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[16] viXra:2609.0017 [pdf] submitted on 2026-09-07 05:26:48
Authors: Harris V. Georgiou
Comments: 21 Pages.
In Urban Search & Rescue (USAR) operations after large-scale earthquakes, time is of essence for the survival of trapped victims. There are too many parameters that define the conditions, severity and survivability window for each victim entombed under debris. Hence, worksite assessment and triage is primarily an empirical procedure that is based on incomplete and mostly qualitative information. On the other hand, if statistical rescue data from previous USAR missions are available, appropriate probabilistic models can be developed for estimated rescue counts and live victims remaining over time. This study explores the availability of such historic data and, based on these, several probabilistic models are designed. These include Exponential and Weibull for inter-rescue times, non-homogenous Poisson for rescue counts and Generalized Extreme Value (GEV) for the tails of the underlying data distributions. All the models converge to very similar results for survival windows and in accordance to real rescue data. Namely, the 95% and 99% quantiles point to 115-118 hours (4.8-4.9 days) and 177-181 hours (7.4-7.5 days), respectively. A mixed-model approach is proposed for more accurate approximations, selecting GEV for the beginning (up to day 2) and ending phases (days 5-8), Weibull for the middle (days 3-4) and non-homogenous Poisson everywhere else (days 2-3, 4-5), with a relative approximation error no more than 4.5% compared to real rescue data throughout the typical USAR operational period of eight days. Finally, the GEV model is also used for investigating the effect of under-reporting live rescues during the first 24-hour window of USAR operations, providing hints of a factor at the order of 1-in-5 to 1-in-8 or more, especially during the first six hours. These results provide valuable insights for better planning and team deployment in such USAR missions after large-scale earthquakes.
Category: Statistics
[15] viXra:2609.0016 [pdf] submitted on 2026-09-07 18:15:38
Authors: Min Min Oo
Comments: 19 Pages. (Note by viXra Admin: Please cite and listed scientific references!)
This paper develops a Prime Pair Framework for studying twin primes using structured sequences of odd composites. The base sequenceO_1=9+6r_1, r_1≠((1+2x)^2-13)/6 " or" ((1+2x)^2-7)/6 provides intervals containing two odd integers, which may form twin primes if both are prime. When the general sequencesO_a=(2a+1)^2+(2+4a) r_a (a={2ⓜ,3ⓜ,4ⓜ,u2026ⓜ,k})and O_1are in proper alliance, the conditions are formed through lower, upper and double twin prime formation mechanisms.
Category: Number Theory
[14] viXra:2609.0015 [pdf] submitted on 2026-09-07 18:09:48
Authors: Hadrijan Crnčić Jurasić
Comments: 14 Pages. hadrijan.crncic-jurasic@skole.hr
In this paper we formally construct (mathbb{M}), a number system that contains three dimensions and forms a bridge between the complex numbers and the quaternions. In this system we define the operation of division by zero (1/0=infty). The third dimension of the system is the scalar infinity (s), which does not mix with real or complex numbers.Historically, a system with exactly three dimensions was impossible because of the multiplication of two new axes. In the quaternions these are (i) and (j), whose product must give (k), creating a new dimension because (ij) cannot be displayed in those three dimensions. Historically, taking the square root of (-1) was not allowed. This was solved by the new number (i), which introduced the complex numbers and achieved the transition from (mathbb{R}) to (mathbb{C}) by adding the new number (i) such that (i^2 = -1). (mathbb{R}) is one-dimensional, and (mathbb{C}) is a two-dimensional number system, so the question arises whether there are number systems above (mathbb{C}).The answer was first found by William Rowan Hamilton when he tried to construct a three-dimensional number system. By adding one new axis (j) such that (j^2 = i^2 = -1), he encountered the problem of what the product of (i) and (j) would give. He realized that it would give (k), a new spatial axis, and so he constructed a four-dimensional number system with axes (1,i,j,k) such that (k^2 = j^2 = i^2 = -1). Thus the three-dimensional algebra was skipped because no matter which axis we add, the product of two axes must always give something new, namely a fourth dimension.Later Frobenius and Hurwitz formalized this and proved that number systems are possible only in dimensions (2^n), where (n) is a natural number: namely 1 ((mathbb{R})), 2 ((mathbb{C})), 4 ((mathbb{H})), 8 ((mathbb{O})), and so on, up to 256 dimensions and beyond. This is the Cayley-Dickson construction, and the number systems obtained after the sedenions are no longer particularly interesting or useful for study because they lose critical properties such as associativity, alternativity, and commutativity.All these systems do not solve the problems for which new systems are introduced, namely the definition of undefined numbers. Just as the complex numbers define the square root of (-1), which was undefined in the real numbers, so the definition of (n/0) brings with it the definitions of other undefined numbers, such as the zeroth root and zero to the zeroth power.
Category: General Mathematics
[13] viXra:2609.0014 [pdf] submitted on 2026-09-07 18:34:15
Authors: Ayush Samanta
Comments: 37 Pages.
Finite-time transport in the circular restricted three-body problem (CR3BP) can change qualitatively under perturbations to initial conditions, making robustness difficult to characterize using smooth trajectory sensitivities alone. This work investigates whether geometric distance to an outcome-change boundary can provide a usefulmeasure of transport robustness for a two dimensional family of invariant-manifold seeds generated from planar L1 Lyapunov orbits in the Earth—Moon CR3BP. A 160 × 33 parameter atlas comprising 5280 initial conditions was classified by first-passage outcome, and adaptive refinement produced 484 numerical samples of the resultingoutcome boundaries. To avoid arbitrary Euclidean distance in the family parameters, the seed-state map was used to induce a local pullback metric, defining a family-constrained boundary-distance diagnostic ρη. The metric construction was numerically consistent, and ρη revealed strongly nonuniform proximity to the resolved transportinterfaces. Its ordering, however, depended on the prescribed state weighting, with Spearman correlations ranging from approximately 0.794 to 0.999 across the tested metrics. Direct perturbation tests also rejected a guaranteed-radius interpretation: one outcome change occurred at approximately 0.5ρη, while finite directional searches at five representative points recovered no independent minimum flip distance. These results support ρη as a family- constrained geometric diagnostic of proximity to resolved finite-time outcome boundaries, but not as a certifiedoutcome-preserving radius or validated transport condition number. A stronger robustness measure requires converged boundary resolution, physically specified uncertainty geometry, and direct computation of minimum outcome-changing perturbations.
Category: Astrophysics
[12] viXra:2609.0013 [pdf] submitted on 2026-09-08 00:52:38
Authors: Clark M. Thomas
Comments: 3 Pages.
The recent Phase 3 trial of a customized Moderna mRNA cancer vaccine, along with Merck’s Keytruda, to fight melanoma skin cancer, points to possible long-term remission, if not yet a permanent cure. The hope is that future mRNA vaccines can work similarly for other types of cancer, along with Keytruda. This 2026 medical news points toward the general promise of AI in other medical areas, and for understanding cellular life itself. This essay points to emerging synergies between human and AI research tools.
Category: Artificial Intelligence
[11] viXra:2609.0012 [pdf] submitted on 2026-09-06 09:13:25
Authors: Jacqueline Fernandes
Comments: 4 Pages.
This paper explores the transition boundary where classical escape velocity thresholds intersectwith relativistic coordinate transformations. Using observational mass configurations from Sagittarius A*, we analyze how super luminal escape velocities (ve > c) force a geometric inversion ofthe local Minkowski metric tensor. We demonstrate that the information loss paradox is fundamentally a consequence of the future light cone compressing and tilting past the vertical axis, renderingoutward spatial paths geometrically non-existent to an external observer.
Category: Astrophysics
[10] viXra:2609.0011 [pdf] submitted on 2026-09-06 14:39:55
Authors: Herbert Weidner
Comments: 10 Pages.
We report the detection of continuous microhertz waves originating from Jupiter, recovered from two decades of atmospheric pressure measurements across Germany. Barometers act as largeu2011aperture antennas for lowu2011frequency signals, allowing coherent recovery of a carrier near 55.97 $mu$Hz, which corresponds to twice the rotation frequency of Jupiter’s solid core. A directu2011conversion receiver iteratively compensates all known phase modulations caused by Earth’s orbit and the four Galilean moons, concentrating the wave’s energy into a narrow spectral line with a signalu2011tou2011noise ratio of 100. We measure the longu2011term frequency drift of Jupiter’s core and determine the modulation indices associated with each moon. The phaseu2011modulation pattern is stable across 318 independent realizations. Additional spectral features indicate that Jupiter hosts multiple internal oscillators with distinct frequencies. These results demonstrate that Earth’s atmosphere responds coherently to microhertz waves generated by nearby planets.
Category: Astrophysics
[9] viXra:2609.0010 [pdf] submitted on 2026-09-06 21:45:10
Authors: Volodymyr Krasnoholovets
Comments: 49 Pages. Journal of Advanced Physics 5, No. 2, 145—167 (2016). DOI: 10.1166/jap.2016.1232
This paper reviews major approaches to the description of subatomic particles, suchas leptons, quarks, hadrons and nucleons. Among these approaches are quantum chromodynamics, soliton models, bag models and others. The main accent is on a theory of thereal physical space that acts as a scene on which all high-energy events take place. Wediscuss how a lepton and quark appear in the space constituted as a tessellation lattice ofprimary topological balls — the only structure that mathematics (i.e. set theory, topologyand fractal geometry) offers to the constitution of ordinary physical space. Since leptonsand quarks emerge in the tessellattice from a topological ball, they must interact withthis substrate. The principles of the interaction of subatomic particles with space andthrough space between themselves are considered in detail. The approach: i) states thatreal quarks possess the integer charge ±e and they periodically change to the monopolestate (hence, canonical particles are dynamic dyons); ii) naturally solves the problem ofconfinement of quarks; iii) reveals the dynamics of quarks in hadrons; iv) discloses an innerstructure of the proton and neutron; v) calculates the radius of the proton; and vi) derivesthe nuclear forces as the result of both direct coalescence of surfaces of the nucleons andthe overlapping of spatial excitations (named inertons) generated by the nucleons at theirmotion through the tessellattice. Experimental results showing nuclear transformationsin samples affected by artificially generated inerton fields are demonstrated.
Category: High Energy Particle Physics
[8] viXra:2609.0009 [pdf] submitted on 2026-09-06 22:07:09
Authors: Teo Banica
Comments: 400 Pages.
This is an advanced introduction to the various types of normal random variables, with most of the needed preliminaries included. We first discuss the probability basics, standard central limits, and the theory of the usual, real normal variables, with examples, illustrations and numerous formulae. Then we go on a similar discussion regarding the complex normal variables, and the Rayleigh variables too. We then move to arbitrary dimensions, with a discussion regarding the Gaussian vectors, and related probability laws, featuring some functional analysis, and geometry and physics too. Finally, we provide an introduction to the quantum versions of the normal variables, and notably to those coming from free probability and random matrices.
Category: Statistics
[7] viXra:2609.0008 [pdf] submitted on 2026-09-05 08:44:33
Authors: Anatoly V. Belyakov
Comments: 10 Pages. 4 Fig.
Physical models based on J. Wheeler’s geometrodynamics, when applied to planetarysystems and pulsars, agree well with modern observational results and predict new ones.The current geometrodynamic model explains the appearance of the "hot Neptunian desert"region, the existence of an "airy super-Earth", the construction of compiled pulsar spectra,the calculation of their "death line", the calculation of braking indices for various pulsarpopulations, and much more.
Category: Astrophysics
[6] viXra:2609.0007 [pdf] submitted on 2026-09-06 00:56:45
Authors: Edward Larson
Comments: 24 Pages. (Note by viXra Admin: Future submission of AI assisted article will not be accepted)
Gödel's intuition accurately zeroed in on a core truth: that the expressiveness of non-trivial mathematical theories outpaces the efficacy of any inference engine. His paradoxical form of argumentation, however, begat immense confusion and pessimism, which this essay examines critically and aims to undo. His actual technical analysis exposed a historic oversight in classical set theory: the lack of internal structural variation within the Cantor sets $aleph_{0}$, $aleph_{1}$, etc. The paradoxical argumentation amounts to an indirect proof (reductio ad absurdum) of internal differentiation within $aleph_{0}$.This paper introduces a new concept of structural grade separation (SGS) within the Cantor sets and examines their foundational role and implications within formal mathematical frameworks, challenging the traditional conception of coarse set cardinality. By introducing a comprehensive SGS scheme, we demonstrate how structural stratification illuminates transfinite set theory without sacrificing logical consistency. The theoretical bounds of this construction against established axioms of arithmetic and set theory are analyzed, illustrating how explicit structural hierarchy resolves ambiguities inherent in standard set theory and cardinal assignments. The broader mathematical significance of graded set structures for decision algorithms and formal reasoning engines are explored.
Category: Set Theory and Logic
[5] viXra:2609.0005 [pdf] submitted on 2026-09-03 04:06:45
Authors: Dave E. Dunstan
Comments: 4 pages. 3 Figures.
The Pantheon + SHOES data is interpreted using transformed coordinates with distances that have origin at the beginning of the Universe. Distances (R) taken from the beginning of the Universe (R~0 and t~0) increase toward Earth and reveal a Newtonian Gravitational redshift (z<0.1). Distances determined in this way are the inverse of the luminosity distances measured from Earth. The revised coordinate frame yields a 1/R dependence of the redshift consistent with a Newtonian gravitational redshift. An alternative to the Hubble-Lemaitre expanding Universe is presented. The alternative Universe suggested is determined by Gravity, is static in size and contains Galaxies that show a Gaussian distribution of velocities. This is the model of the Universe first considered by Einstein.
Category: Relativity and Cosmology
[4] viXra:2609.0004 [pdf] submitted on 2026-09-03 15:49:44
Authors: Martin Kraus
Comments: 9 Pages.
According to a recently proposed vibrational interpretation of the Schrödinger equation for hydrogen-like atoms, stationary single-electron wave functions describe vibrations that are driven by phase waves associated with a bound electron moving on precessing orbits similar to orbits of the old quantum theory by Bohr and Sommerfeld. Based on this interpretation, the objective of this work is to provide insights into the structure of these wave functions by constructing similar wave functions from the corresponding electronic orbits and their associated phase waves without explicitly solving the three-dimensional Schrödinger equation. The proposed construction extends solutions of the two-dimensional Schrödinger equation into three dimensions and takes precession of the orbital angular momentum into account by a weighted average over all rotations about the quantization axis. The constructed wave functions are structurally similar to the standard wave functions of hydrogen-like atoms in spherical coordinates; thus, the proposed construction provides a new way of understanding the structure of these wave functions.
Category: History and Philosophy of Physics
[3] viXra:2609.0003 [pdf] submitted on 2026-09-04 00:18:43
Authors: Antoine Khai Nguyen
Comments: 17 Pages. (Note by viXra Admin: For the last time please cite and list scientific references!)
The Cosmic wavefunction model that governs the cosmic world, and the Nuclear wavefunction model that governs the quantum world.These two discovery-postulated Quantum wavefunction models are separated by their action realms but very similar in their ingrained structural mechanisms.The core element of this Quantum wavefunction model set is the concept of orbital/motion frequencies for both cosmic and quantum objects, and the quantization principle of the ingrained feature determination mechanisms for these objects.Each wavefunction model can demonstrate that the orbital positions (from the captor out) of all the captives inside their system are not random, but are coordinated according to the model's mechanism which uses the orbital/motion frequencies as the shared factor.
Category: Quantum Gravity and String Theory
[2] viXra:2609.0002 [pdf] submitted on 2026-09-01 20:46:50
Authors: Nigel B. Cook
Comments: 5 Pages.
Reference 1 shows that when multipath interference is treated correctly, the imaginary term, i sin S, is unnecessary; the real term cos S suffices, therefore Euler’s exp(iS) = i sin S + cos S reduces to exp(iS) → cos S. Can this same principle be applied to complex phase amplitudes in gauge theory phase ransformations? Gauge invariance only requires a continuous group action in real space, not the complex phase structure suggested by textbooks. The complex exponential hides the physics. The conversion of gauge theory to real space phase changes makes explicit the physical mechanism of gauge theory.
Category: Quantum Physics
[1] viXra:2609.0001 [pdf] submitted on 2026-09-02 11:37:02
Authors: Aleksandr Nikitin
Comments: 4 Pages.
My theoretical developments of the new scientific paradigm lead to the conclusion that any movement of matter, including gravity and low-energy nuclear reactions (LENR), occur as matter-neutrino induction.Any fundamental prime mover (sail, water wheel, steam engine, internal combustion engine, gas turbine, jet engine, nuclear reactor, electric current generator) is a nuclear fusion generator.The motion of matter, i.e. any change, including gravitational, electromagnetic and low-energy nuclear reactions LENR, the description of which is the task of science, can be further cognized solely on the basis of a new scientific paradigm:
Category: Nuclear and Atomic Physics
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