comes from nothing. Since you cannot produce something from nothing, and something exists today, the fundamentals for said something have always existed. As shown below, time therefore has always passed. We therefore need to consider a model of the universe in which time has always passed, and the universe was organized from fundamentals that have always existed.
Category: Relativity and Cosmology

Active Learning for Question Difficulty Prediction

Authors: Shashwat Gupta, Jibril Frej, Paola Mejia, Tanja Kaesar
Comments: 18 Pages.

This paper focuses on question difficulty estimation (calibration), and its applications in educational scenarios and beyond. The emphasis is on the use of Active Learning to bound the minimum number of labelled samples that we need. It also explores using various SOTA methods for predicting question difficulty, with a specific focus on German textual questions using the Lernnavi dataset. The study refines preprocessing techniques for question data and metadata to improve question difficulty estimation.
Category: Artificial Intelligence

Diff+STN Architectures for External Orientation Correction

Authors: Shashwat Gupta, Vidit Singh, Mathieu Salzmann
Comments: 20 Pages.

STNs are highly efficient in warping the input image for a downstream task. However, cascaded STNs are found to be able to learn more complex transformations. We attempt to leverage the multistep process of diffusion models to produce module(s) that has a similar effectto cascaded STNs.
Category: Artificial Intelligence

Non-Convex Min-Max Optimization

Authors: Shashwat Gupta, Sebastien Breguql, Martin Jaggi, Nicolas Flammarion
Comments: 4 Pages.

In this short study, we aim to gain deeper insights to Keswani’s algorithm [1] for sequential minimax optimisation, by comparing the behaviour with 2 other algorithms : Gradient Descenet Ascent (GDA) and Online Mirror Descent (OMD).
Category: Artificial Intelligence

KBC Void and the Non-Uniform Pion Tetrahedron Condensate

Authors: Rami Rom
Comments: 10 Pages.

We propose that the QCD vacuum pion tetrahedron condensate density should vary in space and should drop in the Kennan, Barger and Cowie (KBC) void for example in analogy to earth’s atmospheric density drop with elevation from earth. Based on Modified Newtonian Dynamics (MOND) theory, we propose to calculate the non-uniform pion tetrahedron condensate density in space and propose a formula for the gravitation acceleration based on the non-uniform pion tetrahedron condensate. A microscopic mechanism for the MOND acceleration crossover at the galaxies’ edges is proposed in terms of the non-uniform pion tetrahedron condensate. The major difference between classical and quantum physics may be the antimatter and the non-empty vacuum discovered by Dirac. The central roles of antimatter and the non-empty QCD vacuum in physics were not anticipated by both general relativity (GR) and quantum mechanics (QM). Their central roles are not fully understood still and the KBC voids and the non-uniform pion tetrahedron condensate are two examples that need further study.
Category: High Energy Particle Physics

A Modified Born-Infeld Model of Electrons and a Numerical Solution Procedure

Authors: Martin Kraus
Comments: Revision fixes equations (2), (5), (6), (16), and adds footnote on page 4.

This work presents a modified Born-Infeld field theory and a numerical solution procedure to compute electron-like solutions of this field theory in the form of rotating waves of finite self-energy. For the well-known constants of real electrons, the computed solution results in a Born-Infeld parameter of 5x10^22 V/m, which is consistent with previous work.
Category: Classical Physics

Stringy Motivic Spectra II: Higher Koszul Duality

Authors: Ryan J. Buchanan
Comments: 11 Pages.

This is a rendition of [2]. We study stringy motivic structures. This builds upon work dealing with $mathbb{F}_p$-modives for a suitable prime p. In our case, we let p be a long exact sequence spanning a path in a pre-geometric space. We superize a nerve from our previous study.
Category: Set Theory and Logic

Uncovering a New Physical Interpretation of the Fine-structure Constant

Authors: Tong Wang
Comments: 5 Pages.

The fine-structure constant is an important dimensionless constant in physics. Several well-known physical interpretations of this phenomenon have been presented. In this study, we propose a new physical interpretation that connects the elementary charge and the Planck mass.
Category: Quantum Gravity and String Theory

A Better Quantum Extremal Surface and Island Interpretation that Explains the Associated Massive Gravity

Authors: Stephane H. Maes
Comments: 38 Pages. All related details of the projects (and updates) can be found and followed at https://shmaesphysics.wordpress.com/shmaes-physics-site-navigation/.

The multi-fold theory describes the evolution of black holes, their evaporation and entropy. It recovers the correct Page curve, and resolves the black hole information paradox. It encounters a quantum extremal surface, as proposed by others using the conventional approach of the island and replica trick. In a subsequent paper, we show that the definitions of the quantum extremal surfaces coincide, while our physical interpretation are rather radically different: an horizon for the multi-folds attached to virtual particles in the multi-fold universe, versus an island à la Wheeler’s bag of gold for the conventional replica trick. We dispute a widely held view that Wheeler’s bag of gold could isolate most of their content from the parent universe. Others have questioned the replica trick with its use of JT gravity, and shown that it implies massive gravity, which might not correspond to a universe where General Relativity (GR) reigns. We show, in multi-fold scenarios, that the inability for multi-folds to escape the quantum extremal surface implies massive gravity effects, while remaining able to recover GR. Therefore, we can provide microscopic mechanisms to explain how massless gravity becomes massive. We also justify relying on JT gravity, by the 2D massless Higgs bosons dilaton random walks. In an asymptotic AdS universe, the replica trick requires the introduction of a reservoir for the evaporated particles, beyond the boundary of AdS. We provide new microscopic interpretations to these scenarios, explaining away these issues, and dealing with the encounter of quantum extremal surface outside the black hole in the presence of a thermal bath. Doing so, we confirm the better suitability of the multi-fold interpretation of the quantum extrema surface, and island, while supporting the replica trick and island formula approach, and resolving the black hole information paradox.The multi-fold analysis applies to our real universe, and the paper provides a microscopic interpretation of quantum extremal surfaces, the correct page curve, the resolution of the black hole information paradox, and the apparition of massive gravity associated to quantum extremal surfaces.From the island formula and replica trick at low masses, we encounter hints of our past proposal for new life cycles of black holes (small extremal black holes splitting into another extremal black hole and an evaporating black hole), which invalidate the strict Weak Gravity Conjecture, and justify the Ultimate Unification (UU) proposal. It is quite a confirmation.
Category: Quantum Gravity and String Theory

Implications if the Electric Field Will be Recognized as a Form of Acceleration

Authors: Moshe Segal
Comments: 19 Pages.

Gravity is already recognized as form of Acceleration, but the nowadays Science of Physics does not recognize (yet) the Electric Field also as a form of Acceleration. However, Structural Identities between Newton's Universal Gravitational Law and Coulomb's Law, strongly indicate that the Electric Field should be also recognized as a form of Acceleration. The implications resulting from the realization, that the Electric Field might be also recognized as a form of acceleration, might not seem to be very significant implications, at first glance. However, this paper does present that, the implications resulting from the realization that the Electric Field might be also recognized as a form of acceleration, are indeed very significant. One immediate implication, from the realization that the Electric Field might be also recognized as a form of acceleration, presented in this paper, is the realization that Newton's Second Law of Motion (F=ma) might not be always valid. Newton's Second Law of Motion is accepted, by the nowadays Science of Physics, as a Universal Law, and as such, it is accepted as being valid for any scenario containing a Force exerted on a massive body. However, as presented in this paper, if the Electric Field might be also recognized as a form of acceleration, then, Newton's Second Law of Motion might not be valid for Electrically Charged bodies attracted or repelled under Coulomb's Law, and, in such a scenario, Newton's Second Law of Motion should be replaced by a different Law. In addition to the above, additional more significant and revolutionary implications, regarding how Humans perceive, the very Nature of the entities of Space and Time, also arise, if the Electric Field might be also recognized as a form of acceleration, which also might provide an answer to the question: why Electric Charges attract or repel each other? That question is still a mystery today, although the answer to the question: why Mass bodies attract each other? is already provided by Einstein's General Relativity theory. The above might also provide a lead to achieve a simple Unification between Gravity and Electricity, a quest which the nowadays Science of Physics is still struggling with, without achieving yet satisfactory results. In addition to presenting very convincing arguments that the Electric Field might be also recognized as a form of acceleration, based on Structural Identities between Newton's Universal. (Truncacted by biXra Admin to < 400 words)
Category: Relativity and Cosmology

An Alternative Approach in General Relativity Describing Gravitational Redshift, Black Holes Without Singularities and Dark Matter

Authors: Wim Vegt
Comments: 33 Pages.

Differently than in General Relativity, the Interaction between Gravity and Light [35] fundamentally has been based on the sum of the "Stress Energy Tensor" and the introduced "Gravitational Tensor". The theory describes "Gravitational-Electromagnetic Interaction" resulting in a mathematical Tensor presentation for BLACK HOLEs. (Gravitational Electromagnetic Confinements) [1] The "Electromagnetic Energy Gradient" creates a second order effect "Lorentz Transformation" which results in the Gravitational Field of BLACK HOLEs which determines the interaction force density between the confinement of Light (BLACK HOLE’s) and the Gravitational Field.Einstein approached the interaction between gravity and light by the introduction of the "Einstein Gravitational Constant" in the 4-dimensional Energy-Stress Tensor (1). In this alternative approach related to General Relativity, the interaction between gravity and light has been presented by the sum of the Electromagnetic Tensor and the Gravitational Tensor (2) . The new approach presents mathematical solutions for the BLACK HOLEs (Gravitational Electromagnetic Interaction) introduced in 1955 by Jonh Archibald Wheeler in the publication in Physical Review Letters in 1955 [1]. The mathematical solutions for BLACK HOLEs are fundamental solutions for the relativistic quantum mechanical Dirac equation (Quantum Physics) in Tensor presentation (35). Assuming a constant speed of light "c" and Planck’s constant ħ within the BLACK HOLE, the radius "R" of the BLACK HOLE with the energy of a proton, is about 1% of the radius of the hydrogen atom (14). The New Theory has been tested in an experiment with 2 Galileo Satellites and a Ground Station by measuring the Gravitational RedShift in an by the Ground Station emitted stable MASER frequency [2]. The difference between the calculation for Gravitational RedShift, within the Gravitational Field of the Earth, in "General Relativity" and the "New Theory" is smaller than 10-16 (12) and (13). In all "General Redshift Experiments" General Relativity and the New Theory predict a Gravitational RedShift with a difference smaller than 15 digits beyond the decimal point which is beyond the accuracy of modern "Gravitational Redshift" observations. Both values are always within the measured Gravitational RedShift in all observations being published since the first observation of the gravitational redshift in the spectral lines from the White Dwarf which was the measurement of the shift of the star Sirius B, the white dwarf companion to the star Sirius, by W.S. Adams in 1925 at Mt. Wilson Observatory.Theories which unify Quantum Physics and General Relativity [32], like "String Theory", predict the non-constancy of natural constants. Accurate observations of the NASA Messenger [11] observe in time a value for the gravitational constant "G" which constrains until ( /G to be < 4u2009×u200910-14 per year) . One of the characteristics of the New Theory is the "Constant Value" in time for the Gravitational Constant "G" in unifying General Relativity and Quantum Physics.
Category: Relativity and Cosmology

On the Nonexistence of Solutions to a Diophantine Equation Involving Prime Powers

Authors: Budee U. Zaman
Comments: 7 Pages.

This paper investigates the Diophantine equation pr + (p + 1)s = z2 Where p > 3, s ≥ 3 , z is an even integer. The focus of the study is to establish rigorous results concerning the existence of solutions within this specific parameter space. The main result presented in this paper demonstrates the absence of solutions under the stated conditions. The proof employs mathematical techniques to systematically address the case when the prime p exceeds 3, and the exponent s is equal to or greater than2, while requiring the solution to conform to the constraint of an even z. This work contributes to the understanding of the solvability of the given Diophantine equation and provides valuable insights into the interplay between prime powers and the resulting solutions.
Category: Number Theory

The Tunisian Land Information System (TLIS)

Authors: Abdelmajid Ben Hadj Salem
Comments: 63 Pages. In French

To celebrate the launch of the "Tunisian Land Information System (TLIS)" project, we would like to recall some of the history of Tunisian geodesy since its inception, and describe in detail the terrestrial and spatial geodetic systems that have been used since then.
Category: Geophysics

Tumbug: a Pictorial, Universal Knowledge Representation Method

Authors: Mark A. Atkins
Comments: 349 pages, 337 figures

Since the key to artificial general intelligence (AGI) is commonly believed to be commonsense reasoning (CSR) or, roughly equivalently, discovery of a knowledge representation method (KRM) that is particularly suitable for CSR, the author developed a custom KRM for CSR. This novel KRM called Tumbug was designed to be pictorial in nature because there exists increasing evidence that the human brain uses some pictorial type of KRM, and no well-known prior research in AGI has researched this KRM possibility. Tumbug is somewhat similar to Roger Schank's Conceptual Dependency (CD) theory, but Tumbug is pictorial and uses about 30 components based on fundamental concepts from the sciences and human life, in contrast to CD theory, which is textual and uses about 17 components (= 6 Primitive Conceptual Categories + 11 Primitive Acts) based mainly on human-oriented activities. All the Building Blocks of Tumbug were found to generalize to only five Basic Building Blocks that exactly correspond to the three components {O, A, V} of traditional Object-Attribute-Value representation plus two new components {C, S}, which are Change and System. Collectively this set of five components, called "SCOVA," seems to be a universal foundation for all knowledge representation.
Category: Artificial Intelligence

Euler’s Totient Function, Sum of Divisors and Primes

Authors: Rédoane Daoudi
Comments: (Note by viXra Admin: Future stub page/paper will not be accepted!)

Here I present a conjecture about Euler’s totient function, sum of divisors andprimes.
Category: Number Theory

How Like Cures Like

Authors: Clark M. Thomas
Comments: 5 Pages.

Relationships among species exist within our entirebiosphere, best envisioned as a system of systems.Human bodies appear to bacteria and viruses asnutrients. We humans prefer to minimize visceralmicroscopic predators. Synergies among the verysmall and the large help determine the fate ofentire species. Webs with multiple size dimensionshost many "like-cures-like" events.
Category: General Science and Philosophy

A Promising Visual Approach to Solution of 82% of Winograd Schema Problems Via Tumbug Visual Grammar

Authors: Mark A. Atkins
Comments: 22 pages, 10 figures

This 2023 document is a wrapper that embeds the author's original 2022 article of the above title that has never been publicly available before. The embedded article is about Phase 1 (which is about Tumbug) and Phase 2 (which is about non-spatial reasoning) of the 5-phase Visualizer Project of the author, a project that is still in progress as of late 2023. The embedded article is currently being re-released by the author to supply more information about that project to the public, and for historical reasons. The embedded article was written before a much more thorough article about Phase 1 (viz., "Tumbug: A pictorial, universal knowledge representation method") became available in 2023, but the embedded article describes results from Phase 2 that have not yet been documented elsewhere.
Category: Artificial Intelligence

Superconducting Principles

Authors: Baihua Qi, Tian Qi
Comments: 18 Pages. (Correction made by viXra Admin to conform with scholarly norm)

This paper explores superconducting principles. Whether a substance is a superconductor depends on whether it has a global electron energy level orbit
Category: Condensed Matter

A Postulate-Free Treatment of Lorentz Boosts in Minkowski Space

Authors: Archan Chattopadhyay
Comments: 4 Pages.

Fundamental results of special relativity, such as the linear transformation for Lorentz boosts, and the invariance of the spacetime interval, are derived from a system of differential equations. The method so used dispenses with the need to make any physical assumption about the nature of spacetime.
Category: Relativity and Cosmology

On the Notion of Carries of Numbers 2^n-1 and Scholz Conjecture

Authors: Theophilus Agama
Comments: 16 Pages.

Applying the pothole method on the factors of numbers of the form $2^n-1$, we prove that if $2^n-1$ has carries of degree at most $$kappa(2^n-1)=frac{1}{2(1+c)}lfloor frac{log n}{log 2}floor-1$$ for $c>0$ fixed, then the inequality $$iota(2^n-1)leq n-1+(1+frac{1}{1+c})lfloorfrac{log n}{log 2}floor$$ holds for all $nin mathbb{N}$ with $ngeq 4$, where $iota(cdot)$ denotes the length of the shortest addition chain producing $cdot$. In general, we show that all numbers of the form $2^n-1$ with carries of degree $$kappa(2^n-1):=(frac{1}{1+f(n)})lfloor frac{log n}{log 2}floor-1$$ with $f(n)=o(log n)$ and $f(n)longrightarrow infty$ as $nlongrightarrow infty$ for $ngeq 4$ then the inequality $$iota(2^n-1)leq n-1+(1+frac{2}{1+f(n)})lfloorfrac{log n}{log 2}floor$$ holds.
Category: Number Theory

A Proof of the Wen-Yao Conjecture

Authors: David Adam
Comments: 24 Pages. In French

In this article, we characterize monomials in de facto values.Carlitz-Goss rielle defined on the complement of Fq (T) in a finite place which arealgebraic on Fq (T ). In particular, this confirms Wen-Yao's conjecturestated in 2003. This gives a necessary and sufficient condition on an en-p-adic tier so that the value of the Carlitz-Goss factorial in it is algebraic on Fq (T ). When restricted to rational arguments, we determinenot all algebraic relations between the values u200bu200btaken by this function, this which gives the counterpart for finite places of a result of Chang, Papanikolas, Thakur and Yu obtained in the case of infinite place.

Dans cette article, nous caractérisons les monômes en les valeurs de la facto-rielle de Carlitz-Goss définie sur le complété de Fq (T ) en une place finie qui sont algébriques sur Fq (T ). En particulier, cela confirme la conjecture de Wen-Yaoénoncée en 2003 . Celle-ci donne une condition necessaire et suffisante sur un en-tier p-adique pour que la valeur de la factorielle de Carlitz-Goss en celui-ci soit algébrique sur Fq (T ). Lorsque restreint aux arguments rationnels, nous détermi-nons toutes les relations algébriques entre les valeurs prises par cette fonction, cequi donne le pendant pour les places finies d’un résultat de Chang, Papanikolas, Thakur et Yu obtenu dans le cas de la place infinie.
Category: Number Theory

Uchida's Identities and Simple Results of 1/0=0/0= Tan(π/2)= Cot(π/2)=0

Authors: Saburou Saitoh
Comments: 4 Pages.

In this note, we would like to show the simple results 1/0=0/0= tan(π/2)= cot(π/2)=0 based on the simple identities that are discovered by Keitaroh Uchida. The logic and results are all reasonable and exceptionally pleasant lookings for high school students.
Category: General Mathematics

Homogenization of the First Initial-Boundary Value Problem for Periodic Hyperbolic Systems. Principal Term of Approximation

Authors: Yulia Meshkova
Comments: 17 Pages.

Let $mathcal{O}subset mathbb{R}^d$ be a bounded domain of class $C^{1,1}$. In $ L_2(mathcal{O};mathbb{C}^n)$, we consider a matrix elliptic second order differential operator $A_{D,varepsilon}$ with the Dirichlet boundary condition. Here $varepsilon >0$ is a small parameter. The coefficients of the operator $A_{D,varepsilon}$ are periodic and depend on $mathbf{x}/varepsilon$. The principal terms of approximations for the operator cosine and sine functions are given in the $(H^2ightarrow L_2)$- and $(H^1ightarrow L_2)$-operator norms, respectively. The error estimates are of the precise order $O(varepsilon)$ for a fixed time. The results in operator terms are derived from the quantitative homogenization estimate for approximation of the solution of the initial-boundary value problem for the equation $(partial _t^2+A_{D,varepsilon})mathbf{u}_varepsilon =mathbf{F}$.
Category: Functions and Analysis

One Tile Suffices

Authors: Volker W. Thürey
Comments: 3 Pages.

We have found for all k larger than two a possibility to tile the plane completely with k-gons. We use infinite many copies of a single tile. The proofs are not by written words, but by pictures. Amongst others, we use the well-known tiling with hexagons. We show for k larger than 4 new ways to cover the plane.
Category: Geometry

Introduction to the Theory of Time Frames: (2) Time Frames and Time Transformations

Authors: Branimir Špigel
Comments: 18 Pages.

This paper extends the ideas presented in our previous work, "Introduction to the Theory of Time Frames: 1) Time Flow."Central to this theory is the notion that time can flow at different rates in different regions of space, leading to a reevaluation of time dilation.As a logical consequence of observing inertial reference frames within the context of different time flows, the need to introduce the concept of "time frames" became apparent. The concept of time frames includes inertial frames of reference within a region of space with a definite flow of time.To compare physical phenomena between time frames with distinct time flows, we introduced a set of relations or formulas referred to as "time transformations." These time transformations enable observers to translate and relate measurements made in one time frame to those made in another time frame with a different time flow.Within the framework of time transformations, several novel concepts were additionally introduced. These concepts include the "time flow coefficient (p)," the "time flow ratio ()," and the "time deceleration coefficient (δ)," which are necessary for furthering our understanding of the relationship between different time frames with varying flows of time.It should be noted that the theory of time frames departs from Einstein's established theories of relativity, rejecting the concept of four-dimensional spacetime and describing a universe with three spatial dimensions and time as a separate, variable entity.This unconventional viewpoint aims to open up new perspectives on the underlying nature of time and its role in shaping the universe.With these advancements, we have laid a solid foundation for the theory of time frames and established a robust framework for its ongoing exploration and refinement.
Category: Relativity and Cosmology

Stringy Motivic Spectra

Authors: Ryan J. Buchanan
Comments: 18 Pages.

We consider strings from the perspective of stable motivic, homotopical QFT. Some predictions for the behavior of gauginos in both a Minkowski light cone and $5$-dimensional $mathcal{A}dmathcal{S}_5$-space are given. We show that there is a duality between working locking in a system of dendrites, and threshold edging at the periphery of a manifold.This work extends the work of [4] and [7] by providing a more mathematical interpretation of the realization of quasi-quanta in open topological dynamical systems. This interpretation incidentally involves the category of pure motives over $mathfrak{C}$, and projections of fiber spectra to the category of stable homotopies.
Category: Topology

Space Time PGA in Geometric Algebra G(1,3,1)

Authors: Robert Benjamin Easter, Daranee Pimchangthong
Comments: Pages.

In Geometric Algebra, G(1,3,1) is a degenerate-metric geometric algebra being introduced in this paper as Space Time PGA [STPGA], based on 3D Homogeneous PGA G(3,0,1) [3DPGA] and 4D Conformal Spacetime CGA G(2,4,0) [CSTA]. In CSTA, there are flat (linear) geometric entities for hyperplane, plane, line, and point as inner product null space (IPNS) geometric entities and dual outer product null space (OPNS) geometric entities. The IPNS CSTA geometric entities are closely related, in form, to the STPGA plane-based geometric entities. Many other aspects of STPGA are borrowed and adapted from 3DPGA, including a new geometric entity dualization operation J_e that is an involution in STPGA. STPGA includes operations for spatial rotation, spacetime hyperbolic rotation (boost), and spacetime translation as versor operators. This short paper only introduces the basics of the STPGA algebra. Further details and applications may appear in a later extended paper or in other papers. This paper is intended as a quick and practical introduction to get started, including explicit forms for all entities and operations. Longer papers are cited for further details.
Category: Algebra

Study Proposal: Towards Streptococcal Infections With Nonspecific Symptoms

Authors: Arturo Tozzi
Comments: (Note by viXra Admin: Future stub page/article will not be accepted)

In 2023, increases in scarlet fever's incidence have been detected throughout Europe. Based on general pediatricians' experience, we hypothesize that a shift has occurred in both group A streptococcus (GAS) clinical findings and age of onset. Therefore, we propose to evaluate whether the well-standardized signs and symptoms leading to GAS diagnosis still hold.
Category: Quantitative Biology

Speculation on A Multidimensional Exploration of Dark Matter, Dark Energy, and Quantum Realities

Authors: Pedro Filipe Soares Pinto
Comments: 7 Pages. (Correction made by viXra Admin to conform with scholarly norm)

The cosmos, in perpetual expansion, conceals intricacies beyond our perceptual grasp. This manuscript delves into the interwoven dimensions of dark matter, dark energy, and quantum realities that orchestrate the cosmic symphony. Initiating from the birth of gravity in the aftermath of the Big Bang, we traverse the multifaceted tapestry of our universe.
Category: General Science and Philosophy

Quadratic Phase Quaternion Domain Fourier Transform

Authors: Eckhard Hitzer
Comments: 12 Pages. Published in: Bin Sheng, Lei Bi, J inman Kim, Nadia Magnenat Thalmann, Daniel Thalmann (eds), Advances in Computer Graphics. CGI 2023. LNCS, vol 14498. Springer, Cham, First Online: 24 Dec. 2023. https://doi.org/10.1007/978-3-031-50078-7_21

Based on the quaternion domain Fourier transform (QDFT)of 2016 and the quadratic-phase Fourier transform of 2018, we introduce the quadratic-phase quaternion domain Fourier transform (QPQDFT) and study some of its properties, like its representation in terms of the QDFT, linearity, Riemann-Lebesgue lemma, shift and modulation, scaling, inversion, Parseval type identity, Plancherel theorem, directional uncertainty principle, and the (direction-independent) uncertainty principle. The generalization thus achieved includes the special cases of QDFT, a quaternion domain (QD) fractional Fourier transform, and a QD linear canonical transform.
Category: Functions and Analysis

Calculating the Curvature of Space-Time

Authors: Fernando Salmon Iza
Comments: 6 Pages. (Correction made by viXra Admin)

We are working on concrete applications of the relativistic Schwarzschild metric to the cosmos. In this report we calculate the Gaussian curvature of space-time. The relativistic Schwarzschild metric solves Einstein's equations exactly assuming a point gravitational mass and empty space in its vicinity. This metric leads to a static and symmetric solution 2D of the mathematical equation of space-time that allows to calculate the Gaussian curvature at each point. We have calculated some curvature values and found a simple equation to calculate them which allows us to extend the results to a wider range of distances. Finally using this equation and the Birkhoff—Jebsen theorem we have studied the curvature in a homogeneous and isotropic universe with a constant energy density and obtain a value very close to zero for the curvature at any inner point of that universe.
Category: Astrophysics

The Transformation of Bursa-Wolf of Seven Parameters

Authors: Abdelmajid Ben Hadj Salem
Comments: 9 Pages. In French

In this note, we present the Bursa-Wolf seven-parameter transformation from one geodetic system to another, showing how to determine the 7 parameters by the method of least squares and calculate them numerically.
Category: Geophysics

Explaining Imbalance of Tidally Ejected Stars from Open Stars Clusters Without Mond

Authors: Stephane H. Maes
Comments: 18 Pages. All related details of the projects (and updates) can be found and followed at https://shmaesphysics.wordpress.com/shmaes-physics-site-navigation/.

Results from a recent paper, and accompanying popular articles, have argued that the observed asymmetry in the numbers, and distributions, of stars tidally ejected in front, versus at the tail of open stars clusters, would favor the MOND theory (Modified Newtonian dynamics), over Newton gravity, and hence General Relativity (GR). This paper disputes such conclusions by showing that the observed asymmetry can equally well be qualitatively explained with multi-fold mechanisms, which propose that macroscopic entanglements between real particles are behind the effects of Dark Matter, and that entanglements of virtual particles explain gravity. This is captured by the E/G conjecture. Considering other similar results, and the fact that we encounter hints of multi-folds in our real universe, in particular with GR at Planck scales, we believe that the explanation proposed in our paper is another viable alternative to relying on MOND. As the multi-fold theory recovers GR, our approach does not require modifying GR, with ideas like MOND. In such a universe we can justify why more starts are ejected in the front than at the tail of galaxy clusters, where the galaxies tends to dilute.
Category: Relativity and Cosmology

Method of Listing Finite and Infinite Decimals Simultaneously: the Simplest Proof of Countability of Real Numbers

Authors: Hongyi Li
Comments: 5 Pages.

The finite and infinite decimals of binary are listed one by one at the same time, thus completely proving that the real numbers are countable. This paper will completely rewrite the history of mathematics. Because there are lots of errors in Cantor's theory, and the uncountability of real numbers is only one of them, it is necessary to launch a campaign to crack down on false and correct errors, lest these errors continue to destroy the normal capacity of human thinking and continue to mislead people.
Category: Set Theory and Logic

Newton’s Theory of Universal Gravitation — A Critique Leading to A Revised Version

Authors: Bijon Kumar Sen, Subha Sen
Comments: 16 Pages; 3 Figure

A close look into Newton’s theory of gravitational attraction reveals some controversial statements. The theory does not corroborate with the experimental observations on the properties of gravitational constant. An ‘external push’ is suggested instead of the well accepted theory of ‘attractive pull’ between two masses. This new concept is able to resolve the inconsistencies and drawbacks present in Newton’s theory. An alternative approach is proposed for the theory of evolution of the Universe (Big Bang), that can account for the lacunas noticed in the existing theory.
Category: Classical Physics

On Uniformly-accelerated Motion in an Expanding Universe

Authors: Alireza Jamali
Comments: 6 Pages. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Comments and objections are welcome.

Null geodesics of a spacetime are a key factor in determining dynamics of particles. In this paper, it is argued that, within the scope of validity of Cosmological Principle where FLRW model can be safely employed, expansion of the Universe causes the null geodesics to accelerate, providing us with a universal acceleration scale a_0=cH_0. Since acceleration of null rays of spacetime corresponds to null rays of velocity space, demanding the invariance of acceleration of light a_0 yields a new metric for the velocity space which introduces time as a dimension of the velocity space. Being part of the configuration space, modification of distance measurements in velocity space alters the Euler-Lagrange equation and from there the equation of motion, Newton's Second Law. It is then seen that the resulting modification eliminates the need for Dark matter in clusters of galaxies and yields MOND as an approximation.
Category: Relativity and Cosmology

Solvable Quintic Equation X^5 45X + 108 = 0

Authors: Quang Nguyen Van
Comments: 2 Pages.

We have previously proposed a quintic equation that is outside the available arguments of the solvable quintic equation . In this article, we give another quintic equation in Bring - Jerrard form and its root.
Category: Algebra

Authentication Link: A Novel Authentication Architecture in IoT/IoB Environment

Authors: Gi-Yoon Jeon
Comments: 5 Pages.

The authentication is the process of determining whether someone or something is, and there are many authentication methods for digital environment. The digital authentication is divided into three main categories, 'What you have', 'What you know', and 'Who you are'. Furthermore, there are multi-factor authentications using a combination of two or more of these. However, these methods are always exposed to the risk of forgery, tampering, and stealing. This paper proposes a novel authentication architecture that is suitable for Internet of Things (IoT) and Internet of Behaviors (IoB) environment. In the aspect of technology, the proposed architecture is token based authentication method. However, this architecture is continuous, mimics real analog world, and has the advantage of being immediately recognizable in counterfeiting.
Category: Data Structures and Algorithms

A New Approach to Unification Part 2: Deducting Particle Physics

Authors: Jürgen Kässer
Comments: 10 Pages.

In a series of 4 papers an approach to a unified physics is presented. In part 1 the foundation of such an approach is given. Here in part 2 it will be shown how particle physics follows. In part 3 gravitational physics will be derived. In part 4 open fundamental questions of actual physics are answered and the concept of a new cosmology is introduced.
Category: Quantum Gravity and String Theory

SKYNET 2023 Conception of the Artificial Super Intelligence Project. A System Approach. Second Edition. ver. 4 - 2024 UPDATE

Authors: Alexander Novikov
Comments: 425 Pages. Version 4 (16) - 2024 UPDATE

This Book (White Paper) proposes a Project Conception of Artificial Super Intelligence ASI, based on (strong) system approach and wide theoretical-methodological framework — Cybernetics, Synergetics, Semiotics, Mathematics, Cognitology and Artificial Intelligence. Contents: I. IDEOLOGY & STRATEGY of the ASI Project II. THEORY & METHODOLOGY of ASI Development III. CONCEPTUAL MODEL of ASI System IV. PRE-PROJECT R&D Task Setting V. CONCLUSION & DISCUSSION, incl. AI Safety (A) APPENDICES with reviews of relevant scientific and R&D areas, incl. frontier AI Models The Book may be useful and interesting for the staff of organizations & enterprises concerned with AI R&D and implementations in different areas, firstly — perspective AGI/ASI systems. In addition — for Customers, Investors and Sponsors of such R&Ds, private, public and states — its owners & officials. Of course - all intellectual, educated and ethical people with progressive worldviews, interested or anyway considered in above presented problematics. This version 4 (16) with 2024 UPDATE — new Chapters and Appendices
Category: Artificial Intelligence

Nervous Equivariant Holonomy

Authors: Ryan J. Buchanan
Comments: 6 Pages.

One of the possible explanations for entanglement is a sort of perverse holonomy which acts on sheaves whose germs are eigenvectors for a tuple of local variables. We take baby steps towards realizing this model by introducing an equivariant form of holonomy. As a test category, we take U(1)-bundles whose outbound fibrations are Koszul nerves of degree (p+q)=n.
Category: Topology

On Wilker-Type Inequalities

Authors: Yi-Chieh Huang, Li-Chang Hung
Comments: 6 Pages.

In this paper, we present elementary proofs of Wilker-type inequalities involving trigonometric and hyperbolic functions. In addition, we propose some conjectures which extend and generalize the Wilker-type inequalities.
Category: Functions and Analysis

On Generalized li-Yau Inequalities

Authors: Li-Chang Hung
Comments: 11 Pages.

We generalize the Li-Yau inequality for second derivatives and we also establish Li-Yau type inequality for fourth derivatives. Our derivation relies on the representation formula for the heat equation.
Category: Functions and Analysis

About CMBR

Authors: Gerd Pommerenke
Comments: 48 Pages.

Because the CMBR follows the Planck's radiation law more or less exactly, it should, because of the indistinguishability of individual photons, apply to a whatever black emitter. Therefrom arises the guess, that the existence of an upper cut-off frequency of the vacuum could be the cause for the decrease in the upper frequency range. Since the lower-frequent share of the curve correlates with the frequency response of an oscillating circuit with the Q-factor ½, it is examined, whether it succeeds to approximate the Planck curve by multi-plication of the initial curve with the dynamic, time-dependent frequency response of the above mentioned model. Reason of the time-dependence is the expansion of the universe. This work is based on a model published in [7]. It is shown, that the Planck graph can be approximated by application of the cumulative frequency response given by the model, upon the spectrum of an oscillatory circuit with the Q-factor ½. Furthermore the progression of frequency, energy and entropy is analyzed. The results point out, that origin and progression of the CMBR have elapsed in a totally different manner than generally assumed. Because photons behaved like neutrinos immediately after BB they did not interact with other matter then. Thus, we can exactly calculate back to 8.08·10—106s instead of 379,000 years after BB. Section 6. has been reworked.
Category: Relativity and Cosmology

Complete Operations

Authors: Pith Peishu Xie
Comments: 27 Pages.

The Operator axioms have produced complete operations with real operators. Numerical computations have been constructed for complete operations. The classic calculator could only execute 7 operator operations: + operator operation(addition), - operator operation(subtraction), $times$ operator operation(multiplication), $div$ operator operation(division), ^{} operator operation(exponentiation), $surd$ operator operation(root extraction), log operator operation(logarithm). In this paper, we invent a complete calculator as a software calculator to execute complete operations. The experiments on the complete calculator could directly prove such a corollary: Operator axioms are consistent.
Category: Number Theory

Critical Analysis of Classical Wave Equation

Authors: Temur Z. Kalanov
Comments: 12 Pages. (Correction made by viXra Admin to conform with scholarly norm)

A detailed proof of the incorrectness of the classical wave equation is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The proof leads to the following irrefutable statement: the classical wave equation and the derivation of the classical wave equation are a gross error in mathematics and physics. The proof of this statement is based on the following irrefutable main results: (1) The first gross error is the following approximate relationship: "sine of angle is approximately equal to tangent of angle; cosine of angle is approximately equal to 1". This relationship means (implies) that the quantity of the angle and the right-angled triangle do not exist. Consequently, the relationship between the tangent of the angle and the derivative of the displacement with respect to coordinate does not exist; (2) The second gross error is that the second-order derivative of the displacement with respect to coordinate does not exist, because the dimensions of displacement and coordinate are "meter", the first-order derivative of the displacement with respect to coordinate is dimensionless quantity (i.e. the first-order derivative of the displacement respect to coordinate has no the dimension "meter"); (3) The third gross error is that the first-order derivative of the displacement with respect to coordinate cannot be expanded into the Taylor series, because the second-order derivative of the displacement with respect to coordinate does not exist;(4) The fourth gross error is as follows: (a) the left side of the wave equation contains the condition that time is a variable quantity, and the coordinate is a constant quantity; (b) the right side of the wave equation contains the condition that time is a constant, and the coordinate is a variable. This means (implies) that the equation contains contradictory conditions (propositions). Therefore, the equation represents a violation of the formal-logical law of the lack (absence) of contradiction; (5) The fifth gross error is that the standard derivation of the equation relies on the following false theories: negative number theory, complex numbers theory, trigonometry, vector calculus, differential calculus, and Newton's second law.Thus, the classical wave equation does not satisfy the criterion of truth and is not a scientific achievement.
Category: Mathematical Physics

The Fatal Absence of Evidence for Extraterrestrial Intelligence and its Consequence for Humanity

Authors: Richard Michael Blaber
Comments: 21 Pages. Creative Commons License BY-NC-ND 4.0 (Note by viXra Admin: Please do not put a period "." after the title)

The lack of any radio signals or other astronomical evidence supportive of the existence of intelligent extraterrestrial life possessed of technology of sufficient sophistication to bring itself to our attention here on Earth is not, per se, evidence of an absence of life, or even intelligent life, in the cosmos itself, but it does indicate that any such advanced societies, if they have come into existence at all, may be extremely rare and comparatively short-lived, destroyed by the very technology that might have brought them to our notice. This, it will be suggested, is the solution to Fermi’s famous ‘paradox’, and the reason no SETI signals have been detected. The lessons we should learn are that life like that on our planet is very rare and precious, and we must not risk destroying it.
Category: General Science and Philosophy

Fine-tuning BERT for HTTP Payload Classification in Network Traffic

Authors: Mayur Sinha, Sangram Kesari Ray, Khirawadhi
Comments: 5 Pages.

Fine-tuning pre-trained language models like Bidirectional Encoder Representations from Transformers (BERT) has exhibited remarkable potential in various natural language processing tasks. In this study, we propose and investigate the fine-tuning of BERT specifically for the classification of HTTP payload representations within network traffic. Given BERT's adeptness at capturing semantic relationships among tokens, we aim to harness its capabilities for discerning normal and anomalous patterns within HTTP payloads. Leveraging transfer learning by fine-tuning BERT, our methodology involves training the model on a task-specific dataset to adapt its pre-trained knowledge to the intricacies of HTTP payload classification. We explore the process of fine-tuning BERT to learn nuanced representations of HTTP payloads and effectively distinguish between normal and anomalous traffic patterns. Our findings reveal the potential efficacy of fine-tuned BERT models in bolstering the accuracy and efficiency of anomaly detection mechanisms within network communications.
Category: Artificial Intelligence

Convergence Condition for the Newton-Raphson Method: Application in Real Polynomial Functions

Authors: Juan Jorge Isaac Lopez
Comments: 5 Pages.

The Newton-Raphson method applies to the numerical calculation of the roots of Real functions, through successive approximations towards the Root of the function. The Newton-Raphson method has the drawback that it does not always converge. This work establishes the convergence condition of the Newton-Raphson method for Real functions in general; once the convergence condition is met, the method will always converge towards the Root of the function. In this work, the development of the application of the convergence condition is established to specifically solve Real polynomial functions.
Category: General Mathematics

A Configuration of Graviton

Authors: Tong Wang
Comments: 10 Pages.

Some commonly agreed upon behaviors of graviton are that it is massless, propagates at the speed of light, is emitted, and is absorbed between matter particles, acts like a gravitational force carrier. In this essay we propose a novel configuration for gravitons. It is a massless object with zero net mass. When a quantum of energy is transferred to it, it can store the energy internally and travel at the speed of light. When the quantum of energy that it carries is transferred out of it, it becomes massless, and its momentum is zero. By exchanging this massless object, energy can be transferred between matter particles. The net effect of this exchange is the apparent gravitational interaction between matter particles. Therefore, we consider this massless object to behave like graviton.
Category: Quantum Physics

Interference Field as Quantum Randomness Generator.

Authors: Pierre Leroy
Comments: 9 Pages.

This document presents a principle of a wave field contained in a closed space producing fluctuations with random appearances at any point in the space. A 2D simulation shows that interference patterns produced by the interaction of this field with physical objects contained in the space make it possible to produce non-zero correlation measurements between distant points in space and specific to the objects position configuration. These correlations properties are used to explain experimental coincidences measurements having non-local appearance.
Category: Quantum Physics

SunQM-6s9: Reformulating Schrodinger Equation/Solution to Show Its r-1D Reversed-Diffusion Character for Solar System’s {N,n} QM Structure Formation (Drafted in January 2020)

Authors: Yi Cao
Comments: 23 Pages.

A pre-Sun ball (quantum) collapse process can be intuitively thought as a (mass) reversed diffusion process in r-dimension. It has been noticed for many years (and by many QM scientists) that there is similarity between Schrodinger equation and a diffusion equation. In the current paper, 1) By using Euler formula’s complex space (that was defined as the "i-space" in this article), I reformulated the expression of the orbital energy E = K + V to be K = Kθφ + iKr and V = Vθφ + iVr , and then E = K + iV* = (Kθφ + Vr) + i(Kr + Vθφ); 2) I assumed that a plane-like wave can be used as the solution (i.e., the wave function) of Schrodinger equation (either for an H-atom, or for Solar system), and then separate this 3D plane-like wave into two parts, one in r-1D only, and one in θφ-2D only; 3) Accordingly, (by guessing, not by the mathematical deduction), I separated a traditional spherical 3D Schrodinger equation into two: one in θφ-2D only, and one in r-1D only; 4) While the θφ-2D-only Schrodinger equation is almost same as the traditional one, the r-1D-only Schrodinger equation can be further degenerated into a r-1D diffusion equation with the diffusion constant D= ℏ/2m ; 5) At a citizen-scientist-level, I confirmed that the θφ-2D plane-like wave function is the solution of the θφ-2D-only Schrodinger equation, and the r-1D plane-like wave function is the solution of the r-1D-only Schrodinger equation as well as the r-1D diffusion equation. In this way, I demonstrated that Schrodinger equation may can be directly degenerated into a diffusion equation (at least in r-dimension). Furthermore, according to this explanation, the other QM scientists’ previous result of D → iℏ/2m may can be re-explained as that, the diffusion constant D= ℏ/2m not only radially diffuses in r-1D, but also laterally diffuses in θφ-2D through RF (RotaFusion, or rotation diffusion). If this explanation is correct, then the function of analyzing the E = K + V in an "i-space" maybe is to filter out the RF (the lateral diffusion) in θφ-2D, so that a pure r-1D diffusion can be obtained. Even I am not sure whether this method is correct or not, this deduction certainly opened a new route to reformulate Schrodinger equation and solution. This work may also have created a completely new way to study the relationship between the RF and the energy of the orbital motion. (Note: This article was drafted in Jan. 2020).
Category: Quantum Physics

On the Origins of Mass

Authors: Moshe Szweizer, Rivka Schlagbaum
Comments: 20 Pages.

Probability, as manifested through entropy, is presented in this study as one of the most fundamental components of physical reality. It is demonstrated that the quantization of probability allows for the introduction of the mass phenomenon. In simple terms, gaps in probability impose resistance to change in movement, which observers experience as inertial mass. The model presented in the paper builds on two probability fields that are allowed to interact. The resultant probability distribution is quantized, producing discrete probability levels. Finally, a formula is developed that correlates the gaps in probability levels with physical mass. The model allows for the estimation of quark masses. The masses of the proton and neutron are arrived at with an error of 0.02%. The masses of sigma baryons are calculated with an error between 0.007% and 0.2%. The W-boson mass is calculated with an error of 1.3%. The model explains why proton is stable while other baryons are not.
Category: Mathematical Physics

A Proof of a Result of James Stirling

Authors: Hervé Gandran-Tomeng
Comments: 2 Pages.

A recent paper contains a proof of a result of James Stirling,$sum_{n=1}^inftyfrac{1}{n^2binom{2n}{n}}=frac{1}{3}sum_{n=1}^infty frac{1}{n^2}$What is following is another proof of this equality.
Category: Number Theory

It is a Good Day to Say "Yes to Life" Reclaiming the Human Spirit in a Weary World

Authors: Florentin Smarandache, Victor Christianto
Comments: 11 Pages.

Beneath the surface of modern society's ills, from commercialism and corporatocracy to moral decay and social division, whispers a deeper malady: a collective forgetting of how to say "yes" to life. This article delves into the essence of this dis-ease, drawing inspiration from diverse sources like Indigenous wisdom, Judeo-Christian values, and the concept of "wetiko," a spiritual virus described by some analysts. It argues that the antidote to this existential malaise lies in a conscious choice: a daily decision to embrace life's vibrancy, interconnectedness, and inherent worth.(This is a draft version)see also: https://www.academia.edu/111617591/It_is_a_Good_Day_to_Say_Yes_to_Life_Reclaiming_the_Human_Spirit_in_a_Weary_World_draft_version_
Category: Religion and Spiritualism

Interactions in Deformed Special Relativity

Authors: Clemens Heuson
Comments: 10 Pages.

In deformed special relativity with commuting coordinates transforming according special relativity and deformed plane waves the field equations and interactions in coordinate space remain unchanged. However in momentum space Dirac and Weyl equations become deformed together with helicity spinors and Mandelstam variables resulting in deformed amplitudes for massive and massless particles.
Category: High Energy Particle Physics

Redshift Distances in Modified Flat Friedmann-Lemaître-Robertson-Walker Spacetime Containing G00(t)

Authors: Steffen Haase
Comments: 50 Pages.

In the present paper we use a modified flat Friedmann-Lemaitre-Robertson-Walker metric containing g_00(t) describing a spatially homogeneous and isotropic universe to derive the cosmological redshift distance in a way which differs from that which can be found in the general astrophysical literature. Using the flat Friedmann-Lemaitre-Robertson-Walker metric the radial physical distance is described by R(t) = a(t)r. In this equation the radial co-moving coordinate is named r and the time-depending scale parameter is named a(t). We use the co-moving coordinate r_e (the subscript e indicates emission) describing the place of a galaxy which is emitting photons and r_a (the subscript a indicates absorption) describing the place of an observer within a different galaxy on which the photons - which were traveling thru the universe - are absorbed. Therefore the physical distance - the real way of light - is calculated by D = a(t_0)r_a - a(t_e)r_e ≡ R_0a - R_ee. Here means a(t_0) the today’s (t_0) scale parameter and a(t_e) the scale parameter at the time t_e of emission of the photons. The physical distance D is therefore a difference of two different physical distances from an origin of coordinates being on r = 0. Nobody can doubt this real travel way of light: The photons are emitted on a co-moving coordinate place r_e and are than traveling to the co-moving coordinate place r_a. During this traveling the time is moving from t_e to t_0 (t_e ≤ t_0) and therefore the scale parameter is changing in the meantime from a(t_e) to a(t_0). Using this right physical distance we calculate some different redshift distances and some relevant classical cosmological equations (effects) and compare these theoretical results with some measurements of astrophysics (quasars, SN Ia and black hole). We get the today’s Hubble parameter H_0a ≈ 65.2 km/(s Mpc) as a main result. This value is a little smaller than the Hubble parameter H_0,Planck ≈ 67.66 km/(s Mpc) resulting from Planck 2018 data. Furthermore, we find for the radius of the so-called Friedmann sphere R_0a ≈ 2,586.94 Mpc. This radius is not the maximum possible distance of seeing within an expanding universe. Photons, which were emitted at this distance, are not infinite red shifted. The today’s mass density of the Friedmann sphere results in ρ_0m ≈ 9.09 x E-30 g/cm3. For the mass of the Friedmann sphere we get M_Fs ≈ 1.94 x E+55 g. The mass of black hole within the galaxy M87 has the value M_BH,M87 ≈ 1.56 x E+43 g. The redshift distance of this object is D ≈ 19.60 Mpc but its today’s distance is only D_0 ≈ 12.27 Mpc. The radius of this black hole is R_S ≈ 1.498 x E-3 pc.
Category: Relativity and Cosmology

A Two-dimensional Time to Reconcile Quantum Theory and General Relativity

Authors: Augustin Rousselet
Comments: 43 Pages. In French

Currently modern physics considers space-time in 4 dimensions (3 spatial, 1 temporal) and is facing the problem of unifying the two major theories: quantum theory and general relativity.To circumvent the obstacles to this unification, we propose to think of a space with 5 Dimensions (3 spatial, 2 temporal). We thus make the hypothesis of a decomposable time in a two-dimensional orthonormal space, just like a distance is decomposable in a 3-dimensional space:- The first dimension: the classical time Tc that we know, that of mass in the sense of intuitive perception, but in fact that of matter, or "corpuscular" time and therefore our reference time in our perceived reality. In our thought experiment, this will be the time T of the macroscopic observer - Second dimension: quantum time Tq Which is imperceptible to us and only intervenes at the microscopic level.The time of any system is therefore the time ��̇ which is the component of its two temporal dimensions Tc and Tq. The proper time of any system is then defined by ��̇ = sqrt(Tc^2+Tq^2)We will show in this work that this conception of time makes it possible to integrate the mathematical models of Quantum Physics and General Relativity into a broader theoretical framework which retains the results of each of them when applied in their field of validity. We will first verify that the formalism of these two major theories is compatible with the framework that is proposed, then that the interpretation of quantum phenomena is also consistent with the results, with in particular the role of measurement. Then we will verify that the major open questions of current physics (dark matter, dark energy, preponderance of matter over antimatter, the vacuum catastrophe) also find an answer or possible answers in this new theoretical framework.Finally, specific fields of physics such as superconductivity or superfluidity and even the big bang are approached to open a new look at these phenomena in this new theoretical framework.
Category: Quantum Gravity and String Theory

Galois Connections on a Brane

Authors: Ryan J. Buchanan
Comments: 5 Pages.

On an absolute frame of reference, a Galois connection to a d-brane may be prescribed such that the data of the frame becomes locally presentable. We describe these connections briefly.
Category: Quantum Physics

Fixed Point Properties of Precompletely and Positively Numbered Sets

Authors: Marat Faizrahmanov
Comments: 14 Pages.

In this paper, we prove a joint generalization of Arslanov’s completenesscriterion and Visser’s ADN theorem for precomplete numberings. Then we considerthe properties of completeness and precompleteness of numberings in the context ofthe positivity property. We show that the completions of positive numberings are nottheir minimal covers and that the Turing completeness of any set A is equivalent to theexistence of a positive precomplete A-computable numbering of any infinite family withpositive A-computable numbering.
Category: Set Theory and Logic

Seven Internal Contradictions of Set Theory

Authors: Wolfgang Mückenheim
Comments: 3 Pages. (Correction made by viXra Admin to conform with scholarly norm)

Seven internal contradictions of set theory are discussed.
Category: Set Theory and Logic

Complex Curvature and Complex Radius

Authors: Cavași Ioan Abel
Comments: 3 Pages.

I define the notions of complex curvature and complex radius and prove that one of these complex numbers is exactly the inverse of the other.
Category: Geometry

The Excess Mortality is Strongly Underestimated

Authors: Hans Lugtigheid
Comments: 15 Pages.

This article analyses the conjecture that excess mortality is underestimated with the pandemic.I use the numbers from the CBS (Dutch Central Bureau for Statistics) as an example. As a baseline we take the expected mortality for 2021 and 2022 from 2019. I correct this expected mortality with the estimated number of people who died in earlier years than expected because of the pandemic. For 2021 this correction is 8K. The CBS expects the mortality to be almost equal to the estimate from 2019. Then the excess mortality increases from 16K (CBS) to 24K.I present the following idea to explain the difference. At the beginning of very year the numbers of people in year groups are usually adjusted by applying a historical determined percentage to the population at January first. Covid hits the weakest the hardest. This changes the distribution of the expected remaining life years in the year group. And thus the average expected remaining life years. Hence the percentage has to be adjusted. Then the expected mortality decreases and the excess mortality increases.The excess mortality within a year are people who for example died in April from covid but who would have died in October without the pandemic. With this number total excess mortality rises with 6K to 30K.Excess mortality is divided in covid and non-covid. De large increase in non-covid deaths is striking.The analysis supports the conjecture that excess mortality is underestimated.Note: The numbers in this article are for the Netherlands. For you own country use the appropriate numbers.
Category: Statistics

Expected Mortality: Adjustment for Distribution in Age-Groups

Authors: Hans Lugtigheid
Comments: 4 Pages.

This article discusses the influence of a disturbance like covid on the calculation of life expectancy in year groups etcetera. Life expectancies in year-groups are usually adjusted in the beginning of the year based on the population in the beginning of the year. This is done with a percentage based on previous years. This percentage is a reflection of volume. With the pandemic the weak were hit heavily by covid. A consequence is that the distribution of life expectancy changes in the year groups. This increases the life expectancy and decreases the expected mortality in the year group. Then the calculation for the year groups has to be adjusted accordingly. In this article I give an example of such adjustment. One can accordingly adjust likewise statistics.
Category: Statistics

On Non-Principal Arithmetical Numberings and Families

Authors: Marat Faizrahmanov
Comments: 13 Pages.

The paper studies Σ-0-n-computable families (n ⩾ 2) and their numberings. It is proved that any non-trivial Σ-0-n-computable family has a complete with respect to any of its elements Σ-0-n-computable non-principal numbering. It is established that if a Σ-0-n-computable family is not principal, then any of its Σ-0-n-computable numberings has a minimal cover.
Category: Set Theory and Logic

Gravitational Waves Background, as Well as Some UFO, FRB and Supernova Flares, Are Due to Compressibility of the Spacetime

Authors: Evgeny A. Novikov
Comments: 4 Pages. Accepted for publication in JHEPGC

The recently observed gravitational wave background is explained in terms of the quantum modification of the general relativity (Qmoger). Some UFO, FRB and supernova flares also can be explained in terms of Qmoger.
Category: Astrophysics

Geometric Entity Dualization and Dual Quaternion Geometric Algebra in PGA G(3,0,1) with Double PGA G(6,0,2) for General Quadrics

Authors: Robert Benjamin Easter, Daranee Pimchangthong
Comments: 76 Pages.

In Geometric Algebra, G(3,0,1) is a degenerate-metric algebra known as PGA, originally called Projective Geometric Algebra in prior literature. It includes within it a point-based algebra, plane-based algebra, and a dual quaternion geometric algebra (DQGA). In the point-based algebra of PGA, there are outer product null space (OPNS) geometric entities based on a 1-blade point entity, and the join (outer product) of two or three points forms a 2-blade line or 3-blade plane. In the plane-based algebra of PGA, there are commutator product null space (CPNS) geometric entities based on a 1-blade plane entity, and the meet (outer product) of two or three planes forms a 2-blade line or 3-blade point. The point-based OPNS entities are dual to the plane-based CPNS entities through a new geometric entity dualization operation J_e that is defined by careful observation of the entity duals in same orientation and collected in a table of basis-blade duals. The paper contributes the new operation J_e and its implementations using three different nondegenerate algebras {G(4),G(3,1),G(1,3)} as forms of Hodge star dualizations, which in geometric algebra are various products of entities with nondegenerate unit pseudoscalars, taking a grade k entity to its dual grade 4-k entity copied back into G(3,0,1). The paper contributes a detailed development of DQGA. DQGA represents and emulates the dual quaternion algebra (DQA) as a geometric algebra that is entirely within the even-grades subalgebra of PGA G(3,0,1). DQGA has a close relation to the plane-based CPNS PGA entities through identities, which allows to derive dual quaternion representations of points, lines, planes, and many operations on them (reflection, rotation, translation, intersection, projection), all within the dual quaternion algebra. In DQGA, all dual quaternion operations are implemented by using the larger PGA algebra. The DQGA standard operations include complex conjugate, quaternion conjugate, dual conjugate, and part operators (scalar, vector, tensor, unit, real, imaginary), and some new operations are defined for taking more parts (point, plane, line) and taking the real component of the imaginary part by using the new operation J_e. All DQGA entities and operations are derived in detail. It is possible to easily convert any point-based OPNS PGA entity to and from its dual plane-based CPNS PGA entity, and then also convert any CPNS PGA entity to and from its DQGA entity form, all without changing orientation of the entities. Thus, each of the three algebras within PGA can be taken advantage of for what it does best, made possible by the operation J_e and identities relating CPNS PGA to DQGA. PGA G(3,0,1) is then doubled into a Double PGA (DPGA) G(6,0,2) including a Double DQGA (DDQGA), which feature two closely related forms of a general quadric entity that can be rotated, translated, and intersected with planes and lines. The paper then concludes with final remarks.
Category: Algebra

Theory of Ultra Particle

Authors: Gjelard Karrica
Comments: 9 Pages. (Note by viXra Amdin: Please list scientific references and stop using grandiose words!)

This paper aims to present new ideas in the field of physics; the content is tailored to be easily comprehensible by readers of diverse backgrounds and expertise. This [] hypothesis offers a fresh perspective that may challenge current scientific beliefs. However, it seeks to make a meaningful contribution to our understanding of quantum particles and the fundamental principles of matter across all scales. While the prevailing knowledge about electrons is that they are elementary particles since they are not composed of smaller particles, this theory proposes otherwise. It suggests that electrons, like protons and neutrons, are composed of other components, so our current understanding of elementary particles needs to be revised. This paper proposes that everything in the universe, including electrons, protons, neutrons, quarks, and everything else, comprises something much smaller called the "ultra-particle" (UP). The reason it is called "ultra" is because its scope is quite remote from ordinary particles. The ultra-particle is a fundamental particle that explains all the forces and fields of the universe, quantum behaviors, and the motion of celestial bodies, including black holes. Although unimaginably small, the ultra-particle permeates the universe, making everything we know of possible.
Category: Classical Physics

The Possibility of a Multi-fold Time-Varying Hubble Constant

Authors: Stephane H. Maes
Comments: 20 Pages. (Note by viXra Admin: Future regurgitation will not be accepted!)

The multi-fold theory provides microscopic interpretations to the universe accelerated expansion, inflation mechanisms and dark energy. From the beginning, the multi-fold dark matter main mechanisms have been identified as being stronger in the presence of matter, or energy increasing spacetime curvature. One could therefore naively expect that these mechanisms will also be globally time-dependent, when it comes to the early epochs of the universe. Indeed, during these eras, including pre-CMB, different matter densities and curvatures reigned. Each would lead to a different global average cosmological constant. Such a reasoning would predict a Hubble constant that is larger for early time than late time observations.Proposing a time-varying dark energy density can obviously be a simple way to address the Hubble constant tension: early time estimates would correspond to such a different value, and no Hubble constant tension would exist. However, in our naïve initial analysis above, obtaining larger pre-CMB values could a priori go in the wrong direction when it comes to observations: one would expect a larger Hubble constant at early times.Considering the multi-fold dark energy mechanisms, in all the early stages of the universe, which led to the CMB, plasma, dominated by electromagnetic and possibly other interactions, occupied the whole concretized spacetime. Multi-fold dark energy effects were partially countered by more dominant interactions, and the resulting accelerations of expansion were reduced. It can explain why current early time estimates for the Hubble constant would differ from late time results, and lead to a smaller Hubble constant value at early time However, note that recent papers show that a short term increase of the dark energy (5% for redshift z > 5000), can resolve the tension, by pushing up the CMB inferred Hubble constant, i.e. early time estimates, and better match overall the ΛCDM. Combining the two considerations above, our paper shows that multi-fold dark energy mechanisms intrinsically, and microscopically, justify such a behavior that can resolve the Hubble tension. It is another hint in favor of the multi-fold mechanisms, to add to several others. There is also a range where a multi-fold universe appear fractal, which may result into scaling of the cosmological constant, and reducing its value, during this period; again a move in the right direction.The result extends to the real universe, if it is multi-fold, as hinted by past results.
Category: Quantum Gravity and String Theory

The Deep Mystery of the Universe Behind Zeno’s Paradox

Authors: Henok Tadesse
Comments: 13 Pages.

Zeno's paradoxes of motion are four related paradoxes created by an ancient Greek philosopher in 500 B.C. In one of the well-known paradoxes, Achilles, who is a fast runner, chases a tortoise who is initially at a point P ahead of him and moving slowly forward. Zeno argued that, by the time Achilles arrives at point P, the tortoise will have moved forward to another point P1. Although Achilles is now closer to the tortoise, he will not catch up on the second try again because by the time Achilles arrives at point P1, the tortoise will have moved to another point P2 and so on. Therefore, Achilles will never catch up with andovertake the tortoise. But we know that a fast runner can overtake a slow runner in reality. This paradox has puzzled philosophers, mathematicians and scientists for millennia. This paper reveals the mystery of the universe behind Zeno's paradoxes. There is no entity called an electron or an atom or a ball movingfrom one point to another point in space as we know it. It is profound that philosophers were able to probe the deep mystery of the universe by logic alone 2500 years ago!
Category: Quantum Physics

Rediscovering Ramanujan

Authors: Edgar Valdebenito
Comments: 14 Pages.

In this note, we revisit Ramanujan-type series for 1/pi .
Category: Number Theory

Comprehensive Systemization of Weak Kam Theory and Some Open Problems

Authors: Jong In Jae, Jong U. Hwan, Ra Ju Gwang
Comments: 37 Pages.

In this paper, we performed comprehensive systemization of weak KAM theory, the ultramodern theory in mathematics domain that is being regarded as important in theoretical and application aspect and is being studied actively in the world in present. Moreover we also systemized comprehensively the conjectures, the open problems, and the point at issue that are proposed in weak KAM theory. They contain 17 of the points at the issue that are newly proposed in this paper.
Category: Mathematical Physics

Unifying Gender Perspectives: Bridging the Divide with Gender Acknowledgement Theory

Authors: Bryce Petofi Towne
Comments: 89 Pages.

In the evolving discourse on gender diversity, the distinction between social recognition and acceptance of transgender and non-binary (TGNB) individuals remains inadequately explored, despite its critical importance for both theoretical understanding and practical application. This paper introduces the Gender Acknowledgement Theory (GAT), a novel theoretical framework designed to bridge the existing gap in understanding gender diversity by advocating for a combined approach that intergrates both biological and psychological aspects to acknowledge gender. Through a comprehensive analysis of societal attitudes towards TGNB individuals in both the United States and China, this study reveals a significant polarization in the U.S. and a neutral to slightly negative perspective in China regarding social recognition and acceptance. However, the introduction of GAT and the "Ta" pronoun demonstrates a potential for improving social recognition and acceptance across diverse cultural contexts. The empirical investigation highlights the broader applicability of GAT, suggesting its role in enhancing understanding, communication, and societal integration of TGNB individuals. The findings contribute to the ongoing debate on gender identity, offering insights into the complexities of gender diversity and proposing a path forward for achieving greater inclusivity and understanding in society.KeywordsGender Diversity, Transgender, Non-Binary, Social Recognition, Social Acceptance, Gender Acknowledgement Theory (GAT), "Ta" Pronoun, Societal Attitudes, Cultural Contexts, Inclusivity
Category: Social Science

Collatz Conjecture: a Countably Infinite Sequence

Authors: Vishesh Mangla
Comments: 2 Pages. CC BY-SA (Note by viXra admin: The article needs an abstract and scientific references are required

In this paper, I have explored the Collatz conjecture and presented a new result regarding the behavior of the sequence. The proof demonstrated that for natural numbers n subjected to the Collatz Algorithm, the sequence can potentially havea countably infinite number of terms.
Category: Number Theory

Unification of Gravity and Electromagnetism

Authors: Stephen J. Kennedy
Comments: 21 Pages. This article explains relationship between gravity and electromagnetism

Maxwell wrote that he wanted to "leaven" his Treatise on Electromagnetism with Quaternions. Maxwell died before doing this. Silberstein and Conway accomplished this partially.This presentation claims the Lorentz condition field is the gravitational potential. Resulting in a Gravitic-Electromagnetic unification.
Category: Quantum Gravity and String Theory

Abraham Sharp's Formula

Authors: Edgar Valdebenito
Comments: 9 Pages.

In 1699,Abraham Sharp calculates pi to 72 decimal places by taking x=1/sqrt(3) in Gregory's series.
Category: General Mathematics

Deciphering the Wilton House Shakespeare Statue Scroll

Authors: Stuart J. Nettleton
Comments: 2 Pages. (Abstract added by viXra Admin)

The Wilton House Shakespeare statue scroll shows Macbeth's famous soliloquy upon the death of Lady Macbeth. There appears to be stenographic cipher in the unusual capital letters of scroll with an anagram solution "The woman who sustained Dyer's AA Fellowship" referring to Countess Mary (Sidney) Herbert whom the statue commemorates. This solution does not identify the Countess as an author. There is also an unsatisfactory solution that identifies to Christopher Marlowe as the sole author.
Category: Social Science

Modelling of Atomic Nucleus’ Structure

Authors: V. G. Bondarev, L. V. Migal
Comments: 19 Pages.

The structure of light atomic nuclei, such as hydrogen, helium and lithium nuclides, was studied based on the cluster approach. Atomic nuclei are formed as systems consisting of free and bound lovetons, as well as neutron electrons and electron-positron pairs. The work focuses on the mass of the atomic nucleus and its binding energy as the main basic characteristics. There were determined the mechanisms considered binding nucleons into clusters, as well as the main patterns of changes in binding energy depending on the structure of the nucleus.As part of this study, atomic nuclei were visualized and the dependence of the nuclear binding energy on the number of lovetons, electron-positron pairs and neutron electrons was revealed. The possibility of forming a shell structure of an atomic nucleus consisting of cluster associations of α-particles has been shown. An algorithm for constructing the structure of the atomic nucleus is presented. The conditions for choosing the number of nuclear elements included in the atomic nucleus are determined. As additional results, an estimate of the binding energies of hypothetical hydrogen nuclides 8H and 9H was obtained, and their mass formulas were constructed. The charge radii of a number of hydrogen, helium and lithium nuclides have been calculated. The possibility of using the spiral structure of nuclei instead of the shell representation has been revealed. The nature of the occurrence of the binding energy of the atomic nucleus is explained. Comparison of the obtained values of binding energies and charge radii with experimental data allows us to assert an adequate approach to the formation of the structure of the atomic nucleus.
Category: Nuclear and Atomic Physics

A New Explanation of the Mechanism of Hadley Circulation

Authors: Wei Huang
Comments: 26 Pages.

A New Explanation of the Mechanism of Hadley CirculationThe Hadley circulation (or Hadley cell) is traditionally described as a large-scale atmospheric circulation phenomenon driven by differential heating of the Earth’s surface: warm, moist air rises near the equator, diverges poleward in the upper troposphere, and subsides in the subtropics. In this article, the mechanism of the Hadley circulation is revisited and a new model is provided to explain its mechanism. The new model is based on a form of the atmospheric dynamic equation which substitutes pressure with temperature and density; thereby categorizing weather systems into thermal and dynamic systems. Such classification is useful for explaining large-scale weather systems such as the Hadley cell. The proposed explanation for the mechanism of the Hadley circulation argues that subtropical highs are the driving force of the Hadley cell, rather than the conventionally-believed ITCZ (Intertropical Convergence Zone). To support our theory, we analyze the atmospheric air density flux divergence with the results from the Community Earth System Model (CESM) and derive a new continuity equation by adding source/sink terms, in which evaporation serves as the air-mass source, and precipitation (condensation) as the air-mass sink. Results found that the equatorial easterlies could be linked to the solar diurnal cycle, demonstrating that the trade wind can be generated by the solar diurnal cycle, especially in the spring and fall seasons, as well as from the equatorial branch of the subtropical high.Keywords: Hadley Cell; ITCZ; solar radiation; dynamic equation; continuity equation; density flux divergence
Category: Climate Research

The True Universe with Cosmic Inertia

Authors: Dong-Yih Bau
Comments: 11 Pages.

Will the universe allow us to talk past each other forever? Impossible! All theories of the universe proposed by physicists and humanity will eventually compete for a theory of everything, the true universe. For most physicists, a theory of everything has not yet been discovered. However, as a free individual, I used Einsteinian science to discover how cosmic inertia governs the true universe in 2021. Sadly, no physicist knows Einsteinian science (a fact I consider the ultimate absurdity of science), or the true universe would have been uncovered earlier than 2021, and science would have already transformed itself. Whereas Einsteinian science has a sympathetic understanding of the universe, physicists have a cold understanding of the universe. This paper focuses on how Einsteinian science analyses the universe as a single significant whole by highlighting how it tackles intelligibility and avoids and overcomes intellectual obstacles in order to uncover cosmic inertia ruling the true universe. Physicists seek theories of the universe using disciplinary physical research within a cosmic synthesis paradigm as opposed to the cosmic analysis paradigm in Einsteinian science, which leaves them ill-equipped to pursue the true universe. This paper expands on Einsteinian science with the true universe and cosmic inertia, the beginning or ending point of science, the future work of science, and the new role of physicists.
Category: Relativity and Cosmology

The Classical Derivation of the Remnant Mass of a Quasi-Binary Black Hole

Authors: Alexis Zaganidis
Comments: 7 Pages.

In the present article, we classically derive an analytic formula of the Remnant Mass of a Quasi-Binary Black Hole. The Quasi Black Hole concept comes from a Theory Of Everything we have developed few years ago.
Category: Astrophysics

The Cosmos as a Chronosphere

Authors: Richard Michael Blaber
Comments: 16 Pages. Creative Commons License, CC BY-NC-ND 4.0.

As shown by Larmor (1927a & b), Gödel (1949) and Kühne (2002), absolute time is indispensable at the cosmic scale, and is required by the General Theory of Relativity. Melia (2007; 2012) and Melia and Shevchuk (2012) have argued that FLRW-type metrics reduce to the Minkowski metric, and the Hubble horizon is a ‘gravitational horizon’, as defined by Melia (2018), as opposed to either a particle or an event horizon, as these are defined by Rindler (1956). Their argumentdepends on the mass of the Hubble sphere being variable, whereas, if it is constant, its radius becomes that of a black hole, and its horizon is an event horizon. In every direction we look, total cosmic distance is given by the present age of the Universe multiplied by the speed of light in vacuum. If we abandon the cosmological principle as defined by Milne (1933), we can see we are at the centre of a chronosphere, with the ‘Big Bang’ singularity at its circumference. Eddington (1939) would doubtless have seen the numerical ‘coincidences’ that arise in cosmology as proof of God’s existence and creation of the Universe.
Category: Relativity and Cosmology

Multi-fold Discrete Fractal Spacetime, and the Viability of Local vs. Non-Local Hidden Variables

Authors: Stephane H. Maes
Comments: 27 Pages. All related details of the projects (and updates) can be found and followed at https://shmaesphysics.wordpress.com/shmaes-physics-site-navigation/.

The multi-fold original paper, in its spacetime reconstruction phase, attributes spacetime to the locations concretized by the random walks, and creation, of (massless) particles, resulting into a discrete, (multi-)fractal spacetime that is non-commutative and yet Lorentz symmetric. The fractal or multi-fractal was inferred from the random walks, but it was actually the only part not explicitly derived. Multi-fold universe are expected to probably have a Cantor-like ��-infinity fractal spacetime.In this paper, we resume these discussions, but now, we provide microscopic interpretations for spatial and temporal, and so spacetime, (multi-) fractal properties of the multi-fold universe, and their observability, only within a range of cosmological scales, as observed in our real universe. We also relate discreteness of spacetime to the complex scalar field of the Higgs boson, and encounter further corroboration of the fundamental role of the massless Higgs boson.Fractal state space plays a role in interpreting experiments about the Bell theorem, and related hidden variables. The paper discusses two models, which do not imply that the result of Bell experiments would forbid local hidden variables. The Bell Theorem, and handling of EPR entanglements, was the motivation for proposing the multi-fold mechanisms, which implement non-locality with local Physics. Interestingly, with discrete spacetime, the multi-fold W-type hypothesis, massless Higgs boson random walks, and fractal properties, multi-fold universes can support all these models: local physics and hidden variables seem to be reconcilable with the Bell experiments, as was the original intent for the multi-fold theory. And there is no need to give in to super determinism, retro-causality, or to lose free will.
Category: Quantum Gravity and String Theory

A New Approach to Unification Part 1: How a Toe is Possible

Authors: Jürgen Kässer
Comments: 12 Pages.

As in spite to intense search at present apparently there is no approach leading to a theory including the standard model of particle physics and general relativity, it is discussed whether such a theory is possible at all. In the following is shown that a ToE is possible if the either/or condition of current unification theories for background-dependent or -independent is replaced by a both/and. In this part 1, the foundation of such a theory is presented. In the following parts 2 and 3 particle and gravitational physics are derived from this foundation and in part 4 fundamental open fundamental questions of actual physics are answered by a new interpretation of physical quantities and an outline of a new cosmology is given.
Category: Quantum Gravity and String Theory

TransBERT Polymer Informatics: A Fusion of Transformer Language Modeling and Machine-Driven Chemistry for Accelerated Property Predictions

Authors: Bhaumik Tyagi, Pratham Taneja, Akshita Gupta, Daamini Batra, Keshav Chandra
Comments: 8 Pages.

This research introduces a pioneering framework named TransBERT that capitalizes on the capabilities of two sophisticated language models, TransPolymer and polyBERT, to comprehensively advance the polymer informatics field. TransPolymer, a Transformer-based language model, predicts polymer properties by leveraging self-attention mechanisms. The model employs a polymer tokenizer imbued with chemical awareness, facilitating the extraction of meaningful representations from polymer sequences. Moreover, TransPolymer benefits from rigorous pretraining on extensive unlabeled datasets through Masked Language Modeling, underscoring the pivotal role of self-attention in effectively modeling polymer sequences. In conjunction with TransPolymer, polyBERT contributes a fully automated polymer informatics pipeline designed to expedite the identification of application-specific polymer candidates with heightened speed and accuracy. Drawing inspiration from Natural Language Processing concepts, polyBERT operates as a chemical linguist, treating the chemical structure of polymers as a unique language. The pipeline integrates a polymer chemical fingerprinting capability and a multitask learning approach to map polyBERT fingerprints to diverse polymer properties effectively. Notably, polyBERT outperforms existing polymer property prediction methods based on manually crafted fingerprint schemes by achieving a remarkable two orders of magnitude increase in speed while maintaining high accuracy and integrating TransPolymer and polyBERT results in a robust computational tool poised to propel the fields of polymer design and structure-property relationship understanding. This combined framework strategically harnesses the strengths of Transformer models and machine-driven informatics, offering unparalleled efficiency in the prediction and identification of polymer properties. This synergistic approach holds significant promise for scalable deployment, including applications in cloud infrastructures, thereby making substantial contributions to the advancement of polymer science and informatics.
Category: Artificial Intelligence

Background-Free Relativity

Authors: Barbara Spangenberg
Comments: 6 Pages. (Author name added to the article by viXra Admin - Please conform!)

Starting at the volume element of four-dimensional space-time and the determinant of the metric tensor as Einstein did in his derivation of his field equations in 1915, we want to try here to tread a new path to derive field equations for gravity. Here, in contrast to Einstein’s work in 1915, the space itself is treated as the field of gravity, not its curvature as in general relativity. The newly derived field equations become astonishingly simple and comprise the well-known solutions within solar systems. However, they lead to an increased gravity for galactic systems.
Category: Relativity and Cosmology

Generalized Newtonian Gravity and Dark Matter

Authors: Adnan Choudhary, Abdur Rahim Choudhary
Comments: 8 Pages.

We use dark matter as a mass complement to the central galactic mass in Newton’s Universal Law of Gravity. The generalized Newtonian gravity thus obtained puts on theoretical footing many of the observations obtained only experimentally.
Category: Astrophysics

Galileo's Undone Gravity Experiment: Part 2

Authors: Richard Benish
Comments: 198 Pages.

Certain preconceptions about the physical world inherited from antiquity as yet permeate our established theories of physics and cosmology. Tacitly prominent in this world view is the fact that humans evolved on a 5.97 x 10^24 kg ball of matter.One of the consequences is the "relativistic" point of view, according to which accelerometers may or may not be telling the truth, whether they fall (a = 0) or when they are "at rest" on a planet’s surface (a > 0). The result of an experiment proposed by Galileo in 1632, but not yet performed, would unequivocally prove whether this schizoid relationship with accelerometers rings true or not.An imaginary alien civilization (of Rotonians) evolved on a rotating world in which the truthfulness of accelerometers is never doubted. Adopting a Rotonian perspective leads to a model of gravity according to which the result of Galileo’s experiment dramatically conflicts with the predictions of both Newton and Einstein.The consequences of this new perspective bear on and invite a rethink of many facets of established theories of physics and cosmology. Herein we discover that the Rotonian perspective is consistent with what we actually KNOW about the physical world and -- depending on the result of Galileo’s experiment -- it opens the door to a much more coherent, contradiction-free world view, which spans all scales of size, mass, and time.
Category: Relativity and Cosmology

Galileo's Undone Gravity Experiment: Part 3

Authors: Richard Benish
Comments: 134 Pages.

Failure of LIGO physicists to provide a spacetime diagram showing the simultaneous laser paths and gravitational waves propagating through their interferometer is argued to be fatal to the whole enterprise.After establishing the cogency of this argument, the seemingly "unhackable" multi-messenger event GRB170817A is similarly placed under suspicion. Claims to have detected the gravitational waves from a coalescing neutron star binary suffer the red flag of a prominent (and suspiciously placed) glitch which prevented the event from triggering a real time alert to the community.Altogether, we have many reasons to suspect that all the claims of having detected gravitational waves are false. LIGO is a hoax. Perhaps the most dramatic way to expose the charade would be to at last perform the simple gravity experiment proposed by Galileo in 1632. We predict a result that conflicts with both Newton’s and Einstein’s theories of gravity. If our prediction is confirmed, gravitational waves and much else about modern gravitational theory would be falsified.Even if the result of Galileo’s experiment supports Newton and Einstein, we are way overdue to find out directly from Nature, instead of pretending to know, based on faith in popular theories.
Category: Relativity and Cosmology

Bordisms and Wordlines II

Authors: Ryan J. Buchanan, Parker Emmerson
Comments: 7 Pages.

This paper is a continuation of [2]. Here, we discuss twisted branes, the free loop superspace, and, in particular, a deformation of the modal lightcone which allows us to model cobordisms of generically small, portable, locally closed systems.
Category: Mathematical Physics

The Mathematic Expression of Chirality, the Theory of 840 Degrees, Chirality Model of Atomic Nucleus and Their Relationships with Chinese Metrical Poetry

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 38 Pages. 11Figures, in Chinese.

This paper is written in Chinese. It was originally written in Chinese from December of 2017 to March of 2018, and was registered for copyright in the end of March of 2018. In this paper, we originally presented two scientific principles. One is that the chirality (represented by a pair of hands) could be scientifically abstracted to a counterclockwise circle and a clockwise circle corresponding to the right hand and the left hand respectively, and hence should be mathematically expressed as +2π and -2π, ie, chirality=+2π/-2π. The other is that a circle should be divided into 420 degrees instead of the traditional 360 degrees, so the chirality (a pair of hands) should correspond to +420 degrees and -420 degrees or 840 degrees in total, ie, chirality=840°. As there are right-handers and left-handers in human beings, the complete chirality including these two situations (±chirality) should actually correspond to ±2π and ∓2π or ±840 degrees, ie, ±chirality=±840°. The number of 840 can be expressed with its factors in the form of 840=1(2 4 8)(3 5 7), and the products of (2 4 8) times 1 and (3 5 7) or (2 4 8) are called stable numbers of chirality, in which 56 (8×7) is the biggest and most stable. As the atomic nuclei are located in the space or time-space which has the feature of chirality, we suppose that they live in the space of ±840 degrees, so the stable numbers (the magic numbers) in atomic nuclei are products of (2 4 8) times 1 and (3 5 7) or (2 4 6 8), their double numbers and so on, in which the most stable is 56. When the numbers of proton, neutron and total nucleon in atomic nuclei are equal to these stable numbers, these nuclei are stable, so the most stable nuclide is Fe56 and the natural terminus of the atomic elements is the 112th element Cn*. These stable numbers in atomic nuclei correspond to the hands of human beings and to Chinese metrical poetry because they all are derived from the theory of 840 degrees as stated above.
Category: Nuclear and Atomic Physics

The Twin Prime Conjecture - An Analytical Approach

Authors: Patrick DiCarlo
Comments: 37 Pages.

This paper offers a proof of the twin prime conjecture. The basic strategy is to first establish that there is no highest prime number by calculating the rates at which the multiples of each successive prime preclude higher numbers from being prime, and then proving that this rate (in the aggregate) can never reach 100%. The same basic methodology is then used to show that there can also be no highest twin prime.
Category: Number Theory

One Theorem Complementary to the Fundamental Theorem of Arithmetic

Authors: Juan Elias Millas Vera
Comments: 2 Pages.

In this paper I want to show a complementary theorem of the Fundamental Theorem of Arithmetic. Using the delta notation (Δ) I was able to deduce a generic formula involving prime numbers and natural numbers.
Category: Number Theory

New Exact Solution to Einsteins Field Equation Gives a New Cosmological Model

Authors: Espen Gaarder Haug, Gianfranco Spavieri
Comments: 11 Pages.

Haug and Spavieri have recently presented a new exact solution to Einstein’s field equations. In this paper, we will explore how this new metric could potentially lead to a new model for the cosmos. In the Friedman model, the cosmological constant must be introduced ad-hoc in Einstein’s field equations or, alternatively, directly into the Friedmann equation. However, a similar constant automatically emerges in our cosmological model directly from Einstein’s original 1916 field equations, which initially did not include a cosmological constant. We will analyze this, and it appears that the cosmological constant is little more than an adjustment for the equivalence of the mass-energy of the gravitational field, which is not taken into account in other exact solutions but is addressed in the Haug and Spavieri solution. Our approach seems to indicate that the Hubble sphere can be rep- resented as a black hole, a possibility that has been suggested by multiple authors, but this is a quite different type of black-hole universe that seems to be more friendly than that of a Schwarzschild black-hole.
Category: Relativity and Cosmology

Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras

Authors: Dimiter Prodanov
Comments: 22 Pages.

Clifford algebras are an active area of mathematical research with numerous applications in mathematical physics and computer graphics among many others.The paper demonstrates an algorithm for the computation of inverses of such numbers in a non-degenerate Clifford algebra of an arbitrary dimension. This is achieved by the translation of the classical Faddeev-LeVerrier-Souriau (FVS) algorithm for characteristic polynomial computation in the language of the Clifford algebra. The FVS algorithm is implemented using the Clifford package in the open-source Computer Algebra System Maxima.Symbolic and numerical examples in different Clifford algebras are presented.
Category: Algebra

On the Nodal Lines of Eigenfunctions of Laplacian in Plane

Authors: Soo Sun Ha
Comments: 55 Pages.

We prove Payne's nodal line conjecture for any bounded simply connected, possibly non-convex, smooth boundary domain $Omega$ in Plane: Payne conjectured that any Dirichlet second eigenfunction of laplacian in any simply connected boundary domain in Plane can not have a closed nodal line.
Category: Mathematical Physics

Note on the Resolution of the Equation β(φ)=Y Used in Geodesy

Authors: Abdelmajid Ben Hadj Salem
Comments: 9 Pages. In French

In this note, we give a method to resolve the equation β(φ)=Y used in geodesy, where β(φ) is the length of the arc of the meridian of an ellipse or an ellipsoid from the equator to the point of geodetic latitude φ.
Category: Geophysics

New atom model and new SU(5) model

Authors: Wan-Chung Hu
Comments: 25 Pages. (Title modified by viXra Admin - Future non-compliant submission or replacement will not be accepted)

This manuscript provides a new determinative atom model. The magic number 2, 8, 8, 18, 18, 32, 32 can be well explained without using quantum mechanics. In addition, spin-orbit coupling can also be deducted without quantum mechanics. In the final part of the manuscript, modified su(5) model called Hu SU(5) model includes all the fundamental particles and explain mass origin and decay mode in a clear picture.
Category: Relativity and Cosmology

Dark Energy, MOND and the Mirror Matter Universe

Authors: Greg Filewood
Comments: 39 Pages.

The purpose of this study is to entrench the Copernican principle into cosmology with regard to dark energy (DE). A dual-universe solution is proposed for both the scale and coincidence problems of DE which is simple and involves no `fine-tuning'. It is also, in principle, testable and falsifiable. The model enables computation of the total entropy of the universe contained within the horizon expressed holographically projected onto the area of the cosmic horizon in units of Planck area. We subsequently compute the Planck entropy, which takes an irreducibly simple form. A derivation of the relation $[{DE}]={sqrt{m_{pl}.H_0}}$ is provided and we further show that this relation is valid in all (local i.e. $H'_{tau}=H'_0$) observer frames. We prove that the vacuum energy is exactly zero in this dual universe model. Lastly we propose that our analysis implies that the MOND paradigm is due to gravitation interaction of the two universes and we compute the MOND acceleration scale $a_0$ and scale invariant ${cal.{A}}_0$ as a consequence of cosmology, completely independent of galaxy dynamics. Significantly, this allows us to bring the MOND paradigm into a cosmological model without modifying General Relativity.
Category: Relativity and Cosmology

Scattering of Worldlines Along a Bordism

Authors: Ryan J. Buchanan, Parker Emmerson
Comments: 7 Pages.

In this paper, ER bridges are discussed as bordisms. We treat these bordisms as fibers, whose sections are holographically entangled to copies of $S^1$. Diffemorphisms of these fibers are discussed, as well as the implication of replacing $S^1$ with the supercircle, and the replacing its underlying algebra with a Lie superalgebra.
Category: Mathematical Physics

The Vacuum Catastrophe Solved by Taking into Account Hawking-Bekenstein Black Hole Entropy

Authors: Espen Gaarder Haug
Comments: 7 Pages.

We will demonstrate that the vacuum catastrophe can be solved by utilizing Bekenstein- Hawking entropy and applying it to black hole type cosmology models, as well as to a large class of Rh = ct models. Additionally, we will examine a recent exact solution to Einstein’s field equation and explore how it may potentially resolve the vacuum catastrophe rooted in both steady-state universe and possibly growing black hole universe scenarios.
Category: Relativity and Cosmology

Unified Field Theory

Authors: Anatoly Parfyonov
Comments: 5 Pages.

The main problem, the solution of which will lead to the creation of the Unified Field Theory, is the difference in the methods of mathematical description of the charges of elementary particles - electric and color. This article provides a solution to this problem and its result - the Unified Field Theory.
Category: Quantum Gravity and String Theory

Variability of Rydberg Constant and Its Implications on Particle Cosmology

Authors: En Okada
Comments: 16 Pages.

Inspired by numbers of hardly-to-be-coincidence relations between the current state of universe and its Planck scaled precursor, we audaciously propose a hypothesis in which the mass of all elementary particles is generally proportional to the inverse cube of the cosmic scale factor, while their electric charge is inversely proportional to the square of scale factor, both of which are due to a scale factor or time-dependent evolution of the Planck constant. It implies that the Rydberg constant may be actually a variable, urges us to re-examine the raw redshift data and our well-established theory of Big Bang nucleosynthesis, which in turn demystifies the delusion that the matter content of the universe is insufficient to let it expand so fast, let alone accelerate.In spite of its pivotal importance in physics, the entity of time and energy has successfully evaded all attempts for revelation to date. We present a novel theoretical paradigm where all perceivable physical realities can be concretely defined by the degree of asymmetry in a digital field made of Planck scaled spatial quantum. The field has an inherent potential to spontaneously and totally stochastically break its symmetry. Our scheme not only solves numbers of hierarchy problems in one shot but can also theoretically calculate the mass of elementary particles and exotic baryons only with fundamental physical constants and fractional powers of pi or integer or half integer. By providing clearcut physical images for why particular Lie group may rightly characterize its corresponding force, it proves itself as a powerful guide toward the super-unification of all the four fundamental interactions.
Category: Relativity and Cosmology

Fine Structure Constant and Proton/Electron Mass Ratio

Authors: Garry Goodwin
Comments: 3 Pages. Eq 5 and Eq 6 are the centrepiece of this note

In this note a model is put forward whereby the proton has mass and charge shell radii in the ratio 1:1.68. The fine structure constant is proportional to the thickness of the shell. Two new formulae for calculating �� are introduced. Eq 5 and Eq 6 are the centrepiece of this note. These make use of the usual set of fundamental constants, including the proton / electron mass ratio. Eq 6 gives the same value for $alpha$ as standard formulae. However, it is suggested that in an optimal physics, this method with reasonable confidence, gives a slightly lower value for �� reliable to 12 decimal places, i.e., $0.007297352566$. Whether this is the actual fine structure constant depends on the veracity of the model and the accuracy of the proton /electron mass ratio.
Category: Nuclear and Atomic Physics

Electrokinetic Thermonuclear Reactor (Электрокинетический термоядерный реактор)

Authors: Gennady Rudominsky
Comments: 10 Pages. In Russian

In article the concept of the electrokinetic thermonuclear reactor on the facing plazmoids is offered. For ignition of thermonuclear reaction of synthesis it is used as energy of the electric currents flowing in plazmoids and kinetic energy of their headway.

В статье предложена концепция электрокинетического термоядерного реактора на сталкивающихся плазмоидах. Для зажигания термоядерной реакции синтеза используется как энергия электрических токов, текущих в плазмоидах, так и кинетическая энергия их поступательного движения
Category: Classical Physics

Embedding the Einstein Tensor in the Klein-Gordon Equation Using Geometric Algebra Cl(3,0)

Authors: Jesús Sánchez
Comments: 60 Pages.

In this paper, we will use Geometric Algebra to be able to embed the Klein-Gordon equation for a particle in a non-Euclidean field (gravitational field). This way, we will obtain an expression similar to the Dirac equation, but with a slight change in one of the terms. This variation is produced and depends on the curvature of the space where the particle lies in (the Ricci scalar). In a similar manner, we will find variations in the equation for the energy of a particle and in the Einstein gravitational equation that will depend again on the value of the Ricci scalar (the curvature of the space where the particle lies in). An important outcome will be an equation that limits the value of the Ricci scalar depending on the value of the mass that provokes it (the value of the mass not the mass density) highly reducing the possibilities of arriving to singularities. In fact, the value of this R has been found to be equal to the cosmological constant (both in the order of 1E-52) making it a perfect candidate for the dark energy. Also, the magnetic-like effects of gravitation coming from the equations are sufficient to explain the rotation of the galaxies (NGC 1560, NGC 3198 and NGC 3115) without the need of dark matter.
Category: Quantum Gravity and String Theory

Transductive Inference and the Rebalancing Approach

Authors: Shobhit Verma
Comments: 7 Pages. (Correction made by viXra Admin to conform with scholarly norm)

The justification of using parametric regression techniques (like Linear, Polynomial, Neural networks etc.) comes from the close relationship between the regression estimates and the maximum likelihood estimates. However, it is common to use regression.
Category: Artificial Intelligence

Exact Sines and Cosines Including a Small Table

Authors: Claude Michael Cassano
Comments: 12 Pages.

Using half angle formulas and other trigonometric identities sines and cosines for exact angles may be established and such table produced.
Category: Geometry

New Equivalent of the Riemann Hypothesis

Authors: Leonardo de Lima
Comments: 10 Pages.

In this article, it is demonstrated that if the zeta function does not have a sequence of zeros whose real part converges to 1, then it cannot have any zeros in the critical strip, showing that the Riemann Hypothesis is false.
Category: Number Theory

Interdisciplinarity Using the Example of History — Physics. in Memory of Lieselott Enders (1927 — 2009)

Authors: Peter M. Enders
Comments: 11 Pages.

Talk delivered at the Kazakh National Al-Farabi University, Almaty, December 2011 (translated by the author)
Category: General Science and Philosophy

The Mechanism of Matter and Anti-Matter, Dark Matter and Graviton

Authors: GuiHyeon Hwang
Comments: 6 Pages.

Masses of the six quarks were calculated by layer based on the boson-field theory. Most of the values are close to them of the standard model, however, the values in 4D field are vastly different from them of the model even if the error is taken into account. It suggeststhat there is something more in 4D field. The theoretical mass of an up-quark is about three times larger than the actual figure. On the other hand, the actual mass of a down-quark is about two times larger than thetheoretical one. This means that the mass of an up-quark may be under pressure to moveto the down-quark. According to the boson-field theory, there is the mechanism that makesit possible. That is, dark matters are able to play such a role. In the process, dark matters interact with an anti-neutron or an anti-proton, and a graviton is exchanged between the two darks as well. The mass of ordinary matters continues to move step by step to the dark side in the process. Really, the theoretical sum of an up and a down quark is slightly larger than the actual one. The lack of mass strongly supports the hypothesis.For now, the only place is considered as a black hole where an ordinary and a dark matter can encounter. If the black hole itself does not let its mass from the dark side out, ordinarymatters will continue to disappear in the universe.
Category: Quantum Gravity and String Theory

Observational Relativity: The Unity of Newton and Einstein (The First Part: Inertially Observational Relativity)

Authors: Xiaogang Ruan
Comments: 240 Pages.

The Theory of Observational Relativity, the theory of OR for short, is a new discovery and a new theory, which has revealed the root and essence of relativity: All relativistic effects or relativistic phenomena are observational effects and apparent phenomena rather than the objective and true physical reality. In particular, the whole theoretical system of OR has generalized and unified Newton’s mechanics and Einstein’s theory of relativity, integrating such two great theories in physics into the identical theoretical system under the identical axiom system. The theory of OR is divided into two parts: the theory of inertially observational relativity (IOR); the theory of gravitationally observational relativity (GOR). The theory of IOR takes the definition of time as the most basic logical premise and theoretically deduces the spacetime transformation of IOR, so-called the general Lorentz transformation, which has generalized and unified the Galilean transformation and the Lorentz transformation. The theory of IOR has proved an important theorem: the invariance of information-wave speeds. It suggests that the invariance of light speed is only a special case of the invariance of information-wave speeds. Actually, Einstein’s invariance of light speed can only be valid when light acts as the observation medium for transmitting observed information to observers. So, the speed of light is not really invariant. Based on the invariance of information-wave speeds, the author has established the whole theoretical system of IOR which has generalized and unified Newton’s inertial mechanics and Einstein’s special relativity, and moreover, integrated de Broglie’s theory of matter waves into the theory of IOR, marching towards the unification of relativity theory and quantum theory. The theory of IOR is logically consistent not only with Einstein’s special relativity but also with Newton’s inertial mechanics. Such logical consistency and strict correspondence show that the theory of IOR is logically self-consistent, and from one aspect, confirm the logical rationality and theoretical validity of the theory of IOR. In particular, the theory of IOR is supported by observations and experiments, including the Michelson-Morley experiment.
Category: Quantum Gravity and String Theory

Schematic Diagrams of Micro Particle Models

Authors: Bin Dong
Comments: 49 Pages.

This article introduces a new micro particle model using pictures and text, introducing the principles of four fundamental forces, the Big Bang, material formation, antimatter, energy conversion, superconductors, relativity, pulsars, magnetic monopoles, and black holes.
Category: High Energy Particle Physics

Observational Relativity: The Unity of Newton and Einstein (The Second Part: Gravitationally Observational Relativity)

Authors: Xiaogang Ruan
Comments: 406 Pages.

The Theory of Observational Relativity, the theory of OR for short, is a new discovery and a new theory, which has revealed the root and essence of relativity: All relativistic effects or relativistic phenomena are observational effects and apparent phenomena rather than the objective and true physical reality. In particular, the whole theoretical system of OR has generalized and unified Newton’s mechanics and Einstein’s theory of relativity, integrating such two great theories in physics into the identical theoretical system under the identical axiom system. The theory of OR is divided into two parts: the theory of inertially observational relativity (IOR); the theory of gravitationally observational relativity (GOR). The theory of GOR takes the three principles of GOR as its axiom system: (1) the principle of GOR equivalence; (2) The Principle of GOR covariance; (3) the principle of the invariance of information-wave speeds. Based on the three principles of GOR, by following or by analogizing the logic of Einstein’s general relativity, the author has established the whole theoretical system of GOR, including the field equation of GOR and the motion equation of GOR. GOR’s field equation has generalized and unified Einstein’s field equation and Newton’s field equation (i.e., the Poisson equation form of Newton’s law of universal gravitation). GOR’s motion equation has generalized and unified Einstein’s motion equation and Newton’s motion equation (i.e., the second law form of Newton’s law of universal gravitation). The theory of GOR has proved an important theorem: the theorem of Cartesian spacetime which suggests that the objectively real spacetime could never be curved. So, spacetime is not really curved. Finally, the theoretical system of GOR has generalized and unified Newton’s theory of universal gravitation and Einstein’s theory of general relativity. It suggests that the theory of GOR is logically consistent not only with Einstein’s theory of general relativity but also with Newton’s theory of universal gravitation. Such logical consistency and strict correspondence show that the theory of GOR is logically self-consistent, and confirm the logical rationality and theoretical validity of the theory of GOR.
Category: Quantum Gravity and String Theory

A 2-Pitch Structure

Authors: Shao-Dan Lee
Comments: 5 Pages.

We have constructed a pitch structure. In this paper, we define a binary relation on the set of steps, thus the set become a circle set. And we define the norm of a key transpose. To apply the norm, we define a scale function on the circle set. Hence we may construct the 2-pitch structure over the circle set.
Category: Algebra

The Arrow of Time and the Wheeler-Feynman Time-Symmetric Theory

Authors: James Conor O'Brien
Comments: 7 Pages.

A method to constrain the Arrow of Time to the anterograde direction using the Wheeler-Feynman Time-Symmetric theory and four-vector potentials to model electrons as longitudinal electromagnetic scalar potential waves that only progress in the forward direction of Time.
Category: Quantum Physics

A Quantum Generalized Evidence Combination Rule Algorithm

Authors: Yu Zhou, Fuyuan Xiao
Comments: 3 Pages.

In this paper, a quantum generalized combination rule algorithm is proposed to reduce the computational complexity of generalized evidence theory combination rule.
Category: Artificial Intelligence

Spectrum of Sunflower Hypergraphs

Authors: Prajnanaswaroopa S
Comments: 9 Pages.

Hypergraphs are generalization of graphs, which have several useful applications. Sunflower hypergraphs are interesting hypergraphs, which become linear in some cases. In this paper, we discuss the Siedel spectrum of these hypergraphs.
Category: Combinatorics and Graph Theory

Retrocausality and the Directions of Time

Authors: Austin Fearnley
Comments: 10 Pages.

The mystery for the last century at the heart Of Bell’s Theorem is quantum entanglement. This paper explores issues with entanglement and explains that the success of Bell’s Theorem experiments depends upon some particles/photons travelling backwards in time. It is also argued that QED electric charge and QCD colour charge are both directly related to time’s arrow for individual particles.
Category: Quantum Physics

Some Remarks on the Generalization of Atlases

Authors: Ryan J. Buchanan
Comments: 6 Pages.

We generalize atlases for flat stacks over smooth bundles by constructing local-global bijections between modules of differing order. We demonstrate an adjunction between a special mixed module and a holonomy groupoid.
Category: Algebra

Geometric Probability Model for α_em and α_s

Authors: Kevin Loch
Comments: 1 Page. (Notes: Abstract added by viXra Admin. Also scientific references will also be required in any future submission)

A simple geometric probability model for the EM and Strong force coupling constants.
Category: High Energy Particle Physics

Cracking the Collatz Code: a Journey from Conjecture to Certainty Through Infinity

Authors: Eric Lough
Comments: 7 Pages.

The Collatz conjecture, a puzzle that has intrigued mathematicians for decades, has met its resolution through a simple combination of trial and error combined with a spreadsheet. While the primary goal was to definitively prove the conjecture, the exploration revealed unexpected insights into the underlying patterns of the Collatz sequence. This study introduces a novel approach to organizing and analyzing Collatz data, laying bare the formulas governing the sequence's behavior. The results present a conclusive proof of the Collatz conjecture and unveil a spectrum of sets and formulas reaching to infinity, each contributing to a deeper understanding of its workings. Comprehensive instructions are provided, encouraging collaboration and furthering the collective understanding of mathematical sequences.
Category: Number Theory

From Big Bang to Chaotic Complexity: A Theory of Big Evolution

Authors: Nicholas Hoggard
Comments: 29 Pages. (Correction made by viXra Admin to conform with scholarly norm)

One of the mainstays of modern evolutionary biology is that evolution is highly sensitive to initial conditions and that, according to the Butterfly Effect from Chaos Theory, it is impossible to predict evolution in any way. But Chaos Theory is more than the Butterfly Effect, and there are aspects of chaos that - in complete contradiction to the Butterfly Effect - are insensitive to initial conditions. Also known as Universality within Chaos Theory, there is a phenomenon known as a Period-Doubling Cascade, or Feigenbaum Cascade, which is ubiquitous in iterative non-linear dynamic processes with limited resources. And iterative non-linear dynamic processes with limited resources are not exactly uncommon in the universe. Evolution is just such a process.This study examines the spontaneous creation of innovations in Intentional Teaching among animals and early humans. Such innovations occurred during Cultural Evolution, which followed Physical and Biological Evolution. Each of the teaching innovations represents nothing less than a new form of evolution. If one accepts that transmission of cultural information is as legitimate a form of transmission of acquired information as transmission of DNA during biological reproduction, then the innovations in teaching methods are potentially highly significant. There are seven new teaching methods identified by cognitive archaeologists. Each of them transmits a new kind of information that is on a higher cognitive level than previous methods. The co-evolution of tool technology, teaching, and biology, led eventually to spoken language.Examination of the time intervals between these seven evolutionary stages shows that they are compatible with a Feigenbaum Cascade from Chaos Theory. Physical and Biological Evolution also converge to the time pattern of the Cascade, as do the development of information technology in the form of written language, the printing machine, and the computer. This forms the basis of a theory of Big Evolution, which - like Big History - covers the whole of time.
Category: Quantitative Biology

The Magic of Mirror Composite Numbers

Authors: Emilio Sánchez, Óscar E. Chamizo
Comments: 6 Pages.

In this paper, continuation and completion of some previous researches, we fully develop the new concept of mirror composite numbers. Mirror composite numbers are composite numbers of the form 2n-p for some n natural number and p prime. We shall show that the factorization of these numbers have interesting properties in order to face the Goldbach conjecture [2][3] by the divide et impera method.
Category: Number Theory

Complex Dynamics and the Age of the Universe

Authors: Ervin Goldfain
Comments: 12 Pages.

There are growing indications today that complex dynamics of far-from-equilibrium systems lies at the root of primordial cosmology and the ultraviolet (UV) sector of particle physics. We recently pointed out that dimensional fluctuations of the UV sector can reproduce the morphology of the cosmic web. Expanding on the same line of inquiry, this provisional report explores the link between the long-range temporal correlations of critical phenomena and primordial cosmology. Excluding systematic measurement errors, our report sheds new light on the tension in the age of the Universe sparked off by the latest observations of the James Webb Space Telescope (JWST).
Category: Relativity and Cosmology

Watertightization of Trimmed Surfaces at Intersection Boundary

Authors: Hua Li, Lu Zhang, Ruoxi Guo, Zushang Xiao, Rui Guo
Comments: 10 Pages.

This paper introduces a watertight technique to deal with the boundary representation of surface-surface intersection in CAD. Surfaces play an important role in today’s geometric design. The mathematical model of non-uniform rational B-spline surfaces (NURBS) is the mainstream and ISO standard. In the situation of surface-surface intersection, things are a little complicated, for some parts of surfaces may be cut-off, so called trimmed surfaces occur, which is the central topic in the past decades in CAD community of both academia and industry. The main problem is that the parametric domain of the trimmed surface generally is not the standard square or rectangle, and rather, typically, bounded by curves, based on point inverse of the intersection points and interpolated. The existence of gaps or overlaps at the intersection boundary makes hard the preprocessing of CAE and other downstream applications. The NURBS are in this case hard to keep a closed form. In common, a special data structure of intersection curves must be affiliated to support downstream applications, while the data structure of the whole CAD system is not unified, and the calculation is not efficient. In terms of Bezier surface, a special case of NURBS, this paper designs a reparameterization or normalization to transform the trimmed surface into a group of Bezier surface patches in standard parametric domain [0,1]X[0,1]. And then the boundary curve of normalized Bezier surface patch can be replaced by the intersection curve to realize watertight along the boundary. In this way, the trimmed surface is wiped out, the "gap" between CAD and CAE is closed.
Category: Data Structures and Algorithms

[Discussion on] Black Holes

Authors: Pastushenko Vladimir Alexandrovich
Comments: 9 Pages.

We will talk about the properties of "black spheres" called "black holes", within the framework of the properties of dynamic space-matter, which are subject to experimental testing. First of all, the presence of new quanta in the cores of planets, in the cores of stars, in the cores of galaxies, in the cores of quasars and in the cores of quasar galaxies. And first of all, stable quanta of the new substance.
Category: High Energy Particle Physics

Optmizing Automuse with GPT-4 Turbo-128k

Authors: Cadey A. Ratio, Nicole Brennan, Jessica Williams, Ashley Kaplan, Stephanie Williams, Ma Insa
Comments: 5 Pages.

Further improvements to the Automuse system are described. The use of GPT-4 Turbo 128k allows for unique opportunities in increasing output quality and quantity. Further adaptations to modernize scenarios and plots are also described.
Category: Artificial Intelligence

Proof for Specific Type of Continued Fraction

Authors: Isaac Mor
Comments: 9 Pages.

I am going to use telescoping series and then a proof by induction. I am using Lambert's continued fraction for the base case.
Category: Number Theory

Relativity Time Dilation a Two Signal Time Delay Theory

Authors: Harvey Scribner
Comments: 6 Pages.

Special relativity time dilation has until now a un-discovered physics disconnect, "the signals used to derive the expression for time dilation (1) are actually from fixed sources in space". This observation presents a dilemma for the foundation of special relativity where it assumes a moving source emits the signals with time delayΔt'. The physics is shown that two fixed sources emit the signals independent of the velocity of the supposed moving source.
Category: Relativity and Cosmology

Elliptic Curve

Authors: Ian Connell
Comments: 327 Pages.

The first version of this handbook was a set of notes of about 100 pages handed out to the class of an introductory course on elliptic curves given in the 1990 fall semester at McGill University in Montreal. Since then I haveadded to the notes, holding to the principle: If I look up a certain topic a year from now I want all the details right at hand, not in an "exercise", so if I’ve forgotten something I won’t waste time. Thus there is much that anordinary text would either condense, or relegate to an exercise. But at the same time I have maintained a solid mathematical style with the thought of sharing the handbook.
Category: Number Theory

Transverse Relative Time and Length Shift Explained

Authors: Harvey Scribner
Comments: 10 Pages.

A source S moving with a constant velocity v emits a signal s moving with the velocity of light c relative to source S position with time t. The velocity v of signal s is the sum of v and c. The time of flight t for the signal s when emitted from S and observed at O is calculated using purely Galilean transformation of velocities in Euclidean Space Geometry. O must reside in the s light cone to observe s and avoid the artificially introduced infinities that plague classical relativity models. The geometrical interpretation of the physics is valid for velocities greater than c.
Category: Relativity and Cosmology

Rotation of a Spiral Galaxy Without Dark Matter

Authors: Sergo Rekhviashvili
Comments: 2 Pages.

The star emits electromagnetic waves intensely, so its motion must be different from that of the planet. Centripetal acceleration during star rotation around the galactic center and the resulted radiative friction creates a valid alternative to the dark matter concept.
Category: Astrophysics

Exploring the Intersections of Energy, Information, and Consciousness: A Theoretical Framework

Authors: Anthony David Adams
Comments: 7 Pages.

This paper introduces a theoretical framework represented by the equation E = k*I^2*C to explore the interconnections between energy, information, and consciousness. Drawing from advances in quantum mechanics and information theory, the framework suggests a deeper interplay of these elements, challenging traditional notions of their independence. We investigate the implications of this interrelationship, particularly in the context of quantum mechanics, and explore potential applications in fields ranging fromneuroscience to quantum computing. The paper aims to open a dialogue among physicists, information theorists, and consciousness researchers, fostering interdisciplinary approaches to unraveling the complexities of reality.
Category: Quantum Physics

Topology of Saliva

Authors: Arturo Tozzi, James F. Peters
Comments: 8 Pages.

Physical properties like shape, volume and size affect the dynamics of biological systems. Along these lines, we focus on the topological properties of biological fluids and their biochemical and physiological outcomes. We take as a paradigmatic example the salivary fluid and describe how its topological features may affect the physiopathology of the oral cavity. Topological approaches assess the general properties of saliva, ignoring small-scale physical details such as density, flow rate, stiffness, viscosity. Specifically, the mucin aggregates scattered in the salivary fluid can be tackled in terms of topological holes, i.e., vortical clusters that modify the direction, flow, impulse, local rate-of-change and velocity of saliva. While the current methodological approaches are inclined to remove the effects of impurities assessing systems as homogeneous structures, we argue that the occurrence of mucins breaks up the salivary fluid’s homogeneity, leading to unexpected biophysical modifications. We suggest that every collected salivary sample is not reliable for accurate clinical and experimental investigation, since it displays highly local as well as variable chemical, physical and biological features, not reflecting the current physiological state of the oral cavity. Therefore, the assessment of a single salivary sample is not fully reproducible and cannot provide information about the biophysical, enzymatic and microbiological content of the whole saliva. In sum, the very topological features of the saliva - such as volume, shape, antipodal cells, vortex area, whirling fluid mass, segmentation, discretization, triangulation, node numbering - produce unnoticed biological consequences and network connectivity features with intriguing operational implications.
Category: Physics of Biology

The Reciprocal Transformation Between Alpha and Omega Condition of the Steady State Universes and Exercising the Hollow Super Massive Black Holes

Authors: J. W. A. Zwart
Comments: 13 Pages. (Note by viXra Admin: Future regurgitation/repetition will not be accepted)

In the previous paper ref 1 the group symmetric relation of (243 x √2 x 6)2 = 1.375941 1010 years for the age of the universe was stated and not derived. Further also the reciprocal transformation of one year is 8677 or 5 x 1728 = 8640 hours, as it seems as a group symmetric number and determining the time scale of a galaxy around a super massive black hole was used, which was not understood and let alone derived. This will be remedied here in par 1.Another subject also treated in ref 1 was the initial condition, apparently generating the super massive black holes in time sequence for an initial macro mass of M40 = 4.4587 1040 kg compromising the entire universe. The state of these BH from M35 to M40 consequently releasing superfluous dark matter as galaxy matter, was not checked provided these BH states where really possible from the view of the weak gravity condition for the intermediating dark matter medium. This is remedied in par 2.The appendix shows some work from around 2017, about the LIGO gravity wave detection of colliding black holes.
Category: Relativity and Cosmology

Weighted Riemann Zeta Limits on the Real Axis

Authors: Han Geurdes
Comments: 7 Pages.

It is investigated whether for real argument s the (s−1)n+1 weighted Riemann zeta ζ(n)(s) limits s ↓ 1 do exist. Here, we will look into n = 0,1. The answer to the question could very well be that assuming existence to be true gives a confusing outcome. That may support the possibility of incompleteness in concrete mathematics.
Category: General Mathematics

The Nature of Vacuum Energy

Authors: Yvan-Claude Raverdy
Comments: 7 Pages.

The aim here is to show that the consideration of a quantum fluid, therefore granular, to describe space empty of matter and particles, is likely to resolve the question of its energy density in agreement with the data of standard cosmology. The Casimir effect should then make it possible to access its value which can be compared to the local gravitational energy. This also explains why quantum field theory is ineffective in accounting for this quantity.We also show that we can, through this basic hypothesis, give a concrete meaning to "dark energy" and "dark matter".
Category: Quantum Gravity and String Theory

Does "Zero-Point Vacuum Energy" Really Exist for Boson Fields? and Fermion Fields?

Authors: Warren D. Smith
Comments: 30 Pages.

Although this was written as a chapter for my book-in-progress Completing Quantum Electrodynamics and other Quantum Field Theories with "cloud" (and perhaps even creating "quantum gravity" & "theory of everything"), it can stand on its own as a helpful compilation of evidence that "zero-point vacuum energy" exists.
Category: Quantum Physics

Proof of Fermat’s Last Theorem for Odd Primes

Authors: Minho Baek
Comments: 20 Pages. I found a mistake and corrected it.

It was already proved right that xn+yn=zn, (n>2) has no solutions in positive integers which we called Fermat’s Last Theorem (FLT) by Andrew Wiles. But his proof would be impossible in the 17th century. Since Fermat showed he proved n=even by leaving proof for n=4, many people have tried to prove the odd primes. I took the idea from Euler proof and proved in case of n=odd primes by simple method.
Category: Number Theory

A Proof of Riemann Hypothesis by Symmetry and Circular Properties of Riemann Zeta Function

Authors: Tae Beom Lee
Comments: 9 Pages.

Riemann zeta function(RZF) z(s) is a function of a complex variable s=x+iy. Riemann hypothesis(RH) states that all the non-trivial zeros of RZF lie on the critical line, 0.5+iy. The symmetricity of RZF zeros implies that if z(a+ib)=0,0<a<0.5, then z(1-a+ib)=0, too. The graphs of RZF are similar to the graphs of circles with non-uniform radius and argument. These two, symmetry and circular properties of RZF, are the basis of our proof.
Category: Number Theory

The GCDM Model: a Primer

Authors: Martin R. Johnson
Comments: 19 Pages.

This is a presentation of the gas-cold-dark-matter model of Universal development designed for a younger audience. It uses simple language and has elementary development of gas thermodynamic principles appropriate for undergraduates and the general public. The essay also explores the origin of the Hubble tension in more detail than originally provided.
Category: Relativity and Cosmology

A Dark Matter Theory by Gravitation for Galaxies and Clusters

Authors: Manuel Abarca Hernandez
Comments: 39 Pages. V3 version is focused to study the Dark matter at the disk of Milky Way using the DM by gravitation theory.

This paper develops carefully an original theory of dark matter, whose main hypothesis is that DM is generated by the own gravitational field. This work introduces the best version of the theory physical and mathematically, which has been developed and published since 2013.The hypothesis of DM by gravitation has two main consequences: the first one is that the law of DM generation has to be the same, in the halo region, for all the galaxies and the second one is that the haloes are unlimited so the total DM goes up without limit. Both properties are crucial for the success of this theory. The newness of this work regarding the previous paper, [13] Abarca,M. 2023, is the chapter 12, where it is studied the DM by gravitation theory at the disk and halo regions. The numerical method used in this chapter is a bit rough but using the rotation curve at disk and its baryonic mass profile has been possible to estimate roughly DM density at disk depending on the field. Three main conclusions have been got in this chapter.1º at the disk region, there is a clear functional dependence between DM density versus field E according a potential function DDM = Au2022E^B, although the exponent of the power is not 5/3 because the baryonic mass density is not zero in this region.2º at the halo region, the parameters A & B got with a quite rude method are similar to the ones got in chapter 11 with the analytical method. This similarity shows that this rude method may be accepted in order to study the function DM density versus a power of field as a first approximation to this law.3º Even with a method so rough it is possible to estimate the Solar DM density. The result got with that method differs only 15% regarding the current value accepted by the scientific community.To study the DM theory more in depth at the disk region it is needed to solve the Poisson equation using together the baryonic density and the DM density, but unfortunately it is required sophisticated software, however at the halo region the Poisson equation is easy to solve, as it was shown in [13] Abarca,M. 2023, chp.15. Fortunately it is the galactic halo the most important region of galaxies to study DM in Cosmology.
Category: Astrophysics