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| viXra.org > Mathematical Physics > 2603 |
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[8] viXra:2603.0142 [pdf] submitted on 2026-03-31 21:32:27
Authors: Kohji Suzuki
Comments: 22 Pages.
We try to let the '(st)ringy' (viXra:1912.0532 [v1]) explain massive graviton, leptonic spin-3/2 particle, and so on. Meanwhile, we come across a number system which we tentatively call `hexanion', as if it were a by-product.
Category: Mathematical Physics
[7] viXra:2603.0136 [pdf] submitted on 2026-03-29 04:53:33
Authors: Makoto Itoh
Comments: 47 Pages.
In this paper, we show that a voltage-controlled nonlinear resistor can be regarded as a voltage-controlled memristor when its behavior is observed using the time derivatives of state variables. Next, we derive the memristor FitzHugh-Nagumo equation by differentiating the original FitzHgh-Nagumo equation with respect to time. We also show that the trajectory of the memristor FitzHugh-Nagumo equation is highly dependent on the initial flux condition. This trajectory can be changed by applying a small single pulse. Furthermore, the square wave forcing creates many complex behaviors such as chaotic attractors and limit cycles. These behaviors also depend on the initial flux condition. Therefore, it is impossible to predict the trajectory without knowing the initial flux condition. Next, we observe the trajectory's evolution by adding a small DC bias current to the square wave forcing. We show that as time progresses, the trajectory changes shape and eventually shrinks. This resembles the refractory period of neurons. Finally, we study the signal transmission between the two memristor FitzHugh-Nagumo circuits which are connected by a unity-gain buffer. We show that, for the signal to be transmitted almost exactly, the initial flux condition must be identical. Additionally, we derive the memristor Chua circuit equation by differentiating the original Chua circuit equation with respect to time. Our findings are nearly identical to those for the memristor FitzHugh-Nagumo equation. We also study the signal transmission between two memristor Chua circuits that are connected by a unity-gain buffer. We show that nearly perfect transmission requires the identical initial flux condition. It should be noted that requiring the identical initial flux conditions results in more secure communication with the memristor Chua circuits than with the original Chua circuits. Finally, we would like to emphasize the following points: The memristor FitzHugh-Nagumo equation and the memristor Chua circuit equation both exhibit rich dynamics. The identification of the circuit elements depends on the coordinate system used to observe them.
Category: Mathematical Physics
[6] viXra:2603.0135 [pdf] submitted on 2026-03-29 09:19:53
Authors: Tom Robert Franck Cooper
Comments: 10 Pages.
This work investigates the emergence of discrete dynamical structures from classical and relativistic formulations of motion. Using standard differentiation rules, we examine how Newtonian dynamics can be expressed in terms of energy gradients within a consistent formal framework. The relativistic kinetic-energy function is then analyzed in two limiting regimes: the classical limit ($beta to 0$) and the relativistic limit ($beta to 1$), where its asymptotic behaviour becomes singular.In the singular regime, the dominant contributions of the kinetic-energy expansion exhibit a hierarchical structure that naturally leads to weighting factors of the form $(n+tfrac{1}{2})$. This structure is shown to be consistent with the discrete spectrum of the quantum harmonic oscillator, suggesting that certain quantum features may be related to underlying classical asymptotic behaviour.The analysis is complemented by a geometric interpretation of electromagnetic interactions using Gaussian units, together with a generalized functional perspective for handling singular contributions. Within this framework, the introduction of a small interaction scale—analogous to a Yukawa-type modification—provides an effective description of interaction ranges.Overall, this approach provides a conceptual bridge between classical mechanics, relativistic dynamics, and quantum-like discretization, highlighting the role of singular limits, normalization, and geometric structure in the emergence of discrete spectra.
Category: Mathematical Physics
[5] viXra:2603.0134 [pdf] submitted on 2026-03-29 09:22:57
Authors: Tom Robert Franck Cooper
Comments: 11 Pages.
This work presents a unified structural perspective on classical dynamics, emphasizing the interplay between variational principles, conservation laws, and transport formulations. Starting from Newton’s Second Law, we review the derivation of the Euler--Lagrange equations via D’Alembert’s principle and highlight how continuous symmetries give rise to conserved quantities through Noether’s theorem, culminating in the energy--momentum tensor formulation.We show that diverse physical theories — including particle mechanics, continuum mechanics, fluid dynamics, and kinetic theory — can be interpreted as different realizations or projections of a common underlying structure. In particular, dynamical evolution can be expressed as transport of physically relevant quantities along trajectories, fields, or phase-space flows, with the kinetic contributions determining the form of the evolution operator.Building on this perspective, we introduce an alternative kinetic formulation in which the conservation of the energy--momentum tensor naturally gives rise to familiar dynamical equations, including Newton’s Second Law, the Navier--Stokes equations, and the Vlasov equation. This approach emphasizes that apparent differences between dynamical frameworks arise from different projections of the same underlying conservation and variational structure.Finally, we interpret dynamics as evolution within a generalized space of states, where physical trajectories correspond to stationary-action paths selected from the set of admissible configurations. This unifying viewpoint lays the groundwork for further exploration of higher-order or generalized dynamical systems and provides a structural bridge toward Part III, in which interactions are effectively one-dimensional along evolution paths.
Category: Mathematical Physics
[4] viXra:2603.0133 [pdf] submitted on 2026-03-29 09:28:10
Authors: Tom Robert Franck Cooper
Comments: 16 Pages.
This paper develops a geometric reconstruction of the three-body problem starting from a reformulation of the two-body interaction law. In the two-body case, the interaction is separated into two complementary contributions associated with the two masses, combined by an inverse-sum rule, and used to identify the origin of motion relative to the observed body. This reproduces the usual barycentric structure while making the geometric role of the interaction origin explicit.The central question addressed here is whether this construction can be extended to the three-body problem. We show first that the naive extension fails for geometric reasons: the interaction of a given observed body is no longer supported on a single line of centres, but on two generically non-collinear channels. The difficulty is therefore not simply that more terms are present, but that the two-body interaction geometry is no longer globally available.To overcome this obstruction, we construct a local three-body interaction law based on three ingredients: a local interaction scale, a local shape tensor encoding the two-channel geometry, and a frame/self structure that determines the local interaction length. The asymmetry between the two channels is incorporated through dimensionless correction factors associated with channel participation and channel sharing. The resulting local pull axis is then defined by a Newtonian-weighted combination of the two interaction directions, while the motion itself is governed by a scalar pull-only law.The construction is tested on the principal benchmark solutions. It reduces correctly to the two-body problem when one channel disappears, reproduces the equal-mass equilateral Lagrange solution exactly, and the figure-eight choreography to numerical precision. These results indicate that the essential geometric problem of the three-body system lies in the reconstruction of the local pull axis rather than in the need for a fundamentally more complicated force law.The main conclusion is that the two-body problem extends to three bodies not through a direct superposition of pairwise reductions, but through the reconstruction of a local interaction geometry in which axis selection and origin scaling must be separated. Within this framework, a scalar pull-only law becomes sufficient once the correct local pull axis and origin has been identified.
Category: Mathematical Physics
[3] viXra:2603.0113 [pdf] submitted on 2026-03-21 14:34:09
Authors: John Hemp
Comments: 237 Pages.
Bayesian probability, has a long history, but has developed into its most useful, contemporary form, thanks largely to the work of E. T. Jaynes (1922-1997). A brief account of Jaynes’s theory of probability is given in this book, and examples of its profitable use in theoretical physics are given. These include its use in statistical thermodynamics (to clarify, in particular, the meaning of thermodynamic entropy), and its use in the theory of Brownian motion (to derive the diffusion equation and the concepts of particle drift-velocity and probability flux). Also discussed is the way in which rational Bayesian probability theory eliminates the paradoxes that block the way toward a realist interpretation of quantum mechanics, and promises a more rational formulation of quantum mechanics involving complex-valued Bayesian probabilities.
Category: Mathematical Physics
[2] viXra:2603.0089 [pdf] submitted on 2026-03-16 00:46:43
Authors: Shijun LIAO
Comments: 5 Pages.
We prove such a mathematical theorem that solution of the incompressible Navier-Stokes equations under periodic boundary condition has the same spatial symmetry for all t>0 as its smooth initial condition, if there exist the spatial symmetry for initial condition, the external force is steady-state, and the temporal Taylor series of velocity exists and has a non-zero radius of convergence for t >= 0. This theorem can be used to check the correctness and reliability of numerical simulation of Navier-Stokes equations for turbulent flows.
Category: Mathematical Physics
[1] viXra:2603.0061 [pdf] replaced on 2026-03-21 02:59:08
Authors: Barry L. Guevremont
Comments: Corrected version with fixed Lean 4 code, added images (coffee_cup.png and math_monster.jpg), and minor formatting improvements. 10 pages. Physics - Mathematical Physics category.
For any smooth, divergence-free initial velocity field uu2080 ∈ Hˢ(ℝ³) with s ≥ 1/2, there exists a unique, global-in-time smooth solution u(x, t). We prove this by establishing that the Leray-Hopf energy inequality is a strict equality and that the velocity gradient satisfies a uniform L∞ bound for all t ≥ 0. This closes the supercritical scaling gap and satisfies the Beale—Kato—Majda criterion, thereby proving global regularity of the 3D incompressible Navier-Stokes equations.
Category: Mathematical Physics
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