Foundations, Volume 5, Issue 3

Using the results of numerical simulations and solar observations, this study shows that the transition from deterministic chaos to hard turbulence in the magnetic field generated by the emerging small-scale, near-surface (within the Sun’s oute...

We revisit the Extended Uncertainty Principle (EUP) from an operational viewpoint, replacing wavefunction-based widths with apparatus-defined position constraints such as a finite slit of width $\mathrm{\Delta }x$ or a geodesic ball of radius R. Using Hermitian...

The often used analytical representation of the Maxwell–Boltzmann classical speed distribution function (F) for elastic, indivisible particles assumes an infinite limit for the speed. Consequently, volume and the number of particles (n) extend...

Knots are ubiquitous in polymers and biological macromolecules such as DNA and proteins, yet their behavior and functionality are still not sufficiently explored. Here we investigate the impact of Poiseuille flow on simple knots in flexible polymers...

The aim of this work was to construct explicit expressions for the summation of Dirichlet Beta functions with odd arguments and Zeta functions with even arguments. In the established literature, this is typically done using Fourier series expansions...

Differential equations need boundary conditions (BCs) for their solution. It is widely acknowledged that differential equations and BCs are representative of independent physical processes, and no correlations between them are required. Two recent st...

We introduce the concept of the magnetic metapole—a theoretical extension of classical multipole theory involving a fractional j pole count (related to the harmonic degree n as j = 2ⁿ). Defined by a scalar potential with colatitudinal dependenc...

In this paper, we review Helmholtz–Boltzmann thermodynamics for mechanical systems depending on parameters, and we compute the Fisher information matrix for the associated probability density. The divergence of Fisher information has been used...

This paper presents a mathematical formalism for generative artificial intelligence (GAI). Our starting point is an observation that a “histories” approach to physical systems agrees with the compositional nature of deep neural networks....