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| viXra.org > Mathematical Physics > 2509 |
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[7] viXra:2509.0144 [pdf] submitted on 2025-09-28 19:42:10
Authors: Marek Suder
Comments: 6 Pages.
The paper presents an extended analysis of the structure of the hydrogen atom spectral lines, based on the concept of superresonance — a phenomenon in which all Lyman, Balmer, Paschen and Brackett resonances (for n ≤ 7 and m ≤ 4) exhibit complete harmonic relations with respect to the λu2080 wave.The frequency values form a discrete raster with a constant spacing of approximately 18.64 GHz. The results indicate the existence of a universal harmonic structure in the hydrogen spectrum, opening new possibilities in spectroscopy and the theory of atomic interactions.Based on this, the concept of a subquantum (sQ) was introduced, defined as the smallest unit of photon energy with a value of εu2080 ≈ 7.71 × 10u207bu2075 eV, equal to 1/3969 of the H(5→4) transition energy. This unit allows the construction of a resonance grid in which all analyzed transitions are arranged in integer multiples of the fundamental frequency.The proposed approach suggests that the hydrogen spectrum is governed by a simple harmonic system, extending the classical Bohr—Rydberg model with a deeper level of discretization. This method reduces measurement uncertainties and opens up new possibilities for precise spectroscopic calibration, enabling not only the description of known transitions but also the prediction of previously unobserved line parameters.
Category: Mathematical Physics
[6] viXra:2509.0108 [pdf] submitted on 2025-09-18 18:15:10
Authors: Thierry L. A. Periat
Comments: 49 Pages. (Note by viXra Admin: Please submit finalized version only and remove the watermark "Draft"))
This exploration focuses attention on the kernels related to the decomposition of deformed cross products. It tries to use them as commutative operator describing the evolution of the polynomials which are associated with the decomposition of these deformed products. The long-range purpose is the construction of an algebraic dynamics shedding a new light on our reality.
Category: Mathematical Physics
[5] viXra:2509.0079 [pdf] submitted on 2025-09-13 23:04:45
Authors: Kshitiz Prabhakar
Comments: 5 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Euler’s identity e^(iπ)+1 = 0 is a central, rigorously proven result in complex analysis. This note does not dispute its correctness inside that formalism. Instead it isolates a single, widely overlooked modeling choice that arises when the analytic identity is applied to measurable angles in physics and engineering: the implicit treatment of angular measures as if they were plain, unitless real numbers. I (1) explain why the analytic/trigonometric power series force a particular angular normalization (radians); (2) show concretely, via a bradian renormalization and a kilogram counterexample, that the usual "divide-by-1 rad" maneuveris a convention that cannot be elevated to a general principle; (3) formalize the issue as atype/coercion error; and (4) show direct implications for phasor calculus and the Schrodinger plane-wave ansatz. I finish with minimal, implementable prescriptions (explicit coercion or typed wrappers) that preserve numerical results while restoring unit-aware rigor.
Category: Mathematical Physics
[4] viXra:2509.0031 [pdf] submitted on 2025-09-04 18:01:52
Authors: Igor F. Tkachenko, Yuriy S. Miroshnichenko, Victoria I. Miroshnichenko, Konstantyn I. Tkachenko, Sergyi A. Miroshnichenko, Svitlana G. Tkachenko
Comments: 4 Pages.
Based on the early developed analytic model of the nonstationary stochastic processes and well grounded concept of the flat plane Universe originated by the Big Bang and continuing to evolve by now, the well known Casimir effect was considered as a consequent of the Bernoulli law, showing decreasing the static pressure providing the motion of cosmic fluid with increasing its velocity. Novel formula to calculate the stress acting perpendicular the flow direction was derived and the formula similarity with the known Casimir relation obtained using quantum electrodynamics was shown. The stress values calculated using the new formula is in a good agreement with the available experimental data.
Category: Mathematical Physics
[3] viXra:2509.0013 [pdf] submitted on 2025-09-02 20:43:24
Authors: Rayan Bhuttoo
Comments: 5 Pages. License: CC BY-NC-ND 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
We derive Euler’s celebrated result through a novel kinematic-geometric framework. By modeling the orthogonal projection of uniform circular motion (e.g., a rotating blade under collimated light), we identify the universal ratio ∥shadow∥ circumference = 1 π as a fundamental scaling law between rotational and linear kinematics. Interpreting the real number line as a harmonic projection of a rotational system, we demonstrate that the summation reconstructs the curvature lost under projection. This approach naturally extends to higher zeta values ζ(2k), admits quantum-mechanical analogues via projection operators P, and adapts to relativistic regimes where Lorentz contraction modifies shadow geometry. Our work establishes π as a dynamic compression ratio be tween rotational and linear kinematics, offering a physical lens for classical number theory.
Category: Mathematical Physics
[2] viXra:2509.0010 [pdf] submitted on 2025-09-02 21:51:56
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 5 Pages.
We demonstrate, with mathematical rigor, that the Principium Geometricum(PG) force law,F(R) = (rho_v^2 * V1 * V2 * c^2) / (lambda * alpha_U * R^2),is not an arbitrary postulate but the unique consequence of treating matter as vac-uum resonance. We derive it independently via (i) a variational principle, (ii) theflux of momentum through a stress tensor, and (iii) the energy of the field viaGreen’s identity. In all cases, the same 1/R2 dependence and the same prefactorstructure emerge. Dimensional analysis, boundary value problems, self-energy reg-ularization, and calibration with Newtonian gravity and Coulomb electrostatics arediscussed. Thus the PG force law stands as a mathematically consistent unificationof interactions under the same tensional principle.
Category: Mathematical Physics
[1] viXra:2509.0002 [pdf] submitted on 2025-09-01 22:38:41
Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 7 Pages.
We develop a mathematically grounded framework in which what is commonly called "matter" consists of finite—energy, knotted excitations of a nonlinear vacuum field. The model is based on a Faddeev—Skyrme—type Lagrangian for a unit vector field n : R3,1 → S2, coupled to gravity and electromagnetism. Toroidal (Hopf) solitons carry conserved topological charge and exhibit internal "beating" modes. Mass, momentum and spin arise purely from the vacuum stress—energy tensor. The constant αU = keAP (Coulomb constant times Planck area) plays the role of a vacuum rigidity/constitutive scale, controlling EM couplings and regularization. We lay out explicit assumptions, definitions, energy bounds, and geodesic motion of soliton centers, with citations to classical results (Derrick’s theorem, Vakulenko Kapitanskii bound, moduli space dynamics).
Category: Mathematical Physics
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