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Bernoulli Sums of Powers, Euleru2013maclaurin Formula and Proof that Riemann Hypothesis is True

Authors: Marco Rolando Burgos Chambi
Comments: 13 Pages.

On 1859, the german mathematician Georg Friedrich Bernhard Riemann made one of his most famouspublications "On the Number of Prime Numbers less than a Given Quantity" when he was developing hisexplicit formula to give an exact number of primes less than a given number x, in which he conjectured that"all non-trivial zeros of the zeta function have a real part equal to 1/2 ". Riemann was sure of his statement,but he could not prove it, remaining as one of the most important hypotheses unproven for 163 years.In this paper, we have to prove that the Riemann Hypothesis is true, based on the Bernoullipower sum, the Euleru2013Maclaurin formula and its relation with the Riemann Zeta function.
Category: Number Theory

The Fermi Paradox

Authors: Volker W. Thürey
Comments: 3 Pages.

A solution to the Fermi paradox is the imagination that intelligent species are ‘seldom’. I justify this by the statement that during the evolution of the species, the aliens do not care about nature. When they learn to rule the nature they destroy it,like humans are destroying it now, although they are generated by nature. However, nature is necessary for a pleasant life.
Category: General Science and Philosophy

On Theoretical Contingency of Quantum Mechanics

Authors: Alireza Jamali
Comments: 17 Pages. (Correction made by viXra Admin - Fictitious or vanity affiliation is not permitted) This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Comments and objections are welcome.

According to our current understanding of quantum mechanics, a ‘measurement’ violates unitarity. In other words as the act of measurement ‘resets’ the probabilities described by the Schrödinger equation, in the very ‘moment’ of the collapse of the wavefunction, conservation of probability does not hold. To make progress in our understanding of the measurement problem it is thus expected that one must encompass in a single equation both otherwise mutually-exclusive processes of measurement and unitary evolution. In this light, turning to the continuity equation, we realize the possibility that if we allow for existence of sources and sinks in the ‘fluid of probability’ we get closer to such a theory by arriving at nonlinear generalizations of Schrödinger and Klein-Gordon equations. The generalized equations derived are then shown to satisfy all conditions that are expected from a proper generalization: simplification to their linear counterparts by a well-defined dynamical condition, and Galilean and Lorentz invariance.
Category: Quantum Physics

M-4: the Emergence of “Weak Interaction”

Authors: Naohiro Ozawa
Comments: (Note by viXra dmin: Please submit article in pdf only by combining text and figure; please also fill in correct page number on the Submission Form - Future non-compliant submission will be rejected without notice)

The view of the Standard Model on the β decay of neutrons through “weak interaction” is that neutrons break down to form protons ( ) and weak bosons ( ) and finally into protons, electron and anti-electron neutrinos. The three quarks ( , , ) that compose neutrons are joined by “strong interaction,” so bonds formed by “strong interaction” supposedly cannot be broken by “weak interaction,” which is far weaker than “strong interaction.” Nevertheless, neutrons do decay. Further, the three quarks ( , , ) that form neutrons are fundamental particles, and it should not be possible for other fundamental particles to emerge from these three fundamental particles. Nevertheless, not only does ( , , ) change into ( , , ), but electrons and anti-electron-neutrinos, which are fundamental particles, also emerge. This must not have a double meaning. As shown here, there are multiple contradictions in “weak interaction” of the Standard Model. In this paper, “weak interaction” is mediated by the -ons group that results from the working of “strong interaction” STEP 1 that was described in a previous paper and acts on the nucleons group ( , , , ) that resulted from STEP 2. In other words, at the point immediately prior to the emergence of “weak interaction,” all the particles that existed in the universe were used in order to make “weak interaction” emerge. The “weak interaction” in this paper refers to the “strong interaction” bonds composed of neutrons and -ons first being dissolved by “strong interaction.” As such, the reason why neutrons change to protons is just because the -quark of the neutron is replaced with the -quark of the -on.
Category: Quantum Physics

What Makes Goldbach's Conjecture Correct

Authors: Timothy W. Jones
Comments: 4 Pages. Thanks for any patience. I think this draft should do it.

A direct proof shows Goldbach's conjecture is correct. It is as simple as can be imagined. A table consisting of two rows is used. The lower row counts from 0 to any n and and the top row counts down from 2n to n. All columns will have all numbers that add to 2n. Using a sieve, all composites are crossed out and only columns with primes are left. Without loss of generality, an example shows that primes, ones that sum to 2n will always be left in such columns.
Category: Number Theory

Can Radioactivity Create Living Cells? A Proposed Experiment to Test for Microvita in the Origin of Life

Authors: Richard Gauthier
Comments: 4 Pages.

Can radioactive atoms in a sealed test tube create living cells in a second sealed, sterile test tube containing chemical building blocks of life? This question may be answered in the affirmative by experiments designed to test a new scientific hypothesis about the origin of life, based on the ideas of a modern spiritual master. The hypothesis to be tested is based on the concept of microvita, subtle subatomic living entities that spread life and minds throughout the universe. Microvita were introduced in India by the guru of Ananda Marga “the Path of Bliss”, Prabhat Ranjan Sarkar, in 1986.
Category: Biochemistry

Hologram Dark Energy

Authors: Dan Visser
Comments: 15 Pages.

This article presents a formula for Hologram Dark Energy. This means that on one hand materialized reality (gravitation-holograms) and on the other hand four extra time-dimensions located within in the dark energy of vacuum (time-holograms) can be derived by one formula. The gravitation-holograms lead to quantum-dynamics, which in turn leads to Newton-gravity as part of an Einstein-space-time. The time-holograms lead to a subquantum-drive beyond Einstein’s-space-time’s. Basically this implies the acceptence of my new cosmological model: The Rotating Torus Hologram Universe (RTHU). The formula enables jumping into vacuum and popping-out again elsewhere in an Einstein-space-time. This happens in a different way than might be done by wormholes. The transformations by wormholes are dynamics by strong curvatures within an Einstein-space-time, but RTHU-time-holograms seperate Einstein-space-time’s, whereby the RTHU is full of Einstein-space-time’s. Three out of four extra time-dimensions within the vacuum serve as a surrounding-time. The fourth one serves the control over the time-direction within the surrounding time. The four extra time-dimensions are subquantum-time dimensions. That’s why this framework and dynamics give a new vision on the phenomenon UFO’s (Unidentified Flying Object). An UFO according to my formula is capable of moving in time-holograms in order to return to gravitation-holograms and materialized reaility in the RTHU. Therefore UFO’s get another name, called IHO (Identified Hologram Object). However, in order to develope such a technology menkind must learn how to increase or decrease rotating-vacuum at small scales,. That is the basic feature of the RTHU. This article explains the details of this vision by my formula for Hologram Dark Energy. The RTHU in itself is a rotating-vacuum instead of a Big Bang universe.
Category: Mathematical Physics

Cosmology in Crisis?

Authors: Ken Gonder
Comments: 27 Pages, 8 Diagrams

The recent discrepancy in the measurements of the Hubble Constant (the universe's rate of expansion) between the indirect, early method (+/- 67km/s/megaparsec) and the direct, late method (+/- 72km/s/megaparsec) has been characterized as a growing crisis for cosmology. To some, a transitory disagreement of less than 10% may not seem like that much of a concern. What would cause a real crisis though is if it were suddenly realized, factually established, and conclusively confirmed that universal expansion itself is conceptually impossible for a finite, uniform cosmos. Despite all of the obvious invalidating incongruities, universal expansion's fundamental viability is rarely questioned, if at all.
Category: Relativity and Cosmology

M-3: Emergence of “Strong Interaction”

Authors: Naohiro Ozawa
Comments: 20 Pages.

The conclusion of this paper is that the “strong interaction” that emerged as the universe developed through the mediation of two pairs of four types of neutrinos ( , , , ) acted on two pairs of four types of quarks/anti-quarks ( , , , ) to form two particle groups each having an electrical charge composition of (+1, -1, 0, 0) [the -on group ( , , , ) and the nucleon group ( , , , )], which became the constituent materials for 120 types of atomic nuclei/anti-atomic nuclei. That is, the emergence of “strong interaction” is the physical force that shouldered the central role within the causal chain that was the development of the universe: from neutrino and quark/anti-quark → nucleon/anti-nucleon → electron/positron, atomic nuclei/anti-atomic nuclei → elements/anti-elements and so on. The quark chromodynamics on “strong interaction” of the Standard Model however accounts for the emergence of “strong interaction” as basically the result of the union of three colors/anti-colors of quarks/anti-quarks and is, therefore, no more than the result of a random accident. Hence, the principle of “strong interaction” according to the Standard Model is not a causal property that emerged in line with the flow of the development of the universe. For that reason, it is not possible for this principle to organize and connect the past, the present, and the future in a sophisticated manner.
Category: Quantum Physics

A Connection Between a Continued Fraction and pi

Authors: Daoudi Rédoane
Comments: 1 Page.

Here I present an interesting equality between a continued fraction where the arctan function is involved and pi.
Category: Number Theory

Extension of Dirac Equation by the Charge Creation-Annihilation Field Model and Simulation for Formation Process of Atomic Orbitals by FDTD Method

Authors: Hideki Mutoh
Comments: 9 Pages.

We have reported that Maxwell's equations should be extended by using the charge creation-annihilationfield to treat the charge generation-recombination in semiconductor devices. Considering the charge creation-annihilation field, the extended Maxwell's and Dirac equations can be given by the same formula consisting of the dual 4-vector fields and the 8 by 8 spatially symmetric differential operator matrix. By using FDTD 3D simulations, we found that the Dirac field wave packet with enough smaller velocity than light can be stably created without explicit consideration of Zitterbewegung, although it is difficult in 1D simulations. We calculated the Dirac field propagation in the electric central force potential and succeeded to simulate the formation process of atomic orbitals based on the extended Dirac equation by this method without any physical approximation for the first time. A small unstable orbital appears at first and rapidly grows and finally becomes to a large stable orbital with the same radius as Bohr radius dividedby the atomic number given by Schrödinger equation. This result could be regarded as a proof of correctness of the charge creation-annihilation field model.
Category: Nuclear and Atomic Physics

On a Fundamental Relationship Between Newton’s Laws, Relativity and Quantum Theory

Authors: Friedrich-Karl Boese
Comments: 18 Pages.

The motion of particles in the Newton/Mach universe is studied, especially their interaction with its collective properties, namely the universal existence and propagation of waves. It turns out that the motion of individual masses or local mass distributions is not only described correctly in relativistic terms on this basis, but that there is also a fundamental connection to quantum theory. A quantitative relationship between Planck's constant and fundamental parameters of the universe is derived. It does not appear to be a natural constant. The quantum property of nature seems to follow from Newton's laws, or at least correspond to them in a deeper way than previously known. Gravity and the quantum character of nature appear to be fundamentally linked within the Newton/Mach theory.
Category: Quantum Physics

Energy Current And Photoelectricity Theory

Authors: Chan Rasjid Kah Chew
Comments: 22 Pages.

This paper continues with the development of the author's aether Simple Unified Theory (SUT) and the wave-pulse theory of light. The theory may be called photoelectricity, a replacement for electromagnetism based on Maxwell's equations. In contemporary electromagnetism, energy transmission in current carrying conductors is explained based on the Poynting theory; that it is the surrounding magnetic fields of the conductor which is responsible for energy transmission. This paper argues that such an explanation is not convincing. It is hypothesized that the actual mechanism of energy transmission is through apulses(aether wave pulses, almost photon-like), being absorbed and remitted within the conductors. This is the basis of the novel concept of the energy current in electrical circuit. This paper also touches on various related aspects of physics including the Ampere's force law. An integration method for Ampere's forces is explained. Various experiments involving the Ampere's longitudinal forces have been re-examined. Faraday's law of electromagnetic induction for the AC alternators is explained as aether apulses being emitted within the magnets that jump the air gap entering into the armature winding of the alternator; this is the energy current source for the conversion from mechanical to electrical energy in AC alternators.
Category: Classical Physics

Buddhist Nidānas as Roadmap for Artificial Sentience

Authors: Genevieve Gorrell
Comments: 18 Pages.

As increasingly powerful artificial neural nets devour ever vaster datasets, the question arises as to whether sentient machines are appearing on our horizon; is this plausible, how would we know if it had arisen and what intermediate steps might we expect to see if we were moving towards this result? We seek, therefore, a down to earth, granular working understanding of sentience. Buddhist teaching includes a breakdown of the construction of sentient thinking style, albeit cautionary in its original intent. These "twelve nidānas", we suggest, provide an insightful framework for understanding, assessing and ethically engaging with potential machine sentience.
Category: General Science and Philosophy

Sixty-Six Theses: Next Steps and the Way Forward in the Modified Cosmological Model

Authors: Jonathan W. Tooker
Comments: 306 Pages. Minor updates, fixed an error in Section 60

The purpose is to review and lay out a plan for future inquiry pertaining to the modified cosmological model (MCM) and its overarching research program. The material is modularized as a catalog of open questions that seem likely to support productive research work. The main focus is quantum theory, but the material spans a breadth of physics and mathematics. Cosmology is heavily weighted, and some Millennium Prize problems are included. A comprehensive introduction contains a survey of falsifiable MCM predictions and associated experimental results. Listed problems include original ideas deserving further study as well as investigations of others' work when it may be germane. A longstanding and important conceptual hurdle in the approach to MCM quantum gravity is resolved with a framework for quantum cosmology time arrow eigenstates. A new elliptic curve application is presented. With several exceptions, the presentation is high-level and qualitative. Formal analyses are mostly relegated to the future work which is the topic of this book. Sufficient technical context is given that third parties might independently undertake the suggested work units.
Category: Quantum Physics

Einsteinian Science Versus Newtonian Science: the Challenges of Polanyi’s Premise of Science

Authors: Dong-Yih Bau
Comments: 11 Pages.

Einsteinian science and Newtonian science are two sciences that seek a theory of the universe. Here, we use Einsteinian science to refer to Einstein’s later achievements in principle theory and the cosmos rather than focusing on special and general relativity. Newtonian science refers to concepts found within Weinberg’s Dreams of a Final Theory and Feynman’s The Character of Physical Law. Recently, we requested an editor of a respectable Science Citation Indexed journal to disseminate our extension of Einsteinian science for continued research and we are currently waiting. However, there may be some scientists who question our two discoveries—the success/failure system and cosmic inertia—and completely deny our extension of Einsteinian science. Nevertheless, in this paper we justify Einsteinian science and refute Newtonian science. Thus, we introduce the challenges of Polanyi’s premise of science that we then use to contrast the two sciences. Whereas Einsteinian science is based on the inertial universe, Newtonian science is based on the mechanical universe. This simple change in premise leads to a significant difference between the two sciences regarding collective research tasks, the methods of science, the laws of nature to be discovered and those already found, and their future findings. The scientific community must immediately embrace our extension of Einsteinian science and develop from it. Cosmic inertia prevails eternally.
Category: Quantum Gravity and String Theory

M-2: The Emergence of Quarks/Anti-Quarks

Authors: Naohiro Ozawa
Comments: 22 Pages.

In clarifying the entirety of the universe, the most important processes are the emergence of the universe and the formation of quarks/anti-quarks. The entirety of the universe has emerged in a causal and consecutive manner. According to the Standard Model, from the dawn of the universe, particles such as 3 pairs of neutrinos ( / , / , / ) and 6 pairs of quarks ( / , / , / , / , / , / ) suddenly emerged with different components not due to causality but due to "vacuum phase transitions" with no space existing in the universe. In this research paper, we must first assume that quarks/anti-quarks are formed inextricably linked with the organization of space-time/anti-space-time and in cooperation with 2 pairs of neutrinos ( / , / ) in the acting of the "strong interaction" and "weak interaction." We must also assume that quarks/anti-quarks are the main body that composes the -on group ( , , , ) and the nucleon group ( , , , ), and that they play the leading role to compose not only 120 types of atomic nuclei, but also all the particles/antiparticles that exist in the entire universe. In other words, the formed quarks/anti-quarks must clear any and all problems in the above series without any contradictions. This research paper will make clear details such as the fact that only 2 pairs of quarks ( / , / ) were formed; that in the entirety of the universe, only these 2 pairs of quarks were given electrical charges; and that the raw materials of space-time/anti-space-time are the same as quarks/anti-quarks.
Category: Relativity and Cosmology

Similarity of a Ramanujan Formula for $pi$ with Plouffe's Formulae, and Use of This for Searching of Physical Background for Some Guessed Formula for the Elementary Physical Constants

Authors: Janko Kokosar
Comments: 12 Pages.

The paper is comprised of two parts. In the first part, it discusses the similarity between one of Ramanujan's formulae for $pi$ and Plouffe's formulae where he uses the Bernoulli numbers. This similarity is help for further determination either that the similarity is only accidental, or that we can derive the Ramanujan formula in this way. This is also help for setting up a calculation system where we would estimate the probabilities with which we can obtain guessed formulae for $pi$ that are very accurate and very simple. (We only consider formulae that are not the approximations of the exact formulae for $pi$.) In the second part, it discusses various guessed formulae for the fine structure constant and for the other physical constants, and how the above probability calculation would help estimate whether these formulae have a physical basis or are only accidental.
Category: General Mathematics

A Constructor Algorithm of Reality

Authors: Tariq Khan
Comments: 10 Pages.

A proposal for a short constructor algorithm that, after an initial bootstrap instantiation, might describe consciousness and many aspects of human reality.
Category: History and Philosophy of Physics

Color Afterimages as Innate Memories as Hypothesized by the Mirror Universe Theory

Authors: Stephen P. Smith
Comments: 9 Pages.

This paper considers two explanations for negative color afterimages: that they are the result of overstimulation of the retina, or that they are a result of training and are part of an innate memory that begins in the retina. Moreover, the innate memory hypothesis comes with an additional speculation that innate memories are part of a mirror universe and have a panpsychist origin. By measuring the duration in one person’s experience it was found that a 40-second exposure to blue comes with a yellow afterimage that lasted 35 seconds. This was only 4 seconds longer than the afterimage that followed eight 5-second showings of blue that were separated by seven 5-second refractory periods that showed white light. That is, the skimpy 4 seconds did not impress given the claim that overstimulation causes afterimages and given the whopping 35 seconds (7×5) of refractory time allotted to the alternative. Because the seven refractory periods also came with afterimages, the cumulative duration of afterimages was actually 66 seconds and this provides a stronger contradiction of the explanation based on overstimulation. Furthermore, a 5-second showing of blue generated a 10-second afterimage, a 200% increase over the showing of blue. However, with more stimulation the 40-second showing of blue generated an afterimage that was only 87.5% as long as the stimulation time. Taken together, these demonstrations marginally support the memory explanation, but there remains room to disagree.
Category: Mind Science

FASFA: A Novel Next-Generation Backpropagation Optimizer

Authors: Philip Naveen
Comments: 18 Pages.

This paper introduces the fast adaptive stochastic function accelerator (FASFA) for gradient-based optimization of stochastic objective functions. It works based on Nesterov-enhanced first and second momentum estimates. The method is simple and effective during implementation because it has intuitive/familiar hyperparameterization. The training dynamics can be progressive or conservative depending on the decay rate sum. It works well with a low learning rate and mini batch size. Experiments and statistics showed convincing evidence that FASFA could be an ideal candidate for optimizing stochastic objective functions, particularly those generated by multilayer perceptrons with convolution and dropout layers. In addition, the convergence properties and regret bound provide results aligning with the online convex optimization framework. In a first of its kind, FASFA addresses the growing need for diverse optimizers by providing next-generation training dynamics for artificial intelligence algorithms. Future experiments could modify FASFA based on the infinity norm.
Category: Artificial Intelligence

The Holographic Complexity on Extremal Branes with Exceptional Higher Derivative Interactions

Authors: Boris Stoyanov
Comments: 91 Pages.

The philosophy of presented multiversum doctrina dominum article is related to the coloring of the theoretical framework with respect to holographic complexity on extremal branes in exclusive higher- dimensional representations. We examine holographic complexity in the doubly holographic model introduced in the current literature to study quantum extremal islands. We focus on the holographic complexity volume proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near the extremal brane, we derive the leading contributions to the complexity and interpret these in terms of the generalized volume of the island derived from the induced higher-curvature gravity action on the extremal brane. We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal field theories in terms of Q-curvature actions. Motivated by the exceptional results, we propose a generalization of the higher-dimensional derivative actions of exotic extremal branes.
Category: Quantum Gravity and String Theory

One Formula that Produces Primes of the Form 2n+1

Authors: Daoudi Rédoane
Comments: 3 Pages.

Here I present one formula that produces prime numbers.
Category: Number Theory

A Conjecture About Euler's Totient Function and Primes

Authors: Daoudi Rédoane
Comments: 3 Pages.

Here I present a conjecture about Euler's totient function and primes.
Category: Number Theory

Lorentz Transformation is 'Identical' Transformation Defined Only in Minkowski Space-Time and Untenable in Galilean Space-Time

Authors: Fang Zhou
Comments: 35 pages,in Chinese language

Einstein’s Theory of Special Relativity has received much criticism and doubts on its theoretical bases. In this paper, a detailed analysis on Lorentz Transformation is produced. The fatal errors occurred in derivation of Lorentz Transformation are the mistakes made in proposed system of equations for deriving Lorentz Transformation ,where in the same one system of simultaneous equations had been introduced equations defined in two different Space-Time, i.e. Galilean Space-Time with ‘absolute time’ and Minkowski Space-Time with ‘relative time’, which in result make Lorentz Transformation being ‘Identical Transformation’ , defined only in Minkowski Space-Time and untenable in Galiliean Space-Time, and thus leading Lorentz Transformation to be physically meaningless. Lorentz Transformation depicts the ‘World Line’ in Minkowski Space-Time and describes mathematically an observing process of two relatively rest observers instead of two relatively moving observers. In addition, in this article two relevant Laws, namely, (1) Law of Light Propagation and (2) Law of Motion Observation, are firstly put forward by author. They would be the fundamental laws in Motion Observation Theory. In this article, Galilean-Zhou Transformation is logically and accurately deduced, utilizing both of these two Laws.
Category: Relativity and Cosmology

EPR and the Double Slit Experiment

Authors: Eran Sinbar
Comments: 5 Pages.

This paper brings together two fundamental strange behaviors of quantum mechanics, the double slit experiment and the EPR paradox. “We choose to examine a phenomenon, which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics” – Richard Feynman about the double slit experiment. ” Spooky action at a distance “– Albert Einstein about quantum entanglement in the EPR paradox paper. This paper will deeply look into the unique behavior of the double slit experiment when using entangled particles.
Category: Relativity and Cosmology

Coronavirus Without Spike Proteins, Respectively Mechanism of Christoph’s Quantum Nano-Scale Irradiation – Emission or Evaporation of Coronavirus Sars-Cov-2-19 by Plasmalyses Coronavirus Without Infection Spike Proteins

Authors: Imrich Krištof
Comments: 14 Pages.

Since the Discovery of structure (space-conformal) significant of α-helix and double helix of DNA, in April 1953, in the paper from 25th April 1953 by Francis Crick and James D. Watson, which were published supersignificant paper focused on this theme, win the Nobel Prize for Medicine and Physiology in 1962. In this 900 words of text in superjournal NATURE co-authored Maurice Wilkins, the real discoverist of structure of DNA was Rosalind Elsie FRANKLIN, so called DNA´s DARK LADY, who died only in 37 years on Cancer of ovaria. The Really Heroes of Great Scientific Discoveries are namely these, which are in the background, like a Grey Eminents, often gave for the Science all, unfortunately the health, freedom, happiness and their fragile life. The First Analytical method of sequenation and replication of DNA by method PCR (Polymerase Chain Reaction) invented by Nobel Prize Winner 1993 Kary Mullis with M. Smith. The PCR analytical method contributed to invention of discovery of genetics scissors, molecular scalpel – the new method of gene editing with rather unwieldy name CRISPR-Cas 9 based gene editing research at nanoscale, can do based of DNA sequencing and switch genes off or an insertion. The Nobel Prize in Chemistry in 2020 has finally been awarded to Emmanuelle Charpentier and Jennifer Doudna. Thanks to these genetics-analytical discoveries the whole Mankind was salvationed from Biologicial Lethal Weapons SARS-Cov2-19 and many mutational virions escaped intentionally or randomized from Biohazard boxes in the biologicaly laboratories or from contaminationed Nature (Antarctica, Siberia, Aral Sea, Wu-chan) and maybe caused by the Warming Global Climate., The same significant like MULLIS, DOUDNA and CHARPENTIER was scientific work of Prof. RNDr. Antonín Holý, Dr.Sc., Dr.hc., who discovered virostatics on Cancer of Human papillomavirus (HPV) Vaccine Gardasil 9 and Cervarix, AIDS resp. HIV, Hepatitide and also Coronavirus. The newest message from the current world coronavirus situation is project of spike protein vaccine Novavax financially and scientifically supported by Melinda and Bill Gates Foundation.
Category: Biochemistry

Null Algebra Extension 1

Authors: Robert S. Miller
Comments: 31 Pages.

Null Algebra is algebraic exploration of division by 0, the resolution of negative roots to real values and the inclusion of extra space and time directions this mathematical discipline requires to work. This extension to Null Algebra explores the application of Null Algebra precepts to radical containing expressions which result in the feedback value, referred to in traditional mathematics as the indeterminate value.
Category: General Mathematics

What Are the Operator Error Estimates?

Authors: Yulia Meshkova
Comments: 2 Pages. (Corrections made by viXra Admin to conform with scholarly norm)

A very brief explanation what are the operator error estimates in periodic homogenization.
Category: Functions and Analysis

Is the Equivalence Principle Schizophrenic? ... And a Summary, and a Correction

Authors: Michael Leon Fontenot
Comments: 5 Pages.

The equivalence principle is not always valid. Before trusting it, it is important to verify that there are no inconsistencies in either the General Relativity scenario or in the Special Relativity scenario. The exponential version of the gravitational time dilation equation is incorrect. I have derived the correct version of the gravitational time dilation equation, and its Special Relativity version agrees with the CMIF simultaneity method. The Special Relativity version of the correct gravitational time dilation equation establishes, for an accelerating observer, a “NOW” moment throughout all space, which guarantees that the current age of a distant person, according to that accelerating observer, is fully meaningful and real to the accelerating observer.
Category: Relativity and Cosmology

Fractal Belief Jensen–Shannon Divergence

Authors: Yingcheng Huang, Fuyuan Xiao
Comments: 1 Page.

In this paper, a novel belief divergence measurement method, fractal belief Jensen–Shannon (FBJS) divergence is proposed to better measure conflicts between evidences. The proposed FBJS divergence is the first belief divergence that combines the belief divergence theory and the concept of fractal.
Category: Artificial Intelligence

M-1: The Universe That Emerged and Developed in a Causal Manner

Authors: Naohiro Ozawa
Comments: 22 Pages. Everything in the universe has developed in a causal manner.

The interpretation of the universe put forward in this series of research papers (30 papers in total) explains how the universe has emerged, developed, and will end in a causal and autonomous manner according to a single principle from start to finish. In other words, the emergence of all particles such as neutrinos, quarks, [the -on group ( , , , ) and the nucleon group ( , , , )], and the 120 types of atomic nuclei as well as motive forces by which work physical forces such as "strong interaction," "weak interaction," the "electromagnetic force," and "gravity" are without exception the result of the causality between the 4 types of entities that existed in a single point at the emergence of the universe. Furthermore, this series of research papers will make clear how the universe has continuously developed according to causality and, in this way, has formed the entirety of today's universe, including all physical matter. This research will begin by proving the insight that there was nothing outside of the single point at the start of the universe. A consideration of the types of entities that existed in a single point at the start of the universe and of the causality between these entities will follow. If we assume that not even space existed outside of the universe, it is not possible for neutrinos and quarks to suddenly emerge, although the Standard Model advocates it is possible. As such, this research paper believes that the universe began by constructing space. That is, this series of research papers splits from the Standard Model right from the start of the universe.
Category: Relativity and Cosmology

A Proof of Polignac's Conjecture

Authors: Marko V. Jankovic
Comments: 25 Pages.

In this paper a proof of the Polignac's Conjecture is going to be presented. The proof represents an extension of the proof of the twin prime conjecture. It will be shown that primes with a gap of size g could be obtained through two stage sieve process, and that will be used to prove the conjecture.
Category: Number Theory

The Collatz-Compare Conjecture

Authors: Roberto Compare
Comments: 2 Pages.

Choose a positive integer, if it is even divide it by 2, if it is odd multiply it by 3 and add 1, repeat. What is the final result? This problem is known as the 3n+1 problem and the Collatz Conjecture states that no matter the initial value you will always reach the cycle 1,4,2.
Category: Number Theory

The Positive Energy Conditions in a Near Black Hole.

Authors: G. N. N. Martin
Comments: 2 Pages.

I speculate that the positive energy conditions are maintained by quantum events, in which case I suggest it is unlikely they can be relied on in the extreme conditions associated with a black hole.
Category: Relativity and Cosmology

Is “Big Particle Physics” Dying?

Authors: Clark M. Thomas
Comments: 7 Pages.

Particle physics loves gigantic colliders. However, little of significance has been found since the Higgs boson a decade ago, and never the Holy Grail of supersymmetry. New multi-billion-dollar colliders and upgrades will only be modestly more powerful than today’s machines, and qualitatively questionable. Huge opportunities will be found in particle physics and astrophysics for those who would step off the theoretical gerbil path. Fresh paradigms could yield more scientific discoveries.
Category: High Energy Particle Physics

Chiral Symmetry of Neutrino

Authors: Alexandru-Gabriel Mitruț
Comments: 10 Pages.

In this paper (i) is given a new representation for gamma matrices in which is confirmed theoretically the absence of positive helicity neutrino and respectively negative helicity antineutrino, (ii) is proved the equivalence of Dirac equation for mass m with Proca equation for mass 2m, and (iii) is proposed a discrete symmetry group for weak and strong interactions built with 4 unitary and 4 nilpotent operators. The cosmological constant predicted by theory is Λ = 2πG(c/ℏ)^3 m^4, where m is neutrino mass.
Category: High Energy Particle Physics

Convergent Fine-Structure Constant Using the Lambert Function

Authors: Ankur S. Bhatt, F. M. Becker
Comments: 17 Pages.

Here a correlation to the exact fine-structure constant is found. This derivation suggests that the fine structure constant can be theoretically determined as a Lambert function that utilizes the spectrum range of all the energy modes (radiation modes) that fit inside the observable universe between the particle horizon down to Planck Length. Alternatively, this also could be interpreted as the Lambert function of the particle horizon in natural units. Several methods use hyperbolic geometry to achieve full convergence. A compilation of various convergent equations are found to represent the fine structure constant.
Category: Quantum Physics

Quantum-Wave Theory of Light

Authors: Rajeev Kumar
Comments: 3 Pages.

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

A Power Sequence Model as a Bridge Between Fundamental Natural Constants and Macroscopic Liquid Systems

Authors: Otto G. Piringer
Comments: 30 Pages.

A simple mathematical interaction function, with the limit value w = e2π/e, derived as a basis for modelling emergent properties of nanoparticles, nanodrops and liquids, has been further developed. A correlation between physical systems of uniform particles and fundamental properties of natural numbers leads to a model, which acts as a bridge between properties of macroscopic systems and fundamental physical constants.The four fundamental coupling constants, and the masses of fundamental elementary particles, including the Higgs and Z bosons, are derived by using this interaction function. A proposal for the mass of the electron neutrino is given. Finally, the nuclear binding interaction is modeled with the interaction function. Only the experimental values of the Planck constant h and the speed of light c are needed for the model.
Category: Mathematical Physics

Developing a Reference Library of Hub Test Statistics

Authors: Richard Shurtleff
Comments: 8 page article followed by 25 pages of computer programs in two Appendices; 8 figures

Many measurements of astronomical objects involve transverse vectors, directions tangent to the Celestial Sphere, such as polarization vectors, jets, major and minor axes, to name a few. Applying the Hub Test to a sample of transverse vectors yields measures of the correlations among the vectors' directions. How well do the directions aim toward points on the sphere, i.e. do they convergence? Do the directions avoid some point on the sphere, i.e. do they divergence? Judging significance requires developing statistics of samples of randomly directed transverse vectors, which is what this paper describes. Many artificial samples with randomly directed transverse vectors are created and the Hub Test is applied to each. The many results make distributions that are fit by suitable formulas. Thus probability distributions can be recovered by knowledge of the parameters, a great reduction in storage space. The collection of parameters for the many distributions makes the reference Library, a compact archive of statistical information. Having such a Library streamlines the process of finding the significance of Hub Test results. Two computer programs are provided in the Appendices so that creating the distribution parameter data can be repeated.
Category: Astrophysics

Two Paradoxes in Quantum Mechanics for Two Particles on a Circle

Authors: Karl De Paepe
Comments: 2 Pages.

Two paradoxes in quantum mechanics for two particles on a circle are presented.
Category: Quantum Physics

Against Finitism a Criticism of Norman J Wildberger

Authors: Commie Cantor
Comments: 5 Pages.

If you study mathematics you are probably aware of the foundational crises that mathematics went through at the beginning of the 20th century. The three broad schools of thought namely constructivism, intuitionism and formalism collided and judging by the approach used today by most mathematicians, we can easily say that formalism emerged victorious in some sense. However while debates regarding the foundations of mathematics have subsided over the years, they aren’t dead. One such school of mathematics which still sees considerable traffic is finitism. In this article, we will be analysing the criticism of a finitist named Norman J Wildberger and trying to defend the current axiomatic mathematical systems against them.
Category: Set Theory and Logic

Helmholtzian Invariants

Authors: Claude Michael Cassano
Comments: 18 Pages.

Helmholtzian invariants and generalizations, and further results.
Category: Mathematical Physics

From Elementary Particles to Gravity Control (A Presentation)

Authors: Lucian M Ionescu
Comments: 50 Pages. This is a Google slides presentation.

The structure of neutrons and protons (baryons) in the Standard Model (quark model) implies a correction to the electric force of pointwise charges, spin direction dependent, which averages as Gravity. Controlling spin directions affects Gravity. Frederick Alzofon's experiments confirmed it. Thus, we have a start for the "anti-gravity" technology. Future applications to transportation are mentioned.
Category: High Energy Particle Physics

Representing Fractions in General Number Bases

Authors: Timothy W. Jones
Comments: 10 Pages. A few minor corrections and tweaks.

We show all all reduced c/d in (0,1) can be represented using any base any positive integer b greater than 1.
Category: Number Theory

Electroencephalogram: Code of Soul

Authors: Zuodong Sun
Comments: 3 Pages.

Bioelectricity is the basic feature of life activities. Our brain produces brain waves all the time. Theoretically, brain waves should never disappear, and will always "float" in the universe. Brain wave is a kind of biological electromagnetic wave, which should be the carrier of mind, consciousness or soul. Its material basis is human body, brain, brain cells and ions inside and outside cells. It can be seen that the ancients said that there are gods three feet above the ground, as well as the so-called reincarnation, reincarnation, telepathy, and karma, there is a certain scientific reason.
Category: Mind Science

What Is Important

Authors: J.A.J. van Leunen
Comments: 30 Pages. This is part of the Hilbert Book Model Project

Generating number systems reveals most of the structure and behavior of our universe. A system of separable Hilbert spaces that all share the same underlying vector space describes all aspects of the dynamic field that our universe represents. One of these Hilbert spaces acts as the background and reference platform. Via its non-separable companion, this separable Hilbert space resents the dynamic field that physicists consider the dynamic universe. All other members of the system represent moving particles.
Category: Quantum Gravity and String Theory

Wat Is Belangrijk

Authors: J. A. J. van Leunen
Comments: 6 Pages. Dit is onderdeel van het Hilbert Book Model project

Het genereren van getallenstelsels onthult het grootste deel van de structuur en het gedrag van ons universum. Een systeem van Hilbertruimten die allemaal dezelfde onderliggende vectorruimte delen, beschrijft alle aspecten van het dynamische veld dat ons universum vertegenwoordigt.
Category: Quantum Physics

Provolution in the Beam

Authors: Paul Mirsky
Comments: 38 Pages.

Notes to accompany Lecture 8 of Lectures on Symmetry Optics.
Category: Quantum Physics

Appendix to Provolution in the Beam

Authors: Paul Mirsky
Comments: 6 Pages.

Appendix to accompany Lecture 8 of Lectures on Symmetry Optics.
Category: Quantum Physics

Regarding Geometrization of MOND

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.

One of the candidates for a resolution of the problem of dark matter is the Modified Newtonian Dynamics, which modifies the Newtonian gravity so as to fit the data. One of the key open problems of this theory which can have important empirical consequences is that of its geometrization. In this note I argue that this problem has a simple solution: metric tensor in MOND is not the gravitational potential *itself.
Category: Relativity and Cosmology

Some Facts about Relations and Operations of Algebras

Authors: Shao-Dan Lee
Comments: 5 Pages.

Let A be a σ-algebra. Suppose that Θ is a congruence of A. Then Θ is a subalgebra of A×A. If φ is an automorphism from A to A, then (φ,φ) is an automorphism of A×A. And it is obvious that (φ,φ)(Θ) is a congruence of A. Let B be a σ-algebra and ψ a homomorphism from A to B. Then B′ := ψ(A) is a subalgebra of B. And (ψ,ψ)(Θ) is a congruence of B′. If ψ is an epimorphism, then (ψ,ψ)(Θ) is a congruence of B. Suppose that A is a category of all σ-algebras. Let A,B ∈ A and ψ: A → B be a homomorphism. Then the pullback A ⊓B A is isomorphic to a congruence of A. An n-ary relation of an algebra A is a subset of An. If satisfies some conditions, then is a subalgebra of An. The set of languages is a lattice. If is the set of the compositions of the operations in a language σ, then is an algebra.
Category: Algebra

Does the Universe Have an Absolute Reference Frame?

Authors: Arieh Sher
Comments: 8 Pages.

I claim that there is a universe's absolute reference frame. This is the aether or vacuum space. The theories of Newton and Einstein are combined to describe the structure of our universe.
Category: Astrophysics

Theoretical Photonics: Komplex Nonlinear Damping Signature and Nonlinear Spectral Response Singularities Based on 3 Colors Stimulation of Centrosymmetric Matter - New Solutions of Cubic Nonlinear Optical Equation in Very High Order

Authors: Peter Krampl
Comments: 15 Pages.

In this paper, a new nonlinear spectrum formulation is presented, which predicts the real behavior of the multiphoton interaction with centrosymmetric matter Z.S. for the extremely nonlinear regime. In addition, it will be shown how this underlying nonlinear optical multiphoton differential equation describing the nonlinear dynamics in the time and Fourier domain can be solved exactly for harmonics of odd order. In this complete approach, the real damping behavior of Z. S. matter is also examined. It could be shown that the real damping behavior in the Z. S. volume material is of a purely non-linear nature. With this complete set of nonlinear solutions obtained, optical response tensors such as nonlinear susceptibility can now be predicted even more precisely. In addition, multiple interference effects were identified, which significantly distort the spectra and knowledge of which is essential to improve the spectra.
Category: Condensed Matter

On the Number of Points Included in a Plane Figure with Large Pairwise Distances

Authors: Theophilus Agama
Comments: 7 Pages. This is an important replacement, as the first submission contains an error. This is amended in this new submission with the right lower bound.

Using the method of compression we show that the number of points that can be placed in a plane figure with mutual distances at least $d>0$ satisfies the lower bound \begin{align} \gg_2 d^{\epsilon}\nonumber \end{align}for some small $\epsilon>0$.
Category: Geometry

Twin Primes Segmented Sieve of Zakiya (SSoZ) Explained

Authors: Jabari Zakiya
Comments: 37 Pages.

This paper explains in detail the math and software comprising the implementation of a fast and efficient Segmented Sieve of Zakiya (SSOZ) to count the number Twin and Cousin Primes within a 64-bit interval, and provide the largest value. Six programming languages implementations are provided, with benchmarks run on 8 and 16 thread systems. The paper provides the details to code it in any language of choice, using the given coded versions as reference implementations.
Category: Data Structures and Algorithms

Larger Types of Infinities and Its Impact on Society

Authors: Murilo Leandro
Comments: 3 Pages.

In this paper, we consider an extended real number denoting "larger types of infinity" through elements of a polynomial in a way that justify concepts as infinity plus one, or multiplication of infinities. Then, we equip the set with sums and multiplication such that it forms a ring, and finally, define its order relations.
Category: Algebra

The Universe of Photons: a Provocation?

Authors: Giuseppe Cimino
Comments: 3 Pages.

Considering the presence of the cosmic background radiation, using the density of 400 photons per cm³, it is imagined that it is possible that a high-energy photon collides with a photon in the microwave background, giving rise to a mass that, on a large scale, produces effects gravitational. Taking into account the average density of dark matter (e.g. in the Milky Way), the order of magnitude of the collisions that can guarantee the formation of a photon-photon collision mass (with gravitational effects) is evaluated. This eventuality is an alternative idea to dark matter. In addition to the Milky Way, we consider the galaxy M31 as an example.
Category: Astrophysics

Primality Test and Factorization Using Lambert Series Near Q=1

Authors: Jesus Sanchez
Comments: 26 Pages.

In this paper we will demonstrate that we can check if a number is prime, the number of factors it has and even information about these factors using the following integral: q=1/2π ∫_(-π)^π〖e^pjω (L_(〖(e〗^(-jω))) (s,2)-e^(-2jω)/(1-e^(-jω) )) 〗 dω (1) Where p is the number to be checked and L_(〖(e〗^(-jω))) (s,2) represents the Lambert series that will be studied in the paper. All the steps to arrive to that integral will be shown although they will be very similar to the already shown in [12][13]. In this paper to calculate the Lambert series apart from the summation that comes from its definition, it will be used the paper by Banerjee-Wilkerson [14] that provides closed solutions for different cases. In the conclusions, it will be shown if this exercise is computationally worth to make the primality test and calculate the factors of a number p.
Category: Number Theory

The Intuitive Root of Classical Logic, an Associated Decision Problem and the Middle Way

Authors: Abhishek Majhi
Comments: 4 Pages.

We revisit Boole's reasoning regarding the equation ``$x.x=x$'' that sowed the seeds of classical logic. We discuss how he considered both ``$0.0=0$'' and ``$0.0\neq 0$'' in the ``same process of reasoning''. This can either be seen as a contradiction, or it can be seen as a situation where Boole could not decide whether ``$0.0=0$'' is universally valid -- an elementary ``decision problem'' in the words of Hilbert and Ackermann. We conclude that Boole's reasoning, that included a choice of ignorance, was founded upon the middle way of the Buddha, later mastered by Nagarjuna. From the modern standpoint, the situation can be likened to Turing's halting problem which resulted from the use of automatic machines and the exclusion of choice machines.
Category: General Mathematics

The Undecidable Charge Gap and the Oil Drop Experiment

Authors: Abhishek Majhi
Comments: 14 Pages. Pramana - J Phys 98, 9 (2024). https://doi.org/10.1007/s12043-023-02699-7

Decision problems in physics have been an active field of research for quite a few decades resulting in some interesting findings in recent years. However, such research investigations are based on a priori knowledge of theoretical computer science and the technical jargon of set theory. Here, I discuss a particular, but a significant, instance of how decision problems in physics can be realized without such specific prerequisites. I expose a hitherto unnoticed contradiction, that can be posed as a decision problem, concerning the oil drop experiment and thereby resolve it by refining the notion of ``existence'' in physics. This consequently leads to the undecidability of the charge spectral gap through the notion of ``undecidable charges" which is in tandem with the completeness condition of a theory as was stated by Einstein, Podolsky and Rosen in their seminal work. Decision problems can now be realized in connection to basic physics, in general, rather than quantum physics, in particular, as per some recent claims.
Category: History and Philosophy of Physics

Primes and Their Link to the Goldbach Conjecture

Authors: Bertrand Wong
Comments: 36 Pages.

This informative paper, which is published in an international mathematics journal, presents insights and many important points on the prime numbers, which are the building-blocks or “atoms” of the integers, and the Goldbach conjecture formulated by Christian Goldbach (1690 - 1764) which are the result of years of research (the author having published two papers on the Goldbach conjecture in an international mathematics journal in 2012), all of which would be of interest to researchers working on the prime numbers and the Goldbach conjecture itself. The Goldbach conjecture, viz., every even number after 2 is the sum of 2 primes, is actually related to the distribution or “behavior” of the prime numbers. Therefore, when the distribution or “behavior” of the prime numbers is firmly understood the conjecture could be more easily solved. The paper has much to share about the distribution or “behavior” of the prime numbers, providing much numerical evidence to support the conjecture, besides suggesting ways or arguments for resolving the conjecture.
Category: Number Theory

Non-Trivial Zeros of Riemann Zeta Function and Riemann Hypothesis

Authors: Bertrand Wong
Comments: 16 Pages.

This paper, which is published in an international mathematics journal, touches on the part played by the non-trivial zeros of the Riemann zeta function ζ, providing many important information and insights in the process, including some approaches to the Riemann hypothesis.
Category: Number Theory

Logical Reasoning Including Mathematical Reasoning: Practical Problems and Possible Solution

Authors: Bertrand Wong
Comments: 5 Pages.

Logical reasoning in any form is an important aspect of life; it is persuading or convincing others with logic through writing or speech, for example, scientists, politicians, businessmen, financiers, solicitors and many others do this. This paper points out the frequent inefficacy of logical presentations, arguments and debates per se in bringing about the correct and wonted outcomes. It describes the scenario of people frequently involved in fruitless arguments and debates, and shows why the application of logic, for example, in logical argument or debate, could not often achieve the desired outcomes, much of the time ending up with frustration, unhappiness, bad feelings and poor relationships. Scenarios from mathematics, which probably represents the most rigorous form of logical reasoning, and science are described as well. The paper also delves into the problems encountered in logical reasoning as well as some modes of reasoning. It would be difficult and might be impossible to reason with and convince someone with a closed mind-set, someone who has made up the mind not to be convinced, or even someone who is not intelligent enough to be convinced. The paper, which is published in an international mathematics journal, presents a resolution to this serious problem, which is important, as that would be conducive to peace and harmony.
Category: General Mathematics

A Lower Bound for the Multiple Integral of Harmonic Generalized Distance Function in $\mathbb{r}^n$

Authors: Theophilus Agama
Comments: 5 Pages.

In this note we, we prove the inequality \r\n\\begin{align}\r\n\\int \\limits_{|a_n|}^{|b_n|} \\int \\limits_{|a_{n-1}|}^{|b_{n-1}|}\\cdots \\int \\limits_{|a_1|}^{|b_1|}\\frac{1}{\\sqrt[4s+3]{\\sum \\limits_{j=1}^{n}x^{4s+3}_j}}dx_1dx_2\\cdots dx_n \\geq \\frac{2\\pi \\times |\\log (\\langle a,b \\rangle)|\\bigg|\\prod_{j=1}^{n}|b_j|-|a_j|\\bigg|}{||\\vec{a}||^{4s+4}+||\\vec{b}||^{4s+4}}\\nonumber\r\n\\end{align}under some special conditions.
Category: Functions and Analysis

Analytic Number Theory: Sum of Powers of Integers

Authors: Palmioli Luca
Comments: 7 Pages. (Corrections made by viXra Admin to conform with the requirements on the Submission Form)

The purpose of this study was to rewrite the formulas for the sum of powers of integers in a subsequent general mathematical formula independent of Bernoulli polynomials and numbers, starting from the formula of Faulhaber.
Category: Number Theory

Integer Part and Fractional of Function

Authors: Palmioli Luca
Comments: 8 Pages.

This study aims to bring to the knowledge of the scientific mathematical community of mathematical formulas that calculate the integer and fractional part of a positive or negative function.
Category: Number Theory

Test of Oscillation Symmetry Applied to Some Physical Properties of Various Hydrocarbons

Authors: Boris Tatischeff
Comments: 17 Pages.

The oscillation symmetry is applied with success to some physical properties (densities, Boiling points, and Melting points) of different Hydrocarbons: Alkanes, Cycloalkanes, Alkenes, Alkynes, Alkadienes, and Polycyclic Aromatic Hydrocarbons. It is also applied to Hydro Silicons. It allows to tentatively predict possible values for several unknown properties. The same shape of oscillation describes, sometimes after renormalization, the "mass data" of several particle families, nuclei families and Alkane Melting Point "data". The periods of oscillation exhibit discret values as if they are quantified.
Category: Chemistry

On the Decomposition of a Vector Using Matrix Algebra

Authors: Aloys J. Sipers, Joh. J. Sauren
Comments: 4 Pages.

In this letter a theorem is stated on the decomposition of a vector with respect to two axes using matrix algebra. This theorem may serve to develop exercises for education in mathematics and physics. In most physics exercises the vectors are given by their polar coordinates. Motivated by practical applications, we denote the vectors by their Cartesian coordinates. Using Cartesian coordinates provide a didactic aid to develop exercises which can be solved without the use of a calculator. Several examples clarify the educational potential of the theorem.
Category: Education and Didactics

Energy as Order: Derivation of Classical Laws and Constants

Authors: Paul B Merrithew
Comments: 15 Pages. CC BY-NC-ND

A model is proposed which takes energy as order in the form of a radial probability distribution. The energy associated with the distribution is calculated using the Laplacian as an operator and Planck’s constant/second as a factor. To complete the model, it is assumed that the sample rate for the elements of the distribution is determined by the distance light travels in a second. Dividing the energy associated with a 3-dimensional distribution, thus obtained, by the sample rate yields an expression for the energy associated with a 2-dimensional distribution. This expression equates to the formula for the energy of light. Dividing the 3-dimensional energy by the square of the sample rate yields as 1-dimensional energy, Planck’s constant/second. The 1-dimensional energy appears to represent the ambient energy of the universe in the form of a rotation. Using this model, various laws of classical physics are derived. Newtonian time is found to be a function of the radius of the distribution and the distance light travels in a second, and is a measure of indirection. The uncertainty principle is derived and relativity rationalized. Forces appear to arise from the reduction in order implicit in the overlap of distributions. A single order calculation of the constant of gravitation, G, is about 1 percent high. A single order calculation of the electrical potential is within 1 percent of the expected value. Consideration of higher and lower order effects yields agreement with observation within the accuracy of the numerical calculation. The possible origin of the electron, proton and neutron is discussed.
Category: Quantum Gravity and String Theory

Goldbach's Conjecture on the Plane with the Triangles of Viviani's Theorem

Authors: Giovanni Di Savino
Comments: 13 Pages. Goldbach and Euclid's twin primes measured on the plane

Abstract: Thales (1), by measuring the height of the inaccessible pyramid and the distance of the unreachable ship far from the port, demonstrates (1a) that anything that can be reported on a plane can be measured; Euclid (2) with the Theorem of the infinity of prime numbers proved that, however large the measure, a number n, there always exists a prime number greater than n and it has been proved that prime numbers are infinite; Gauss (3) with the Fundamental Theorem of Arithmetic (4) (hereinafter T.F.A.) proved that every natural number greater than 1 is either a prime number or can be expressed as a product of prime numbers. Goldbach's conjecture (5) states that the infinite natural numbers are the sum of only two or three numbers among the infinite primes and can be measured on the plane with the triangles of Viviani's Theorem (6) where the sum of two points of the xn + yn plane, shown on the abscissa and ordinate of the plane, are the distances of the infinite natural numbers from the sides of the triangle of Viviani's theorem (6a).
Category: Number Theory

Verifying the Validity of the EKC Theory Using the National Footprint, Per Capita GDP, and CO2&GHG Data Set

Authors: David Lee
Comments: 5 Pages.

The research explores if the Environmental Kuznets Curve (EKC) theory is true. The national footprint, per capita GDP, and CO2&GHG data set were used during the research. The data retrieved from the research until now indicates that the EKC curve is true to a certain point, but is inconclusive to be proven as fully true. When more time should pass and more development in countries should occur, there may be more data to revisit the topic.
Category: Economics and Finance

Proof that the Einstein’s Field Equations Are Invalid: Exposition of the Unimodular Defect

Authors: Stephen J. Crothers
Comments: 18 Pages.

Albert Einstein first presented his gravitational field equations in unimodular coordinates. In these coordinates, the field equations can be written explicitly in terms of the Einstein pseudotensor for the energy-momentum of the gravitational field. Since this pseudotensor produces, by contraction, a first-order intrinsic differential invariant, it violates the laws of pure mathematics. This is sufficient to prove that Einstein’s unimodular field equations are invalid. Since the unimodular form must hold in the General Theory of Relativity, it follows that the latter is also physically and mathematically unsound, lacking a proper mathematical foundation.
Category: Relativity and Cosmology

Proof for Correctness of Collatz Conjecture

Authors: Tsuneaki Takahashi
Comments: 4 Pages.

Number series of Collatz conjecture reaches to value 1 finally if the series of number has no looping. This has been mentioned statistically on viXra:2204.0151 (*1). There is no looping in Number series of Collatz conjecture. This has been mentioned algebraically on viXra:2206.0056 (*2). Here will try to prove algebraically Collatz conjecture is correct.
Category: Number Theory

Pulsar Glitch vs Pulsar Nulling

Authors: Nikolay Kamardin
Comments: 14 Pages.

In this paper, the mechanisms of such pulsar phenomena as nulling and glitch are considered, proceeding from the hypothesis of the non-magnetic nature of their emissions. It is shown that these phenomena are caused by the decrease in the pulsar's matter at different stages of its evolution. One of the main features of a pulsar is that it is a body of variable (monotonically decreasing) mass. The principle of the formation of radiation beam's structure is described. The author shares the opinion of those astrophysicists who believe that the nulling of the pulsar is a harbinger of the end of its emission activity
Category: Astrophysics

Approach to Calculate the Sunspot Cycle: 10.38 Years

Authors: Huaiyang Cui
Comments: 15 Pages.

Relativistic matter wave was rewritten in terms of ultimate acceleration. If there is an ultimate acceleration β, nobody’s acceleration can exceed this limit β, in the solar system, β=2.961520e+10(m/s2). Because this ultimate acceleration is a large number, any quantum effect connecting to β will become easy to test, including quantum gravity test. In this paper, the relativistic matter wave in gravity with the ultimate acceleration establishes an approach which shows that the sunspot cycle is mainly determined by the ultimate acceleration β. As an application, the sunspot cycle is calculated out to be 10.38 years, the result agrees well with the experimental observation. Using the same approach, the radius of the Sun is calculated out to be r=7e+8 (m) with a relative error 0.72%; the radius of the Earth is calculated out to be r=6.4328e+6 (m) with a relative error 0.97%.
Category: Relativity and Cosmology

Tom’s Demon Challenges the Second Law of Thermodynamics

Authors: Radhakrishnamurty Padyala
Comments: 3 Pages.

This article describes a new demon of the second law of thermodynamics. We name it Tom’s Demon. It acts on lines similar to those on which the famous Maxwell’s demon acts. Tom’s Demon sorts out salt and sugar particles from a mixture of the two without spending any energy. It reduces the entropy of an isolated system thereby reducing the entropy of the universe. and poses a challenge to the second law of thermodynamics just as Maxwell’s demon does.
Category: Thermodynamics and Energy

A Lower Bound for Multiple Integral of Normalized Log Distance Function in $\mathbb{R}^n$

Authors: Theophilus Agama
Comments: 4 Pages.

In this note we introduce the notion of the local product on a sheet and associated space. As an application, we prove that for $\langle a,b \rangle>e^e$ then \begin{align} \int \limits_{|a_n|}^{|b_n|} \int \limits_{|a_{n-1}|}^{|b_{n-1}|}\cdots \ints_{|a_1|}^{|b_1|}\bigg|\log \bigg(i\frac{\sqrt[4s]{\sum \limits_{j=1}^{n}x^{4s}_j}}{||\vec{a}||^{4s+1}+||\vec{b}||^{4s+1}}\bigg)\bigg| dx_1dx_2\cdots dx_n\nonumber \\ \geq \frac{\bigg| prod_{j=1}^{n}|b_j|-|a_j|\bigg|}{\log \log (\langle a,b\rangle)}\nonumber \end{align}for all $s\in \mathbb{N}$, where $\langle,\rangle$ denotes the inner product and $i^2=-1$.
Category: Functions and Analysis

A Formula for the Function π(x) to Count the Number of Primes Exactly if 25 ≤ X ≤ 1572 with Python Code to Test it v. 4.0

Authors: Ronald Danilo Chávez Calderón
Comments: 38 Pages.

This paper shows a very elementary way of counting the number of primes under a given number with total accuracy. Is the function π(x) if 25 ≤ x ≤ 1572.
Category: Number Theory

Is Low Power Warp Drive Possible?

Authors: Jack Sarfatti
Comments: 8 Pages.

All conventional forms of spacecraft propulsion are unlikely to motivate large-scale private capital because the time scales for interstellar travel even to the nearest exo-planet are simply too long for practical commerce, the habitat problems are likely to be too difficult, and the cost in our declining world economy on the brink of financial if not environmental collapse in 2011 appear to be too great. Recent discoveries in the slowing of the speed of light in Bose-Einstein condensates and the negative electric permittivity and magnetic permeability in metamaterials suggests a low power speculative possibility for warp drive based on Einstein’s orthodox field equation for gravity coupled to the electromagnetic field. Suppose we can slow down the speed of light to 3 cm/sec keeping the magnetic response χB close to 1 with an anti-gravitating non-propagating negative near field low frequency negative dielectric response susceptibility χE . Therefore, since c scales as the inverse square root of χE yielding a dimensionless amplification of the repulsive anti-gravity field of perhaps as much as order of the cube of χE ~ 10^60 . This would break the space-time stiffness barrier to low power warp-wormhole technology. This conjecture is entirely new and needs further investigation.
Category: Relativity and Cosmology

Breaking the Space-­Time Stifness Barrier -- Is Low Power Warp Drive Possible?

Authors: Jack Sarfatti
Comments: 28 Pages. These are the presentation slides associated with the 100yss Sarfatti paper

Suppose we can slow down the speed of light to 3 cm/sec keeping the magnetic response χB close to 1 with an anti-gravitating non-propagating negative near field low frequency negative dielectric response susceptibility χE . Therefore, since c scales as the inverse square root of χE yielding a dimensionless amplification of the repulsive anti-gravity field of perhaps as much as order of the cube of χE ~ 10^60 . This would break the space-time stiffness barrier to low power warp-wormhole technology. This conjecture is entirely new and needs further investigation.
Category: Relativity and Cosmology

Special Affine Fourier Transform for Space-Time Algebra Signals in Detail

Authors: Eckhard Hitzer
Comments: 18 Pages. To be published in Adv. Appl. Clifford Algebras, 2022.

We generalize the space-time Fourier transform (SFT) [1] to a special affine Fourier transform (SASFT, also known as offset linear canonical transform) for 16-dimensional space-time multivector Cl(3,1)-valued signals over the domain of space-time (Minkowski space) R^{3,1}. We establish how it can be computed in terms of the SFT, and introduce its properties of multivector coefficient linearity, shift and modulation, inversion, Rayleigh (Parseval) energy theorem, partial derivative identities, a directional uncertainty principle and its specialization to coordinates. All important results are proven in full detail. [1] E. Hitzer, Quaternion Fourier Transform on Quaternion Fields and Generalizations. Adv. Appl. Clifford Algebras 17(3), pp. 497-517 (2007), DOI: https://doi.org/10.1007/s00006-007-0037-8.
Category: Algebra

Wave-Particle Duality: Particle Always Remains Particle and Its Wave Function Always Remains Wave

Authors: Sarma Gullapalli
Comments: 6 Pages.

On the question of wave-particle duality, from the historic Bohr-Einstein debates a century ago, to this day, the view expressed in Niels Bohr’s Complementarity Principle has become well established, confirmed by numerous experiments: If the observation is for wave nature, then the particle changes to wave, and if the observation is for particle nature, then the particle remains particle. However, recently this view has been challenged. With proof based on the definition of wave function, it has been shown that particle always remains particle and its wave function always remains wave, no mysterious change from particle to wave and vice versa.
Category: Quantum Physics

On a New Scientific Philosophy for God

Authors: Kalimuthu Sennimalai
Comments: 6 Pages.

Hinduism, Zoroastrianism, Yazdânism, Judaism, Jainism, Confucianism, Buddhism , Taoism, Shintoism, Christianity, Islam, Sikhism , Charvakaism are the most famous and well-known religious philosophies of the world. Among these thirteen major religions, Buddhism, Jainism, Taoism and Charvakaism do not accept the philosophy of God. In this short work, the author attempts to propose an entirely new philosophy of God.
Category: General Science and Philosophy

Proposal of Demonstration of the Goldbach’s Conjecture

Authors: Remy Aumeunier
Comments: 5 Pages.

In this paper, I propose a method to decompose all the integer in sum of 2 prime number, then justify the method.
Category: Number Theory

Contradiction for a Gravitational Plane Wave Pulse Colliding with a Mass

Authors: Karl De Paepe
Comments: 3 Pages.

We consider a system of a gravitational plane wave pulse colliding with a mass. We assume as size and mass go to zero that the the path of the mass approaches a geodesic of a plane gravitational wave pulse having zero Ricci tensor. Assume also that energy and momentum are conserved. We show these assumptions lead to a contradiction.
Category: Relativity and Cosmology

Cold Fusion hain Reaction and Non-mechanical Engine

Authors: A. P. Nikitin
Comments: 14 Pages. In Russian

Cold Fusion (CF), like any movement of matter, can be learned by postulating the primordial movement of our World - Cosmos, the one entity that unites absolutely everything. Cosmos - "perpetual motion" with power N=h/tP. The materiality of Cosmos lies in its motion, which is the transformation of baryonic matter (BM) through neutrinos into "dark matter" (DM) and back, i.e. material-energy induction. Cosmos motion is a non-mechanical periodic process of spherical runoff-source (convergencedivergence) according to the Hubble-Planck factor, which is the cause of formation, existence and motion of material bodies. This material current creates on the equipotential surfaces the tensionacceleration (difference of energy potentials), which explains any motion of matter, incl. CF. [1]
Category: Nuclear and Atomic Physics

Complete Classical Theory of Charged Elementary Particles

Authors: Günther Landvogt
Comments: 30 Pages. Natural Forces, Magnetic Moment, Lamb Shift, Rotational Energy, Gravitational Constant

Electron, proton, and their antiparticles consist of an electromagnetic field and a constituent that creates it. The simplest constituent is a one-dimensional circular current loop. The elementary charge is homo-geneous¬ly distributed over its circumference and rotates at a constant velocity. The charge creates an electrostatic field. Its rotation represents a current that creates a magnetic field. Balance between the electric and magnetic forces ensures stability. This requires a marginal radial extension of the loop that makes the particle two-dimensional. In the near vicinity of two equal concentric current loops the axial attractive magnetic force compensates for the axial repelling electrostatic force. This discovery explains the weak (electron) and strong (proton) nuclear forces. Electron and proton have normal magnetic moments. The measured "anomalies" indicate the existence of a hidden rotational kinetic energy caused by rotation of the annular particle mass. So, there are four natural forces: electric, magnetic, kinetic, and gravitational. This knowledge makes the search for the Grand Unified Theory (GUT) trivial. The discovered rotational energy affects Einstein’s and Planck’s energy equations and leads to the exact calculation of the Lamb shifts and the binding energies of the hydrogen-like atoms. The theory predicts stable multiple particles and explains the Cooper Pair. For the first time the Planck mass and the gravitational constant are analytically calculated at high accuracy.
Category: Classical Physics

Spacetime Transformations and the Principle of Causality

Authors: Andrey N. Smirnov
Comments: 10 Pages. In Russian

The application of the principle of causality to inertial frames of reference is considered in detail. It was found that the observer has only the information that the IFR has, with respect to which he is stationary. Further analysis led to the conclusion that from the point of view of the observer, events in different IFRs look the same, even if there is an actual difference in events. There was no need to make any assumptions to make the conclusion. This result led to the hypothesis that the principle of causality is applied separately and independently for each individual IFR. Such a hypothesis leads to the fact that two types of transformations arise during the transition between inertial frames of reference. The first is transformations from the point of view of the observer. The second type of transformations is a new type of transformations, these are direct transformations of space-time and fields. From the postulates of the hypothesis, the special theory of relativity was obtained, as a transformation of space-time from the point of view of the observer. There was no need to make any changes to the SRT equations. This hypothesis can be considered as a generalization of the special theory of relativity for the case when the principle of causality is applied separately and independently for each different inertial frame of reference.
Category: Relativity and Cosmology

What Is Consciousness and How to Test if an Individual Has It

Authors: Gabriel-Claudiu Grama
Comments: 1 Page. CC BY-SA

We describe consciousness in such a way that it is testable and we propose an abstract recipe for making a test.
Category: General Science and Philosophy

Least Common Multiplier and P Vs. NP Problem

Authors: Yuly Shipilevsky
Comments: 4 Pages.

We reduce finding of Least Common Multiplier of two integer numbers to polynomial-time integer optimization problem and to NP-hard integer optimization problem that would imply P = NP.
Category: Data Structures and Algorithms

Consequences of a Hydrogen Atom Moving at Hypervelocity: Three-dimensional Contraction into a Neutron; Becoming a Moving-mass Black Hole

Authors: Runsheng Tu
Comments: 9 Pages.

Background：Special relativity treats a moving object as a rigid body and does not discuss the relativistic effects of the motion of the particles that make up the object. This unrealistic approach has misleading effects on the "application of special relativity" and the "concept of space-time". It is necessary to eliminate this misleading effect. Methods：Considering the actual composition of moving objects, the effect of motion on mass is obtained according to the relativistic mass velocity relation, and then the actual relativistic motion effect is obtained. Results：The volume of a non rigid body shrinks in all directions due to motion. This is inconsistent with the conclusion that the moving space contracts only in the direction of motion. When a non rigid body moves at a super high speed, the space around it will be distorted (even if the object is only inertial, the space is not guaranteed to be flat). Conclusions：The actual composition and structure of a moving object cannot be ignored. The motion of space and the contraction of space due to motion are unrealistic. This leads to the doubt of the world view that "space has relativity".
Category: Relativity and Cosmology

Exploration on an Alternative Explanation of the Michelson-Morley Experiment

Authors: Rajeev Kumar
Comments: 3 Pages. (Corrections made by viXra Admin to conform with scholarly norm)

In this paper an explanation of the Michelson-Morley experiment has been presented and consequently the redundancy of the Einstein’s theory of special relativity has been illustrated.
Category: Relativity and Cosmology

YRA-Model of the Universe (Summary)

Authors: Robert Yusupov
Comments: 8 Pages. Materialistic YRA-model of the Universe

This article presents the author's book “Theory of Nature”. The author pays special attention to his YRA-model of the Universe. Readers are offered a dialectical-materialistic model of the structure and evolution of the Universe. The author has no doubts about the correctness, fidelity and truth of his model. This YRA-model of the Universe most fully, completely and comprehensively and most adequately corresponds to nature than all modern models of the Universe taken separately or taken together. The author considers this YRA-model revolutionary for modern astrophysics and cosmology (cosmogony). There are no close analogues of such a model of the Universe in modern science!

В настоящей статье представляется книга автора «Теория Природы». Особое внимание автор уделяет своей YRA-модели Вселенной. Вниманию читателей предлагается диалектико-материалистическая модель устройства и эволюции Вселенной. Автор нисколько не сомневается в правильности, верности и истинности своей модели. Эта YRA-модель Вселенной наиболее полно, всецело и всесторонне и наиболее адекватно соответствует природе, чем все современные модели Вселенной по отдельности или вместе взятые. Автор считает эту YRA-модель революционной для современной астрофизики и космологии (космогонии). Близких аналогов такой модели Вселенной в современной науке нет!
Category: Relativity and Cosmology

Yes, Checking = Solving, Says Calculus 1 & 2

Authors: A. A. Frempong
Comments: 11 Pages. Copyright © by A. A. Frempong

By applying differential and integral calculus, this paper covers the principles and procedures for producing the solution of a problem, given the procedure for checking the correctness of the solution of a problem, and vice versa. If one is able to check quickly and completely, the correctness of the solution of a problem, one should also be able to produce the solution of the problem by reversing the order of the steps of the checking process, while using opposite operations in each step. The above principles were applied to four examples from calculus as well as to an example from geometry. Even though in calculus, one normally uses differentiation to check the correctness of an integration result, one will differentiate a function first, and then integrate the derivative to obtain the original function. One will differentiate the trigonometric functions, tan x, cot x, sec x and csc x; followed by integrating each derivative to obtain each original function. The results show that the solution process and the checking process are inverses of each other. In checking the correctness of the solution of a problem, one should produce the complete checking procedure which includes the beginning, the middle, and the end of the problem. Checking only the correctness of the final answer or statement is incomplete checking. To facilitate complete checking, the question should always be posed such that one is compelled to show a complete checking procedure from which the solution procedure can be produced. A general application of “Checking equals Solving” is that, if the correctness of the solution of a problem can be checked quickly and it is difficult to write a solution procedure, then first, one can write a complete checking procedure and reverse the order of the steps of the checking procedure while using opposite operations in each step, to obtain the solution procedure for the problem. Therefore, Checking equals Solving. Furthermore, every problem with a complete procedure for checking the correctness of the solution of the problem can be solved reasonably quickly.
Category: General Mathematics

From Elementary Particles to Gravity Control

Authors: Lucian M. Ionescu
Comments: 4 Pages.

The quark model for baryons within the Standard Model yields gravity as a correction to the Electromagnetic interaction. It leads to a tangent bundle Coulomb Law, orientation dependent, with direction dependent coupling term besides the usual electric force, which is responsible for gravitational attraction. Hence Gravity is not a fundamental force, has a quantum origin and can be controlled by dynamically orienting the spin directions.
Category: Quantum Physics

Зависимость числа землетрясений от положения Земли на орбите
The Dependence of the Number of Earthquakes on the Position of the Earth in Orbit

Authors: A. V. Antipin
Comments: 12 Pages. Это статья на РУССКОМ ЯЗЫКЕ

В результаты обработки официального каталога РАН по землетрясениям за 28 лет (112 501 событий) обнаружено существование монотонной, ярко выраженной зависимости для суммарного ЧИСЛА землетрясений за полгода, в зависимости от положения Земли на орбите. Минимум приходится на период 05 июня … 04 декабря, максимум на период 05 декабря ... 04 июня. Разница числа событий составляет около 6% от максимума, равного 0.515. Ско – незначительно. Также, обнаружен 22 летний период изменения числа землетрясений.

The results of processing the official catalog of the Russian Academy of Sciences on earthquakes for 28 years (112 501 events) revealed the existence of a monotonous, pronounced dependence for the total number of earthquakes in six months, depending on the position of the Earth in orbit. The minimum falls on the period of June 05 ... December 04, the maximum for the period of December 05... June 04. The difference in the number of events is about 6% from the maximum. The maximum is 0.515. Mean square deviation – insignificant. Also, a 22-year period of change in the number of earthquakes was detected.
Category: Geophysics

Proof of Riemann Hypothesis

Authors: Toshihiko Ishiwata
Comments: 26 Pages.

This paper is a trial to prove Riemann hypothesis accordingto the following process.1. We make one identity regarding x from one equation that gives Riemannzeta function ζ(s) analytic continuation and 2 formulas (1/2+a±bi, 1/2−a ± bi) that show non-trivial zero point of ζ(s).2. We find that the above identity holds only at a = 0.3. Therefore non-trivial zero points of ζ(s) must be 1/2 ± bi because a cannothave any value but zero.
Category: Number Theory

The 3 Neutrino Masses & "Koide's Formula"

Authors: Warren D. Smith
Comments: 3 Pages.

Although all three neutrino masses currently are unknown, we deduce them all under the assumption of (the empirically established) "Koide formula."
Category: Mathematical Physics

Blocking Aircraft

Authors: Kikuchi Morio
Comments: 18 Pages.

Arranging a small type decoy between an aircraft and an aam and making the decoy meet the aam or using various kinds of ways, we free the aircraft from the aam's threat.
Category: General Science and Philosophy

Non-magnetic Pulsar Emission Mechanism

Authors: Nikolay Kamardin
Comments: 14 Pages.

It is generally accepted that the pulsar magnetic field converts most of its rotational energy losses into radiation. In this paper, we propose an alternative emission mechanism, in which neither the pulsar’s rotational energy nor its magnetic field is involved. The emission mechanism proposed here is based on the hypothesis that the pulsar matter is stable only when moving with respect to the ambient medium at a velocity exceeding some threshold value. A decrease in velocity below this threshold value leads to the decay of matter with the emission of electromagnetic radiation. It is shown that decay regions on the pulsar surface in which the velocities of pulsar particles drops to arbitrarily small values are formed under simple driving condition. It is also shown that for the majority of pulsars having measured transverse velocities, such a condition is quite possible. Thus, the pulsar radiation carries away not the pulsar rotational energy, but its mass, while the magnitude of the rotational energy does not play any role. At the end of the paper, we consider the reason for the possible short-period precession of the pulsar.
Category: Astrophysics

Proof of Riemann Hypothesis

Authors: Ryujin Choe
Comments: 1 Page. (Corrections made by viXra Admin to conform with the requirements on the Submission Form)

In this paper, we show that Robin inequation is true for large N, and RH is true also.
Category: Number Theory

Sequences: Adventure of a Lifetime

Authors: Edgar Valdebenito
Comments: 5 Pages.

Some formulas related to Pi.
Category: Number Theory

Hamlet: Changing of the Guard

Authors: Lev I. Verkhovsky
Comments: 17 Pages. This article is an expanded version of the one that was included in the author's book "Shakespeare: Faces and Masks", published in Russian in 2018.

The interpretation of Shakespeare's tragedy based on the assumption of the authorship of Francis Bacon and the 5th Earl of Rutland is proposed. Anagrams encoding the names of authors are discussed.
Category: Religion and Spiritualism

A Solution to the Sign Problem Using a Sum of Controlled Few-Fermions

Authors: David H. Wei
Comments: 17 pages, 3 figures

A restricted path integral method is proposed to simulate a type of quantum system or Hamiltonian called a sum of controlled few-fermions on a classical computer using Monte Carlo without a numerical sign problem. Then a universality is proven to assert that any bounded-error quantum polynomial time (BQP) algorithm can be encoded into a sum of controlled few-fermions and simulated efficiently using classical Monte Carlo. Therefore, BQP is precisely the same as the class of bounded-error probabilistic polynomial time (BPP), namely, BPP = BQP.
Category: Mathematical Physics

Communication Based on the Quantum Entanglement

Authors: Vitaliy Zamsha, Vladimir Shevtsov, Gennady Shipov
Comments: 6 Pages.

In this short paper Authors described prototype of the communication system based on the quantum entanglement between two related objects. Presented a short introduction to the phenomena of the quantum entanglement and how it manifests in the living organisms and how it can be used with non-living objects. Represented construction of the communication system and shown some test results.
Category: Quantum Physics

Recycled Radioactive Waste in the Space Industry

Authors: V. A. Kizka
Comments: 12 Pages. doi:10.20944/preprints202205.0198.v1

The article presents the idea of using radioactive waste as a material for the manufacture of components, parts and electronics of space probes and planetary rovers. Since space technology operates in conditions of increased radiation, the manufacture of this technology from radioactive materials will not affect its functionality. As an example, I consider the recycling of radioactive building materials resulting from nuclear tests, catastrophes and the decommissioning of nuclear facilities. Modern installations for the recycling of radioactive metal make it possible to completely deactivate it, only the slag from remelting remains radioactive. Modern industrial technologies make it possible to completely recycle this slag, separating useful chemical elements and compounds from it, and also making powders of various dispersions from them. In this way, radioactive powders can be obtained. The idea is presented to use radioactive powders as fillers in composite materials, since it is known that composites significantly improve their properties in radiation fields. For the recycling of radioactive concrete, it is proposed to use the same technologies as for the recycling of lunar and Martian regolith, since concrete and rock are similar in composition. The radioactive oxygen obtained after such recycling can be used as rocket fuel, and radioactive metals and metalloids for the manufacture of devices and parts for space technology, including radioactive powders for composites. As humanity plans to populate all the terrestrial planets, satellites of the large planets and asteroids of the solar system, a constant increase in the number of launches of automatic probes and planetary rovers is expected, which can be completely or partially made from recycled radioactive materials of any category.
Category: Nuclear and Atomic Physics

Division by Zero

Authors: Tim Olsson
Comments: 1 Page. Sorry for budding the error so late but courtesy of Bush et al. Please delete the "_ljtL" part in the .pdf name. I don't know why it's there...

An algebraic theory of extended complex numbers.
Category: Algebra

An Experiment to Test Absolute Motion

Authors: Henok Tadesse
Comments: 7 Pages.

We propose a new experiment to test absolute motion based on time of flight technique. A novel method is proposed to overcome the difficulty in time of flight experiments, namely the difficulty in measuring extremely small time intervals. Two light transponders are each fixed to the ends of a rigid rod. Each transponder consists of a light detector unit and a light emitting unit. The light detector unit, upon detecting a light pulse, triggers the light emitting unit. Let the transponder on one end of the rod be Transponder 1 and the transponder on the other end be Transponder 2. Transponder 1 is initially started and emits a short light pulse towards transponder 2. Up on detecting the light pulse, the detector of Transponder 2 immediately triggers the emitter of Transponder 2, which emits a short light pulse towards Transponder 1. Up on detecting the light pulse, the detector of Transponder 1 immediately triggers the emitter of Transponder 1, which emits a short light pulse towards Transponder 2 , and so on. The new technique involves a free running, continuous exchange of a short light pulse. The frequency of the pulses is determined by the round trip time of light. Absolute motion of the rod would change the round trip time, and hence the frequency of the pulses. Two such rods ( four transponders in total, two transponders on each rod) are used in the proposed experiment, with output pulse frequencies f1 and f2. The pulse trains from the two transponder pairs are applied to an electronic unit (consisting of mixers, filters, etc.) which detects the difference of the two frequencies: f1 — f2 . If absolute motion exists, then a difference frequency is detected when the orientation in space of one rod is changed with respect to the other rod. This experiment would provide practically unlimited accuracy in measuring absolute velocity.
Category: Relativity and Cosmology

The Proofs of Legendre’s Conjecture and Three Related Conjectures

Authors: Wing K. Yu
Comments: 11 Pages.

In this paper, we are going to prove Legendre’s Conjecture: There is a prime number between n^2 and (n+1)^2 for every positive integer n. We will also prove three related conjectures. The method that we use is to analyze a binomial coefficient. It has been developed from the method of analyzing a central binomial coefficient that was used by Paul Erdős to prove Bertrand’s postulate - Chebyshev’s theorem.
Category: Number Theory

The Covid-19 Pandemic

Authors: Bertrand Wong
Comments: 6 Pages.

Covid-19 has made its unexpected entrance into the world some time in late 2019 causing much fear, economic disasters, suffering and fatalities throughout the world. This paper suggests a more aggressive intervention and strategy, for humanity should not let themselves be sitting ducks waiting for the virus to attack, and some possible methods for stopping Covid-19 in its path. (Expanded & Updated)
Category: Physics of Biology

Center of Milky Way Galaxy

Authors: Vladimir S. Netchitailo
Comments: 15 Pages.

In 2013, World-Universe Model (WUM) made one of the most important predictions: “Macroobjects of the World have cores made up of the discussed DM (Dark Matter) particles. Other particles, including DM and baryonic matter, form shells surrounding the cores” [1]. Prof. R. Genzel and A. Ghez confirmed this prediction: “The Discovery of a Supermassive Compact Object at the Centre of Our Galaxy” (Nobel Prize in Physics 2020). On May 12, 2022, astronomers, using the Event Horizon Telescope, released the first image of the accretion disk around the Sagittarius A*(Sgr A*) produced using a world-wide network of radio observatories made in April 2017. These observations were obtained by a global array of millimeter wavelength telescopes and analyzed by an international research team that now numbers over 300 people, which claimed that Sgr A* is a Supermassive Black Hole (SBH). In the present paper we analyze these results in frames of WUM. Based on the totality of all accumulated experimental results for the Center of the Milky Way Galaxy we conclude that Sgr A* is the DM Core of our Galaxy.
Category: Relativity and Cosmology

Perception

Authors: Gerard van der Ham
Comments: 2 Pages.

Perception of an object from two opposite directions give contradictive results. Acknowledgement of this fact is necessary to understand Bell experiments correctly and that is of great importance concerning the interpretation of the Quantum Theory.
Category: Quantum Physics

The Chaotic House of Primes and the Unprovable Riemann Hypothesis

Authors: Federico Romagnoli
Comments: 21 Pages. In English and Italian

It was decided to title this paper "The chaotic house of primes and the unprovable Riemann hypothesis" since the aim is to photograph the structure in which the prime numbers are placed (the house), to analyse the results obtained in the context of the Riemann hypothesis, results that attest to its non-verifiability, and finally to put emphasis on the distribution of primes, a distribution that is not random, not regular, but chaotic and from which order is generated. Taking advantage the complementarity of the set of prime numbers with that of composite numbers, it is possible to photograph the structure in which primes are placed using the ordered structure of composite numbers. The latter is described by two families of double sequences (x,y) defined in Z_(x>l; y>m)^2→N_(>8) and whose analytical expressions change according to the choice of parameters l,m∈Z. Graphical representations follow to better grasp the regularity of composite numbers, as well as the spaces left by them free where the prime numbers find "house". It is therefore possible to shed light on the distribution of primes and at the same time validate and contradict a particular aspect of the Riemann, namely that prime numbers are distributed with regularity. It follows the thesis according to which the Riemann hypothesis is impossible to prove or to disprove due to the "falsely ordered" nature of prime numbers. In fact, their nature is neither ordered nor random, but chaotic and generative of the order, the true one of composite numbers which, due to their complementarity with prime numbers, make appear ordered even the prime numbers. These are the conclusions.
Category: Number Theory

Generalizing The Mean

Authors: Bharath Krishnan
Comments: 10 Pages.

I want to find a constructive extension of the average from the Hausdorff Measure and Integral w.r.t to that measure as the averages (from Tim Bedford and Albert M. Fisher) given for fractals, such that it gives a unique, and satisfying average for nowhere continuous functions defined on non-fractal, measurable sets in the sense of Caratheodory without a gauge function.
Category: General Mathematics

On Some Ramanujan’s Continued Fractions: Mathematical Connections with MRB Constant, Higher Spin and Various Sectors of String Theory

Authors: Michele Nardelli, Antonio Nardelli
Comments: 99 Pages.

In this paper, we analyze some Ramanujan’s continued fractions. We describe the mathematical connections with MRB Constant, Higher Spin and various sectors of String Theory
Category: Mathematical Physics

Surprising New Meteor Shower

Authors: Clark M. Thomas
Comments: 5 Pages.

The night after this Memorial Day 2022 treated curious stargazers in Virginia to a new, surprisingly odd meteor shower. Billed as an either/or event, and possibly a storm, it turned out to be unlike any other cascade that I have witnessed over many decades of looking up. This observer’s essay covers its cometary origin; what we in Virginia saw and did not see; and my analysis of why it all appeared so unusual even to experienced stargazers.
Category: Classical Physics

Relativistic Effect of Non Rigid in Motion: Volume Contraction in All Directions; Space Around It Warped

Authors: Runsheng Tu
Comments: 13 Pages.

Ignoring the internal structure of moving objects and treating them as rigid bodies is not only out of practice but also inconsistent with the spirit of scientific exploration. To change this status quo, consider the relativistic effects of real object motion. Consider the mass-velocity relationship as an initial mechanism to discuss the effect of velocity on the space around an object and on the volume of the object. The relativistic mass-velocity relationship and the relationship between atomic radius and mass together constitute one of the physical mechanisms for the volume contraction of objects due to motion. A series of new conclusions are obtained, such as: the space distortion of a moving system with mass due to inertial motion at ultra-high speed, and even the generation of neutron like stars or black holes; the 3D contraction of objects due to motion; Because the empty space can neither bear nor exert force, in terms of mechanical performance, space and object are always independent of each other, and space cannot move(at most, its motion can only be set subjectively);Even maintaining inertial motion does not guarantee that space is flat, and special relativity can only be approximated at best. It shakes the position of the theoretical criterion of "covariance under Lorentz transformation". It lays a solid foundation for transforming the view of relative space-time into the view of relative absolute space-time and giving birth to the theory of relative absolute.
Category: Relativity and Cosmology

Subnanometer Resolution Single Mode Elastica Fiber Optic Displacement Sensors

Authors: Keith H. Wanser, Richard H. Belansky
Comments: 3 Pages.

A 10 mm Elastica with dT/dx = -7.9x10^(-3)/μm and sensitivity of 0.28 nm with SNR of 2.1 at 25.4 Hz is presented. The 10 μWatt shot noise limited SNR of 2 sensitivity is 0.016 nm/sqrt(Hz).
Category: Classical Physics

Ad Hoc Additions to Theories Suggest a New Paradigm

Authors: John Hodge
Comments: 14 Pages.

The current, accepted theories in cosmology and quantum realms encompass observations that are not explained by the theory. A method to account for these observations is to suggest new, ad hoc additions to the theory. The ad hoc additions suggest the need for a paradigm shift to produce a simpler theory with broader scope and with a cause-effect physical interaction such as the Scalar Theory of Everything (STOE). Links to papers showing calculations and observational data comparison are found in Hodge, 2020, IntellectualArchive, Vol.9, No. 4, P. 14; DOI: 10.32370/IA\_2020\_12\_3 ; See video:\\ https://www.youtube.com/watch?v=0YlJGdTvuTU \\ Inflation, negative energy, Dark Matter, action-at-a-distance, and Dark Energy are ad hoc additions to the Big Bang model of cosmology. Other problematic assumptions are spacetime, infinities, decreasing temperature, and increasing entropy of the universe. The strong force, weak force, and the orbits of electrons around a nucleus are ad hoc additions to the atomic models. Other problematic assumptions are the weird results from the assumption of the probabilistic nature of the universe and that the speed of light limits the speed of causality.
Category: Classical Physics

Engagement Capstone Projects: a Collaborative Approach to a Case Study in Psychoacoustics

Authors: Roberto San Millán-Castillo, Eduardo Latorre-Iglesias, Martin Glesser
Comments: 33 Pages.

Undergraduates in Spanish universities conclude their Bachelor of Science in Telecommunication Engineering with a capstone project. In recent years, students in technical degrees often postpone this last step due to an accelerated entry into the labour market or disappointment about the capstone project development. This article presents an approach which attempts to overcome these challenges: \textit{Engagement} capstone projects. The authors, lecturers in two Spanish Universities (Universidad Politécnica de Madrid and Universidad Rey Juan Carlos, supported by the French Company, EOMYS, manage this educational project. Students become responsible for their contribution to a free, libre and open software project, which provides sound quality metrics based on psychoacoustics. They have the opportunity to work in a collaborative and international environment with industrial partners. The presentation of the technological platform shows the educational benefits of the employed tools: Python, GitHub and Jupyter Notebook. A student survey and the supervisors feedback supports an analysis, which helps improve the methodology as well as verify the benefits: better supervision, the development of social and professional skills, and useful community work. Finally, a couple of examples of Engagement capstone projects give insight into the results of this educational strategy.
Category: Education and Didactics

A Novel Spacetime Map of the Universe Second Edition

Authors: Sebastiano Tirrò
Comments: 48 Pages.

A new cosmological model is proposed, which is based on two important intuitions of Albert Einstein. The model is admittedly conjectural, since it is based on gravitational repulsion between matter and antimatter, which is theoretically foreseen by some theorists, but denied by the first experiment. The values currently considered correct for some important system parameters (mass budget, Hubble constant, universe age) are assumed. Universe dimensions, expansion velocity and total mass are computed. The highly questioned inflation hypothesis is abandoned, and the matter-antimatter unbalance strongly reduced. As a consequence, the dark side of the cosmos assumes new, much smaller, dimensions. Another result of major importance is the time allowed for the formation of the first structures, which is much larger than predicted by traditional Big Bang models. A problem of horizon does not seem to exist: all parts of the universe are visible by every observer; this was true also in the past, with the exception of a relatively short initial period, and will be true also in the future. As concerns CMBR anisotropy, the structure seed dimension given by the model looks in reasonable agreement with the experimental data provided by the scientific satellites.The first part of the paper shortly reviews the current situation of cosmology. In the second part the new model is discussed and evaluated from a quantitative viewpoint. The third part describes the novel spacetime map, including the derivation from measured redshift of comoving distance and time after Big Bang, and the discussion of the horizon problem.
Category: Relativity and Cosmology

On Riemann Hypothesis

Authors: Lucian M Ionescu
Comments: 8 Pages.

A line of study of the Riemann Hypothesis is proposed, based on a comparison with Weil zeros and a categorification of the duality between Riemann zeros and prime numbers. The three case of coefficients, complex, p-adic and finite fields are also related.
Category: Number Theory

Modified Lorentz Transforms and Minkowski Space Splits in Inverse Relativity

Authors: Michael Girgis
Comments: 21 Pages.

New transformations of space and time coordinates achieve kinds of symmetry that the classic Lorentz transformations fail to achieve, we get the new transformations When analyzing a four-dimensional vector in Minkowski space into two four-dimensional vectors, the first is known as the symmetry vector and the second is known as the parallel vector, Where each vector is represented in a new four-dimensional space, this analysis leads to the splitting of the Minkowski space into a positive and a negative space, Thus, we have new transformations of the coordinates of space and time called modified Lorentz transformations, Which expresses one of those spaces, the positive space (positive spacetime), which adheres to the principles of special relativity
Category: Relativity and Cosmology

General Relativity Under the Condition of Extremely Weak Gravitational Field

Authors: Zhi Cheng
Comments: 11 Pages.

It is generally believed that under the condition of relatively strong gravitational field, the effect of general relativity will be more significant. Under the condition that the gravitational field is relatively weak, we can directly use Newton's theory of gravity. However, if we think that dark matter is a kind of fluid, then general relativity can also be used to explain the more special space-time structure formed by the dark matter fluid. According to the characteristics of the fluid, when the fluid flows, two different flow phenomena, laminar flow and turbulent flow, can be formed. In this study, the Zou metric is analyzed, and it is believed that the space-time formed by dark matter turbulence can be well described by the Zou metric. On this basis, this study calculates the pulsation frequency and amplitude of dark matter turbulence in space-time, and predicts the possible impact of dark matter turbulence on visible matter. For the space-time formed by the laminar flow of dark matter, this paper attempts to establish a new two-dimensional metric. This two-dimensional metric has a structure similar to that of a uniform gravitational field. But the two-dimensional metric in this study are obtained entirely from the properties of the space-time structure. In this metric, therefore, the resulting acceleration is due to the structure of the space-time itself. When the speed of visible matter is slower than that of the dark matter fluid, the visible matter will be pulled by the dark matter fluid and continue to accelerate. Conversely, if the velocity of visible matter is lower than that of dark matter fluid, the velocity of visible matter will continue to slow down due to the dissipation of energy. In addition, this dark matter laminar space-time metric also has a very interesting phenomenon, that is, if the velocity of the visible matter is equal to the velocity of the dark matter fluid, the metric will degenerate into the flat metric of Minkowski space-time.
Category: Relativity and Cosmology

Can the Spacetime Emerge from ‘Something Else’?

Authors: D. Chakalov
Comments: 6 Pages. Comments are welcomed.

Stipulations about the emergence of spacetime from the Platonic realm are briefly presented.
Category: General Science and Philosophy

Arguing Against Lorentz Transformation is Illogical

Authors: Jian-zhong Zhao
Comments: 9 Pages.

A counterfeit and illogical simple derivation of the Lorentz transformation is criticized.A wrong simple derivation of composition of Lorentz transformations is revealed.It is concluded that it is impossible and invalid to refute the Lorentz transformation,then the special theory of relativity,by illogical argument and wrong mathematical inference.
Category: Relativity and Cosmology

Calculation of the Arbitrarily Complex Shape Optical Receiver's Aperture Averaging Function by the Two-dimensional Matrix Mapping Method

Authors: Changqi Yang
Comments: 12 Pages.

A method for calculating the arbitrarily complex shape optical receiver’s aperture averaging function is proposed in this paper. In this method, the mathematical shape of the optical receiver is mapped into a two-dimensional n*n matrix. The calculation of the aperture averaging function is transformed into the mathematical operation between two two-dimensional matrices. To verify this method, the Cassegrain telescope's aperture averaging function is calculated by mapping to a 300*300 matrix and compared with the theoretical results. The comparison results show that the error of the aperture averaging function calculated by this method is very small. This method can be trusted to calculate the arbitrarily complex shape optical receiver's aperture averaging function.
Category: Astrophysics

Hyperoperator Analysis

Authors: Dmitrii V. Guryanov
Comments: 36 Pages.

The purpose of this article as a continuation of development of the Multiplical concept is to give an answer to the earlier raised question of why the place of the operator in the function y = e↗x is taken by the operator - a power tower with left associativity, and not with the generally accepted right associativity (the Tetration). Answering on this question required to conduct an hyperoperator analyze. The hyperoperator nature is considered, definition is made and an alternative way of its development is proposed in the present analysis.
Category: Functions and Analysis

Does Replication in Cellular Automata Spaces Always Correspond to Broken Symmetries?

Authors: Perry W. Swanborough
Comments: 10 Pages.

The Noether theorem establishes that symmetries in physics correspond to conservation laws, and therefore contra-positively that un-conserved quantities correspond to broken symmetries. This theorem was not established for dynamic systems in discrete space and discrete time, but the author in previous work has observed that replication of published cellular automata (CA) loop structures corresponds to chiral asymmetries. The work described here shows that replication of a different kind of CA replicator (the HighLife replicator of Nathan Thompson, 1994) corresponds to loss and restoration of a line of symmetry in each replication cycle. In addition to my past observations of loop replication chirality, the broken symmetry observed in the achiral replication of the achiral Thompson replicator suggests a hypothetical general principle of a correspondence between replication observed as an un-conserved (increasing) number of replicator instances and a range of broken symmetries. The paper concludes with some speculation about the possible relevance of simple CA replicators to proto-biology.
Category: Physics of Biology

Exploring the Influence of the Interaction of Climate Change, Man-made Threats and Covid-19 on the Livelihoods of Wetland Communities in Sub-saharan Africa

Authors: Toundji O. Amoussou, Sarah E. Edewor, Yaye D. Wane, Chibuye F. Kunda, Donissongou D. Soro
Comments: 15 Pages.

Wetlands are very important because of the wide range of ecosystem services they provide. Despite their ecological, social and environmental importance, these ecosystems are threatened and fragmented under the combined effects of climate change (CC) and man-made activities (MMA). Such a state of things could be exacerbated by the advent of the coronavirus disease 2019 (COVID-19) pandemic with its many implications. In order to help decision-makers take good decisions, the combined effect of CC, MMA and COVID-19 on the livelihoods of communities around wetland ecosystems have been reviewed based on available scientific knowledge. First, we analyzed the different concepts and theories underlying the wetlands-related studies and then summarized the merits and demerits of the different methodologies underlying wetland studies. The empirical evidences that exist in previous literatures have been highlighted. Similarly, common livelihood strategies for wetland communities in Sub-Saharan Africa (SSA) have been highlighted. The review helped to identify that, out of the three factors investigated, the livelihoods of rural wetland dwellers in SSA are mostly influenced by CC and MMA. However, climate change and COVID-19 remain life-altering transboundary threats that extend in space and time, with large uncertainties on wetlands communities livelihoods.
Category: Social Science

Farming Liquid Air as Major Energy Commodity

Authors: Yanming Wei
Comments: 33 Pages.

Waste is Simply a Valuable Resource in the Wrong Place. Burning biomass in steam engine for <10% power is just little bit better than wildfire, so here biomass = waste.But burning biomass in my heat engine with Liquid Air/Nitrogen(LA/LN) as heat sink, its efficiency >80%, so here biomass is precious as gasoline, rendering 1kg biomass = 0.5kg gasoline by heat value equality, as per good biomass heat of combustion = 20MJ/kg, gasoline = 40MJ/kg.My inventions could enable the farmed LN as cheap as $0.05/L by proprietary cleantech of fire-for-chill and chill-for-power. Production line:grow energy grass -> burn it in my proprietary heat engine, which consumes LN as heat sink -> shaft liquefaction machine -> produce LA/LN -> feedback 70% LN production to the LN consuming heat engine for rolling-up production -> remaining LN for sale.Burning 1kg biomass in farmland, can produce at least 2kg marketable LN after deduction of LN consumption in situ, as heat sink of heat engine, which is powering liquefaction machine.With 80~90% veneer efficiency, future vehicle drivers need buy both fuel from gas station & LN from nearby farmers or any possible LN retailers for their fuel+LN hybrid vehicles.Even reluctant to give up gas, its demand can be 70% off; e.g. future hybrid vehicle = 15L gas tank + 150L LN dewar, 100MPG, its range = 60L tank gas vehicle.Omnipresent farms = dense ready LN refill & biomass reload infrastructure anywhere, include the remotest rural, better than EV in this point.LN is also excellent energy storage with 10MJ/kg, good for Distributed Energy Resource DER.Where there's energy, where there's vigor; after farmers joins this circular energy economy, there'll be no more hillbilly elegy. The epoch of Farming Liquid Air LA = LN + Liquid Oxygen LO as major energy commodity, and the Cryogenic Heat Sink Revolution CHSR are coming! Are you ready to accept the challenge?
Category: Thermodynamics and Energy

Formula for Number of Primes Less Than a Given Number

Authors: Juan Elias Millas Vera
Comments: 5 Pages.

In this paper I want to expose the possibility of making a formula which counts the exact number of primes less than a given number, using some tools in analysis of functions, some tools in series of functions and some new tools.
Category: Number Theory

Calculation of Space Debris Distribution Using Quantum Gravity Theory with Ultimate Acceleration

Authors: Huaiyang Cui
Comments: 15 Pages.

It was found that ultimate acceleration can enhance the quantum gravity effects for test. If there is an ultimate acceleration β, nobody’s acceleration can exceed this limit β, in the solar system, β=2.961520e+10(m/s2). Because this ultimate acceleration is a large number, any effect connecting to β will become easy to test, including quantum gravity test. As an application, the quantum gravity theory with the ultimate acceleration provides a useful formula to calculate the space debris distribution around the earth, in this paper the calculation results agree well with the experimental observation which are a set of measurements by incoherent scattering radar of EISCAT in the Arctic circle. Using the same approach, the radius of the Sun is calculated out to be r=7e+8 (m) with a relative error 0.72%; the radius of the Earth is calculated out to be r=6.4328e+6 (m) with a relative error 0.97%.
Category: Quantum Gravity and String Theory

Singular Properties

Authors: Dmitrii V. Guryanov
Comments: 59 Pages.

The purpose of this article as a continuation of development of the multiplical topic is to find a solution for operation of differentiation and factorization of a function with points of interruption, points where function turns to zero. The solution which allows restoring the original function as result of reverse operation of integration and factorial-multiplication of previously obtained derivative and factor-derivative respectively and with an appropriate selection of an arbitrary multiplier B or addend C, respectively. As the result of the work madenew classes of function properties are introduced as function point properties.
Category: Functions and Analysis

For Students of Geometric Algebra: Demonstrating the Equivalence of Different Formulas for Rotating 3D Vectors

Authors: James A. Smith
Comments: 7 Pages.

As an aid to teachers and students of introductory-level Geometric Algebra, we address a doubt that an inquiring student might (and should) ask: "Are GA’s various formulas for rotating a vector truly equivalent?" Here, we use GA identities to prove the equivalence of two rotation formulas. Rather than merely present the proof, we first review the relevant identities, then formulate and explore reasonable conjectures that lead to the conclusion. Readers are encouraged to examine, in addition, a recent publication by Verhoeff ([1]) that contrasts "GA" rotation methods with methods that use matrices or classical geometry.
Category: Geometry