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[23] viXra:2610.0023 [pdf] submitted on 2026-10-06 20:18:35
Authors: R. Köferstein, J. Jacobs, S. G. Ebbinghaus
Comments: 40 Pages. The paper was published in: J. Eur. Ceram. Soc. 45 (2025) 117567. (Open Access, DOI: 10.1016/j.jeurceramsoc.2025.117567).
Lix(Sr0.5Ba0.5)1-x/2Nb2O6 ceramics were prepared by a solid state synthesis and sintered at 1300 °C. XRD investigations reveal single phase samples up to a substitution limit of x = 0.275. For higher lithium contents, the appearance of LiNbO3 as secondary phase was observed. The density of the ceramics increases with lithium content. The microstructures show globular grains which turns to pillar-like grains with rising lithium substitution. Dielectric investigations confirm relaxor ferroelectric behavior and the diffuse phase transition is shifted towards higher temperatures with increasing lithium content from 129 °C (x = 0) to 221 °C (x = 0.275). The diffuseness coefficient increases with the lithium content. From high-temperature XRD measurements the length of the tetragonal cell parameter c decreases with increasing temperature, reaches a minimum at about 150-230 °C (depending on x) and afterward increases with increasing temperature. Additionally, a significant shift of the Nb(2) position with temperature can be observed.
Category: Chemistry
[22] viXra:2610.0022 [pdf] submitted on 2026-10-06 20:16:24
Authors: Charles Ba Oumar
Comments: 8 Pages.
This paper presents a Vector Gravitational Field Theory asymptotically equivalent to standard Minkowski spacetime in the limit of a classical vacuum. From such a theory we then derive a new definition of rest mass energy as well as an approximation of the quantum of gravitational action via a graviton particle of energy ℎ��proportional to the gravitational charge quantified by matter-energy density and compute solar system graviton energy ranges.
Category: Quantum Gravity and String Theory
[21] viXra:2610.0021 [pdf] submitted on 2026-10-05 04:57:22
Authors: Saburou Saitoh
Comments: 65 Pages. (The Third Lecture at Peking University on 5 October, 2026).
In this talk, we will introduce the importance of the division by zero containing the division by zero calculus and its great impact to elementary mathematics and mathematical sciences for some general mathematicians. For this purpose, we will give its global viewpoint in a self-contained manner by using the related references. (The Third Lecture at Peking University on 5 October, 2026).
Category: Functions and Analysis
[20] viXra:2610.0020 [pdf] submitted on 2026-10-06 00:35:46
Authors: Ali Rıza Şahin
Comments: 13 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper establishes a rigorous real-analytic and geometric framework governing the distribution of the non-trivial zeros of the Dirichlet eta function $eta(s)$ across the critical strip $mathcal{S}={sinmathbb{C}:0
Category: Number Theory
[19] viXra:2610.0019 [pdf] submitted on 2026-10-06 00:23:26
Authors: Ali Rıza Şahi̇n
Comments: 8 Pages.
The general theory of relativity fundamentally relies on the metric tensor to describe gravitational phenomena, traditionally eschewing the vector field formulations ubiquitous in electrodynamics and quantum field theories. This study introduces a novel framework that defines the spacetime metric and its inverse via a set of underlying vector fields. By expressing the metric tensor in terms of these fields, we derive the corresponding geodesic and Einstein field equations, revealing striking structural parallels with electrodynamics—most notably, the natural emergence of a covariant Lorentz-like force and a stress-energy tensor mathematically analogous to that of electromagnetic fields. To demonstrate the astrophysical viability of this approach, we solve the equations for a spherically symmetric, static mass distribution, yielding a non-singular alternative to the Schwarzschild metric. The practical validity of this metric is subsequently tested through the recalculation of the perihelion precession of planets and the gravitational deflection of light. The results provide precise agreement with perihelion precession observations while predicting a slightly modified value for light deflection (1.90 arcsec), offering a potential theoretical basis for the historical discrepancies observed between visible light and radio wave measurements during solar eclipses.
Category: Relativity and Cosmology
[18] viXra:2610.0018 [pdf] replaced on 2026-10-06 03:58:41
Authors: Stephen W. Hosier
Comments: 7 Pages.
Spacetime velocity and related time dilation, are presented in a clearer and simpler format. Many example calculations are shown to demonstrate the simplicity of this approach.
Category: Relativity and Cosmology
[17] viXra:2610.0017 [pdf] submitted on 2026-10-04 22:46:29
Authors: Brian Scannell
Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
The Lorentz factor γ(β) =1/ √︁(1 — β^2), where β = v/c, is normally considered for real |β| < 1. Allowing its argument to range over the complex plane gives Γ(z) =1/√(1 — z^2), whose real and imaginary parts generate a striking system of level curves organized around the branch points z = +/-1. The Cauchy—Riemann equations explain why the regular curves from the two families intersect orthogonally. More surprisingly, eliminating the square root shows that each nonzero contour lies on a degree-eight algebraic locus. This apparent complexity is deceptive. Solving instead for z gives z = +/-√︁ (1 — Γ^-2), revealing that the apparently complicated contours in the z-plane are locally the preimages of vertical and horizontal straight lines in the Γ-plane. Thus, a familiar real function from special relativity provides an elementary example in which complicated algebraic contours conceal a simple conformal geometry.
Category: Functions and Analysis
[16] viXra:2610.0016 [pdf] submitted on 2026-10-04 02:31:51
Authors: Roger L. Mc Murtrie
Comments: 5 Pages.
This article identifies a series of foundational mathematical and logical inconsistencies within John Bell’s 1964 formulation and demonstrates that the core discrepancy in Bell’s framework arises from an implicit and unjustified data-mapping assumption which treats the discrete, binary-valued random functions of one expectation value integral as directly equivalent to the continuous, real-valued integrand of another expectation integral. This non-linear transformation incurs a severe loss of contextual information that is mathematically unaccounted for in Bell’s original derivation. By failing to recognize this measure-theoretic mismatch the subsequent deductions, including the assertion that a remote measurement setting must dynamically influence a distant apparatus, are rendered logically invalid. Consequently, the attribution of non-locality to Einstein-Podolsky-Rosen-Bohm (EPRB) systems is shown to be an unfounded artifact of this misapplied probability space rather than an empirical property of physical nature.
Category: Quantum Physics
[15] viXra:2610.0015 [pdf] submitted on 2026-10-04 22:33:00
Authors: Sergey Pavlovich Slukhayevskiy
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
A diffraction observation scheme is proposed that makes it possible to investigate the influence of the shape and size of the undisturbed part of a quasi-parallel light beam on the spatial position of the elements of the diffraction pattern. Experimental observations of the independence of the positions of the pattern elements from thisparameter were performed in the range from 0.01 to 2 mm.
Category: Classical Physics
[14] viXra:2610.0014 [pdf] submitted on 2026-10-03 00:17:02
Authors: Xincai Luo
Comments: 16 Pages. DOI: https://doi.org/10.5281/ZENODO.23089701
We present a novel theory of fundamental particle spin, deriving the energy-frequency relation of quantum theory, the Schwarzschild metric of general relativity, and the fine-structure constant from this single framework. Our theory posits that fundamental particles are composed of fundamental charges (FCs) and derives the energy-frequency relation and spin angular momenta of these particles from the circular motion of their constituent FCs, as described by Newtonian classical mechanics. The conservation of energy and angular momentum necessitates that each fundamental particle possesses wave-like properties, mathematically represented by corresponding wavefunctions in quantum mechanics. The phase angle of the wavefunction directly corresponds to the angle of this circular motion. The energy, which is proportional to the frequency of the FCs' circular motion, is expressed as the result of applying the operator iℏ∂/∂t to its wavefunction. Based on this wave arising from the circular motion of FCs, a particle's energy must propagate at the speed of light. This requirement extends beyond the constancy of the speed of light in all inertial frames proposed by special relativity. In the rest frame of a particle, precisely half of its energy moves forward and the other half moves backward at the speed of light, creating an apparent zero velocity. This constant energy propagation speed implies a constant energy flow rate, which then yields the Schwarzschild metric of general relativity. This work demonstrates that the principles of quantum mechanics and relativity are inherently linked to fundamental particle spins. Furthermore, the spin theory enables the derivation of electroweak coupling constants from first principles. The theoretical fine-structure constant derived from this spin model (without experimental input) exhibits strong agreement with experimental values (a discrepancy of only 0.14%), and the predicted electron charge (1.603×10^-19 C) closely matches the experimentally determined value (1.602×10^-19 C).
Category: High Energy Particle Physics
[13] viXra:2610.0013 [pdf] submitted on 2026-10-03 20:32:33
Authors: Clark M. Thomas
Comments: 3 Pages.
Questions swirling around human artificial intelligence, and visiting space-alien intelligence, are featured all over the media.Speculation clutters major idea gaps where scientific evidence, or at least high quality logic, should be. Ideas range fromoptimistic curiosity, to existential dread. Scientists can fairly well document our human past. Can we wisely envision and prepare for hybrid futures?
Category: Artificial Intelligence
[12] viXra:2610.0012 [pdf] submitted on 2026-10-03 20:31:44
Authors: Xingfeng Chen
Comments: 15 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
We present Difference Power Space Extrapolation (DPSE), a geometric method for computing the n decimal digits of π by combining multiple polygon observations in difference power space. The paper shows that DPSE should be understood as a higher-order development of the Difference-Power Cumulative Method (DPCM), rather than asan unrelated construction. For the polygon semiperimeter surrogate Sk = nksin(π/nk), the geometric increments ∆Sk = Sk+1 − Sk admit a structured boundary-layer expansion that can be cancelled by Richardson-type linear combinations. For fixed extrapolation orderW, this yields the error law Ek,W = O(4−(W+1)k), while the diagonal Neville sequence exhibits an approximately quadratic error exponent in the physical observation index k. Consequently, the required physical observation count for n correct decimal digits is reduced from lineargrowth to order O(√n), while preserving the low-memory character of geometric iteration. Numerical experiments include a direct milliondigit fingerprint verification.
Category: General Mathematics
[11] viXra:2610.0011 [pdf] submitted on 2026-10-03 20:30:01
Authors: Saburou Saitoh
Comments: 15 Pages.
At first, I will introduce simply the analytical and classical reproducing kernels on the complex plane. Here, firstly, we recall the representations of reproducing kernels in terms of the theta functions that were obtained by D. A. Hejhal, J. D. Fay and A. Yamada. Indeed, the materials stated here are in Yamada's papers.Then, we will consider their meanings from the viewpoints of reproducing kernel theory, in particular, from the viewpoint of inequalities. We will find many important open problems. (The Second Lecture at Peking University on 3 October, 2026)
Category: Functions and Analysis
[10] viXra:2610.0010 [pdf] submitted on 2026-10-03 20:22:02
Authors: Guzhva Andrii Oleksandrovich
Comments: 132 pages, diploma thesis 2009, CC BY 4.0
Diploma thesis (Pryazovskyi State Technical University, Mariupol, 2009). Design of an integrated biodiesel production line with ultrasonic cavitation reactor; detailed manufacturing technology for the gearbox shaft part KLB-01,00,01. Supervisor: Andilakhai Oleksandr Oleksandrovych. Keywords: biodiesel, biofuel, ultrasonic cavitation, transesterification, mechanical engineering.
Category: Thermodynamics and Energy
[9] viXra:2610.0009 [pdf] submitted on 2026-10-03 20:25:02
Authors: Richard J. Mathar
Comments: 10 Pages.
The Multiple Zeta Value zeta(2,1) is a double sum over two positive integer indices. If these indices are restricted by parity to cover either only even or only odd positive integers, the Multiple Zeta Value splits into four non-overlapping subseries. The manuscript evaluates these four series in terms of the Riemann Zeta function, pi and log 2.
Category: Functions and Analysis
[8] viXra:2610.0008 [pdf] submitted on 2026-10-02 20:58:54
Authors: Justin Mader
Comments: 25 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper presents a consistent, mathematical-geometric framework describing quantum mechanics, gravitation, and cosmology within a "Bohmian" quantum field theory outside the standard model. By coupling a real helical sub-quantum domain (Helical Spin Theory, HST) with a space-filling background medium in a dynamic tachyonic momentum mode (Higgs-Tachyon-Push Field Theory, HTP), a quantitative reproduction of key astrophysical and quantum mechanical benchmark tests is achieved as an asymptotic limiting case within an absolute Euclidean reference frame. Gravitational light deflection, Mercury's perihelion precession, and the anomalous Pioneer Doppler drift are derived without invoking spacetime curvature via a spat-temporally Variable Speed of Light (VSL). On the microscopic scale, the double-slit paradox is formalized using an ontic, non-local pilot wave in line with De Broglie-Bohm mechanics. On the cosmological scale, the observed Hubble tension is mathematically resolved as a historical averaging effect derived from a degressive mass accumulation rate $Q_M(t)$. Furthermore, the empirical paradox of evanescent states in photon waveguides is interpreted through a media-mechanical phase transition into the superluminal tachyonic mode, while testable Lorentz invariance deviations are predicted for ultra-relativistic regimes. The model thus provides a closed mechanical framework that substitutes the requirements for Dark Matter, Dark Energy, and virtual particles within the macroscopic limit.Official preprint registered and priority-protected via CERN Open Science Repository Zenodo under DOI: 10.5281/zenodo.23088551.
Category: High Energy Particle Physics
[7] viXra:2610.0007 [pdf] submitted on 2026-10-02 12:49:36
Authors: Walter A. Kehowski
Comments: 10 Pages.
The identity x^2 + (x+1)^2 + (x(x+1))^2 = (x^2+x+1)^2 is the motivation for study of the equation d^2 + e^2 + n^2 = x^2, where d and e are conjugate divisors of n, that is, n=de and $d
Category: Number Theory
[6] viXra:2610.0006 [pdf] submitted on 2026-10-02 20:56:55
Authors: Brian Scannell
Comments: 17 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Trees are dynamically complex branched structures in which trunks, branches and higher ordercrown elements possess characteristic motions and are mechanically coupled. In a doctoral thesis completed in 1983 and formally awarded in 1984, Scannell proposed a qualitative mechanical principle termed aeroelastic similarity. Measurements on Sitka spruce suggested approximate relationships between modal frequencies at successive structurallevels, together with direct evidence of coupled branch motion. The original interpretationproposed that overlapping frequency ranges could permit wind-induced mechanical energyto be redistributed through the crown and dissipated, thereby restricting large-amplituderesonant motion. This paper reassesses that hypothesis against four decades of subsequent tree biomechanics research. Later work explicitly tested the named aeroelastic-similarity theory and subsequently developed mass damping, multiple resonance damping and damping by branching.The evidence does not support a universal hierarchy of exact modal equivalence. It does,however, support a broader principle in which frequency-compatible, mechanically coupled treemotions can exchange energy and thereby provide access to distributed dissipative mechanisms.We formulate this surviving idea as dynamically coupled modal compatibility, not modalidentity. A reduced coupled-oscillator model separates conservative energy redistribution fromdissipation, introduces descriptive measures of spectral separation and mode hybridisation,and motivates a hierarchical modal-network interpretation. We then propose a falsifiableexperimental programme based on controlled detuning in numerical models, laboratorybranched structures and living trees. Aeroelastic Similarity is therefore retained not asan exact frequency-scaling law, but as a testable hypothesis concerning the dynamicalorganisation of branched structures.
Category: Physics of Biology
[5] viXra:2610.0005 [pdf] submitted on 2026-10-01 20:59:54
Authors: Saburou Saitoh
Comments: 60 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
The theory of reproducing kernels is very fundamental, beautiful and has many applications in analysis and numerical analysis as in the Pythagorean theorem. In this first lecture, I would like to intoroduce some general viewpoint for reproducing kernels and some essences of reproducing kernels. However, the theory is already much more developing widely and deeply on this century. (The First Lecture at Peking University on 1 October, 2026)
Category: Functions and Analysis
[4] viXra:2610.0004 [pdf] submitted on 2026-10-01 12:45:48
Authors: Volodymyr Krasnoholovets
Comments: 15 Pages. This is the first paper in a series of three works.
This paper presents a deterministic, real-space reinterpretation of the 125 GeV particle discovered at the Large Hadron Collider (LHC) in 2012, commonly designated as the Higgs boson. Submicroscopic physics, developed within the framework of transparent mathematical physics in a series of the author’s previous works, allows us to bypass the complexities of physical mathematics and fine-tuning issues of the scalar Higgs field. Instead, the paper examines the 125 GeV resonance as a highly localised, ultrafast vortex formed by a frontal collision between a +e and -e integer-charged quark pair. This impact forces a massive compression of the discrete spatial lattice (tessellattice), trapping a colossal spatial mass defect (∆m∙c^2≅125 GeV). This dual-quark system forms an ultra-submicroscopic vortex with a radius of approximately 1.58 attometres, stabilised by this localised mass defect. Together with the Coulomb attraction, this structural confinement leads to the formation of a localised deformation coat around the vortex, whose geometric parameters are precisely balanced by the fine-structure constant α.
Category: High Energy Particle Physics
[3] viXra:2610.0003 [pdf] submitted on 2026-10-01 20:53:40
Authors: Hongyuan Ye
Comments: 16 Pages.
In classical electromagnetism, Gauss’s flux theorem in integral form states that the electric flux through a closed surface is proportional to the net electric charge enclosed by that surface. Gauss’s flux theorem in integral form is originally derived from Coulomb’s law of electrostatics. However, electrodynamics wrongly extends Gauss’s flux theorem to time-varying electric fields without additional theoretical and experimental justification, while confining Coulomb’s law to the scope of electrostatics. Through concise and rigorous mathematical derivations, this paper reveals that the integral form of Gauss’s flux theorem in classical electromagnetism does not hold in time-varying electric fields. Furthermore, it is demonstrated that Gauss’s flux theorem in differential form, which is expressed in terms of the flux-density divergence or the nabla-operator divergence, also does not hold in time-varying electric fields. Gauss’s flux theorem does not hold in time-varying electric fields, which poses a serious challenge to Maxwell’s equations and theoretical physics. The inapplicability of divergence to time-varying vectors also presents a significant challenge to fundamental mathematics.
Category: Classical Physics
[2] viXra:2610.0002 [pdf] submitted on 2026-10-01 15:19:27
Authors: Sergey B. Yurchenko
Comments: 20 Pages.
Science has made great strides in answering many questions, but three major mysteries remain unsolved. Although these mysteries belong to different fields of science — physics, biology, and neuroscience — they all confront with the boundary problem. These are scientific investigations into the origins of matter, life, and consciousness, which extend beyond empirical and rational methods in the search for definitive answers. Here, this problem is presented as the search for the lowest boundaries for three forms of existence: physical, biological, and conscious. They are then translated into the context of Big Bang cosmology, abiogenesis, and the neuroscience of consciousness, each representing an ontological singularity with its own epistemological event horizon.
Category: General Science and Philosophy
[1] viXra:2610.0001 [pdf] submitted on 2026-10-01 19:01:14
Authors: Tariq Khan
Comments: 10 Pages.
A speculative essay on the nature of song lyrics and song melodies answering the question of "why humans love music." A proposed shared human subconscious mind can understand language but, while it can communicate with the sleeping mind via images in dreams, it can only communicate to an individual’s awake mind via what appear to the individual as a random recall of a musical song in working memory. Remarkable lyrics of a given song can thus be used by the subconscious as a means to communicate to an awake mind. A theory of subconscious communication, from Cormac McCarthy’s essay The Kekule’ Problem and the research of Jeff Hawkins showing the human brain storing sequences of patterns including songs, is used to support the proposal. Music is considered as "primordial change" or as being equivalent to a fundamental encoding of change in a quantum or digital universe. Music is proposed as possibly being the boot code for any experience.
Category: History and Philosophy of Physics
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