The well-known shooting algorithm has produced important results in solving various linear as well as nonlinear BVPs, defined on unbounded intervals, but has become obsolete. The main difficulty lies in the numerical handling of the domain’s in...
As a contribution to automated set-theoretic inferencing, a translation is proposed of conjunctions of literals of the forms
Global optimization represents a fundamental challenge in computer science and engineering, as it aims to identify high-quality solutions to problems spanning from moderate to extremely high dimensionality. The Differential Evolution (DE) algorithm i...
The structural vibration of industrial droplet dispensers can be modeled by telegraph-like equations to a good approximation. We reinterpret the telegraph equation from the standpoint of an electric–circuit system consisting of an inductor and...
In this paper, we investigate a new class of nonlinear fractional boundary value problems (BVPs) involving
The root mean square deviation (RMSD) is a widely used item fit statistic in item response models. However, the sample RMSD is known to exhibit positive bias in small samples. To address this, seven alternative bias-corrected RMSD estimators are prop...
Perceptual Control Theory (PCT) and the Free Energy Principle (FEP) are two foundational, principle-based frameworks originally developed to explain brain function. However, since their initial proposals, both frameworks have been generalized to acco...
A probabilistic version of geometry is introduced. The fifth postulate of Euclid (Playfair’s axiom) is adopted in the following probabilistic form: consider a line and a point not on the line—there is exactly one line through the point wi...
We consider a class of strongly mixing sequences with infinite second moment. This class contains important GARCH processes that are applied in econometrics. We show the relative stability for such processes and construct a counterexample. We apply t...
This study investigates the origin and amplification of magnetic fields in planets and galaxies, emphasizing the foundational role of a seed magnetic field (SMF) in enabling dynamo processes. We propose a universal mechanism whereby an SMF arises nat...
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
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....
In axisymmetric fusion devices like tokamaks, the winding of the magnetic field is characterized by its safety profile
Using the results of numerical simulations and astrophysical observations (mainly in the WMAP and Planck frequency bands), it is shown that Galactic foreground emission becomes more sensitive to the mean magnetic field with the frequency, resulting i...
Mean–geometric mean (MGM) linking compares group differences on a latent variable
We show numerical evidence for a bipartite
In this survey, we have included the recent results on Lyapunov-type inequalities for differential equations of fractional order associated with Dirichlet, nonlocal, multi-point, anti-periodic, and discrete boundary conditions. Our results involve a...
This paper revisits some aspects connected with the methods for the determination of thermodynamically consistent models. While the concepts apply to the general context of continuum physics, the details are developed for the modelling of deformable...
I dispute the conventional claim that the second law of thermodynamics is saved from a “Maxwell’s demon” by the entropy cost of information erasure and show that instead it is measurement that incurs the entropy cost. Thus, Brilloui...
Ramsey analysis is applied to the problem of the relativistic and quantum synchronization of clocks. Various protocols of synchronization are addressed. Einstein and Eddington special relativity synchronization procedures are considered, and quantum...
Parameter identification problems in partial differential equations (PDEs) consist in determining one or more functional coefficient in a PDE. In this article, the Bayesian nonparametric approach to such problems is considered. Focusing on the repres...
In this paper, we study the fault-tolerant metric dimension in graph theory, an important measure against failures in unique vertex identification. The metric dimension of a graph is the smallest number of vertices required to uniquely identify every...
Vectors are almost always introduced as objects having magnitude and direction. Following that idea, textbooks and courses introduce the concept of a vector norm and the angle between two vectors. While this is correct and useful for vectors in two-...
Artificial neural networks are widely used in applications from various scientific fields and in a multitude of practical applications. In recent years, a multitude of scientific publications have been presented on the effective training of their par...
Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunction seeming to be the primary lens. Our topic is a theory showing “where adjoints...
In glass physics, order parameters have long been used in the thermodynamic description of glasses, but their nature is not yet clear. The difficulty is how to find order in disordered systems. This study provides a coherent understanding of the natu...
In spite of its unbroken PT symmetry, the popular imaginary cubic oscillator Hamiltonian
In this paper, we consider the application of brute force computational techniques (BFCTs) for solving computational problems in mathematical analysis and matrix algebra in a floating-point computing environment. These techniques include, among other...
Low-grade gliomas are a group of brain tumors that mostly affect people in early adulthood. A glioma is a tumor that originates in glial cells. They are classified into four levels according to their level of proliferation, with grades 1 and 2 called...
This study employs advanced structural characterization techniques, including anomalous small-angle X-ray scattering (ASAXS), small-angle X-ray scattering (SAXS), and X-ray photoelectron spectroscopy (XPS), to investigate erbium (Er3+)-doped silica-b...
In fixed item parameter calibration (FIPC), an item response theory (IRT) model is estimated with item parameters fixed at reference values to estimate the distribution parameters within a specific group. The presence of random differential item func...
In this study, we explore the order–disorder transition in the dynamics of a straightforward master equation that describes the evolution of a probability distribution between two states,
Stocking–Lord (SL) linking is a widely used linking method based on item response theory (IRT). This article examines the variability in SL linking parameter estimates within the two-parameter logistic (2PL) model. The uncertainty in SL linking...
In this work, we present a new theoretical approach to interpreting and reproducing quantum mechanics using trajectory-guided wavelets. Inspired by the 1925 work of Louis de Broglie, we demonstrate that pulses composed of a difference between a delay...
This work explores the hyperbolic cosine and hyperbolic secant functions within the framework of the maximum entropy principle, deriving these probability distribution functions from first principles. The resulting maximum entropy solutions are appli...
The rising demand for both water and energy has intensified the urgency of addressing the water–energy nexus. Energy is required for water treatment and distribution, and energy production processes require water. The increasing demand for ener...
The framework of this paper is the presentation of a case study in which university students are required to extend a particular problem of division of polynomials in one variable over the field of real numbers (as generalizing action) clearly influe...
The empirical wavelet transform is a fully adaptive time-scale representation that has been widely used in the last decade. Inspired by the empirical mode decomposition, it consists of filter banks based on harmonic mode supports. Recently, it has be...
The Wilson–Cowan model has been widely applied for the simulation of electroencephalography (EEG) waves associated with neural activities in the brain. The Runge–Kutta (RK) method is commonly used to numerically solve the Wilson–Cow...
Does determinism (or even the incompleteness of quantum mechanics) follow from locality and perfect correlations? In a 1964 paper, John Bell gave the first demonstration that quantum mechanics is incompatible with local hidden variables. Since then,...
This paper presents a comprehensive analytical–numerical algorithm constructed for proprotor performance evaluation, focusing on accommodating large inflow angles. The algorithm’s design, range, and analytical features are clarified, indi...
In part I of this work to appear in Foudations-MDPI 2024, some existence and uniqueness results for the solutions of some equations were reviewed, such as the Korteweg–de Vries equation (KdV), the Kuramoto–Sivashinsky equation (KS), the g...
This paper reviews the results of existence and uniqueness of the solutions of these equations: the Korteweg–De Vries equation, the Kuramoto–Sivashinsky equation, the generalized Korteweg–De Vries–Kuramoto–Sivashinsky eq...
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