This paper brings together methods to solve and/or characterize solutions of some problems of mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. Using surjectivity or variational approaches, one may obtain or characterize we...
Based on the published papers in this Special Issue of the elite scientific journal Mathematics, we herein present the Editorial for “Differential Equations of Mathematical Physics and Related Problems of Mechanics”, the main topics of wh...
This paper brings together methods to solve and/or characterize solutions of some problems of mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. Using the widely debated results of surjectivity or variational approaches, one...
This paper deals with several equations of mathematical physics written in explicit form with their solutions. In Theorem 1, an oblique derivative problem for the string equation is studied. More precisely, the initial-boundary value problem for the...
There are many applications of mathematical physics in several fields of basic science and engineering [...]
This study aims to describe the design and development of a STEM problem-solving activity involving mathematics and physics content. It is an activity whose starting point is a question based on a real problem: to identify the areas of the classroom...
This work presents a solving method for problems of Ambrosetti-Prodi type involving p-Laplacian and p-pseudo-Laplacian operators by using adequate variational methods. A variant of the mountain pass theorem, together with a kind of Palais-Smale condi...
A Hopfield neural network is described by a system of nonlinear ordinary differential equations. We develop a broad range of numerical schemes that are applicable for a wide range of computational problems. We review here our study on an approximate...
The objective of this editorial is to overview the content of the special issue “Machine Learning for Energy Systems”. This special issue collects innovative contributions addressing the top challenges in energy systems development, inclu...
Using assembly theory, we investigate the assembly pathways of binary strings (bitstrings) of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of previous joining operations. We show th...
A novel method for finding the eigenvalues of a Sturm–Liouville problem is developed. Following the minimalist approach, the problem is transformed to a single first-order differential equation with appropriate boundary conditions. Although the...
The logistics and transportation sectors are struggling to manage empty containers (ECs), resulting in unused resources, inefficiencies, and increased CO2 emissions. The Physical Internet (PI) concept provides an opportunity to improve container shar...
This work investigates the use of physics-informed neural networks (PINNs) for solving representative classes of differential and integro-differential equations, including the Burgers, Poisson, and Volterra equations. The examples presented are chose...
A mixed formulation physics-informed neural network (PINN) for solving a forward and an inverse nonlinear Euler–Bernoulli dynamic beam problem is proposed. This approach avoids the computation of fourth-order spatial derivatives in the loss fun...
High-latitude and cold-region environments feature tightly coupled hydrological, cryospheric, and ecological subsystems, where seasonal freeze–thaw cycles, snow cover, permafrost, and river and lake ice fundamentally shape water flows and ecosy...
This work presents the application of a novel evolutional algorithmic approach to determine and reconstruct the specific 3-dimensional source location of gamma-ray emissions within the shelter object, the sarcophagus of reactor Unit 4 of the Chornoby...
In this paper, we propose and use a new approach for a relatively simple technique for conducting MD simulation (MDS) of various molecular nanostructures, determining the trajectory of the MD run and forming the final structure using external force a...
In this study we consider the features of spatial-structure formation in proteins and their application in bioengineering. Methods for the quantitative assessment of the chirality of regular helical and irregular structures of proteins are presented....
This paper demonstrates the application of STEM technologies using the example of the problem of a thread with a load. As a training problem, parameter finding of a flexible inextensible thread with a load sliding along it, as well as with a fixed lo...
On 14 February 2025, the outer cladding of the Chornobyl New Safe Confinement (NSC) was damaged by an explosion caused by a one-way attack unmanned aerial vehicle (UAV), creating a hole of about 15 m in diameter and requiring about 300 penetrations t...
It is my great pleasure to welcome you to Axioms: Mathematical Logic and Mathematical Physics, a new open access journal, which is dedicated to the foundations (structure and axiomatic basis, in particular) of mathematical and physical theories, not...
The polarization switching kinetics of nanosized ferroelectric crystals and the transition between homogeneous and domain switching in nanoscale ferroelectric films are considered. Homogeneous switching according to the Ginzburg-Landau-Devonshire (LG...
Graphene aerogels are of high interest nowadays since they have ultralow density, rich porosity, high deformability, and good adsorption. In the present work, three different morphologies of graphene aerogels with a honeycomb-like structure are consi...
Amphiphilic dendrimers represent a promising class of nanoscale building blocks for functional materials, yet their conformational behavior, solvation, and interfacial activity remain incompletely understood. In this work, we employ atomistic molecul...
This paper addresses discontinuities in the solutions of mathematical physics that describe actual processes and are not observed in experiments. The appearance of discontinuities is associated in this paper with the classical differential calculus b...
Conventional mathematically based procedures in forest data processing have some problems, such as deviations between the natural tree and the tree described using mathematical expressions, and manual selection of equations and parameters. These prob...
Many concepts in mathematics are not fully defined, and their properties are implicit, which leads to paradoxes. New foundations of mathematics were formulated based on the concept of innate programs of behavior and thinking. The basic axiom of mathe...
We studied the conformational behavior of silicon-containing dendrimers during their adsorption onto a flat impenetrable surface by molecular dynamics (MD) simulations. Four homologous series of dendrimers from the 4th up to the 7th generations were...
A comparative analysis of intramolecular dynamics of four types of isolated dendrimers from the fourth to the seventh generations belonging to the siloxane and carbosilane families, differing in spacer length, core functionality, and the type of chem...
Helping students become proficient problem solvers is one of the primary goals of physics courses. In Part I of this article, we summarized the vast research on problem solving relevant for physics instruction, and here we discuss a concrete example...
The field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the...
This article reports on physics teaching in upper-secondary school with a focus on communication and relations made between mathematics, theoretical models in physics, and reality. Video data from four physics classrooms in three different teaching c...
Currently, there is great interest in the correlation between children’s physical activity and their academic performance. In this study, a pre-test/mid-test/post-test experimental strategy was used to avoid any disruption of educational activi...
Hydroxyapatite (HAP) is the main mineral component of bones and teeth. Due to its biocompatibility, HAP is widely used in medicine as a filler that replaces parts of lost bone and as an implant coating that promotes new bone growth. The modeling and...
We present analytical investigations of evolution of localized disturbances during their propagation in an infinite monoatomic nonlinear one-dimensional lattice, specifically the
We hope this work allows one to calculate large prime numbers directly, not by trial-and-error, but following a physical law. We report—contrary to conventional assumptions—that differentiation of discontinuous functions (DDF) exists in t...
Mathematical equations that describe all physical processes are valid only under certain assumptions. One of them is the minimum scales used for the given description. In fact, this prohibits the use of derivatives in the mathematical models of the p...
In this Special Issue, the recent advances in the applications of symmetric functions for mathematics and mathematical physics are reviewed, including many novel techniques in analytic functions, transformation methods, economic growth models, and Hu...
Special polynomials play an important role in several subjects of mathematics, engineering, and theoretical physics. Many problems arising in mathematics, engineering, and mathematical physics are framed in terms of differential equations. In this pa...
Mathematical methods are extensively used in dealing with simulation and approximation problems related to computer science, engineering, physics, and many others [...]
This paper develops mathematical apparatus for the modeling of the electronic structure of semiconductor nanoparticles and the description of sensor response of the layers constructed on their base. The developed technique involves solutions of both...
Well-posedness, dynamics, and control of nonlinear differential system with an initial-boundary value involve many mathematical, physical, and engineering problems [...]
Mathematical modeling and system control are employed in many research problems, ranging from physical and chemical processes to biomathematics and life sciences [...]
This study examines the effects of implementing a movement-integrated instruction (MII) program in third-grade mathematics classes with a focus on students’ mathematical learning outcomes and physical literacy development. The program was desig...
In standard quantum theory, symmetry is defined in the spirit of Klein’s Erlangen Program—the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the defi...
Using molecular dynamics, a comparative study was performed of two pairs of glassy polymers, low permeability polyetherimides (PEIs) and highly permeable Si-containing polytricyclononenes. All calculations were made with 32 independent models for eac...
The generalized hypergeometric functions in one and several variables and their natural generalizations appear in many mathematical problems and their applications. The theory of generalized hypergeometric functions in several variables comes from th...
Mountain Pass Theorem (MPT) is an important result in variational methods with multiple applications in partial differential equations involved in mathematical physics. Starting from a variant of MPT, a new result concerning the existence of the solu...
This work is devoted to the study of nanosized polymer polyvinylidene fluoride (PVDF) thin ferroelectric films (two-dimensional ferroelectrics) and their composites with graphene layers, using molecular dynamics methods to (1) study and calculate the...
The holographic signal-processing method for a single vector scalar receiver (VSR) in the high-frequency band in shallow water is developed in the paper. The aim of this paper is to present the results of the theoretical analysis, numerical modeling,...
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