Mathematical Physics - Science topic

For the first time, the general nonlinear Schrödinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class of related nonlinear partial differential equations that are often used in various areas of theoretical physics...

This reference book is devoted to exact solutions of mathematical equations of various types (algebraic, trigonometric, ordinary differential, partial differential, mathematical physics, integral, functional, delay ordinary differential, delay partial differential, functional differential, etc.). Linear and nonlinear systems of coupled ODEs and PDE...

The CKP tau function has been an important topic in mathematical physics. In this paper, the inverse of vacuum expectation value of exponential of certain bosonic fields, is showed to be the CKP tau function given by Chang and Wu, in the language of CKP Darboux transformation. In fact, computation of the above vacuum expectation value is usually qu...

Nonlinear Schrödinger equations with constant delay are considered for the first time. These equations are generalizations of the classical Schrödinger equation with cubic nonlinearity and the more complex nonlinear Schrödinger equation containing functional arbitrariness. From a physical point of view, considerations are formulated about the possi...

A general solution for a coupled system of eikonal equations $u_\mu u_\mu =0$, $v_\mu v_\mu =0$, $u_\mu v_\mu =1$ is presented, where lower indices designate derivatives, $\mu=0,1,2,3$, and summation is implied over the repeated indices. This solution is of interest by itself due to wide applications of the eikonal equations, but the system conside...

In this research paper, numerical methods Adomian Decomposition Method and Variational Iteration Method is used to solve integral equations .Numerical examples illustrate the accuracy of the Adomian Decomposition Method and Variational Iteration Method. 1. ADOMIAN DECOMPOSITION METHOD The Adomian Decomposition method (ADM) is very powerful method w...

The Italian theorist Gian-Carlo Wick is well known for his work in mathematical physics. Nevertheless, working with Fermi’s group in Rome in the 1930s, he took on several behind-the-scenes roles that resulted in important papers in neutron physics. He clarified Fermi’s methodology for calculating neutron slowing down probabilities; using transport...

With the development of science and technology, new safety requirements have arisen in low-altitude airspace and underwater space, such as low-altitude three-dimensional transportation, disaster rescue, marine ranching, underwater monitoring. In this paper, we mainly focus on the safety issues in Vicinagearth Space. A technology framework of Vicina...

A partir de um estudo investigativo em cursos de licenciatura de uma universidade pública no sul de Minas Gerais, buscamos identificar que aspectos da dimensão política da temática ambiental são enfatizados na formação de licenciandos em Ciências Biológicas, Física, Matemática e Química. Os dados foram coletados a partir dos Projetos Pedagógicos do...

Fractals are mathematical constructs that blend simplicity and complexity, arising from iterative processes that produce infinitely detailed and self-similar structures. These patterns, often found in nature, have had a profound impact on mathematics, physics, computer science, and art. The classical Mandelbrot set, with its iconic cardioid shape a...

For the first time, Schr\"odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such nonlinear equations and mathematical models are expressed. One-dimensional non-symmetry reductions are described, whic...

The spectral theory of operator matrices has several applications in elasticity, quantum mechanics, fluid dynamics, and other fields of mathematical physics. The study of operator matrices is more challenging when the involved operators are not single-valued and should be studied in the context of the theory of relations. In this paper, we utilize...

This manuscript employs the Adomian decomposition technique (ADT) to develop solutions for the fractional space-time nonlinear mKdV system, incorporating an M-truncated fractional order and supposed initial conditions. The technique yields a power series expansion solution without the need for linearization, weak nonlinear assumptions, or perturbat...

This monograph is aiming to serve as a primary introduction to spectral networks, by presenting them and their many applications from the scope of geometry and mathematical physics in a unified way. We do not attempt to treat these two approaches separately but rather provide broad motivation and the necessary background to reach to the frontiers o...

This manuscript presents set-theoretical solutions to the Yang-Baxter equation within the framework of GE-algebras by constructing mappings that satisfy the braid condition and exploring the algebraic properties of GE-algebras. Detailed proofs and the use of left and right translation operators are provided to analyze these algebraic interactions,...

The structural model, static and dynamic characteristics of a nanopiezoactuator for nanoresearch are received from the piezoelasticity equation and the differential equation of a nanopiezoactuator. A nanopiezoactuator is a piezomechanical device for converting electrical energy into mechanical energy and for actuating mechanisms, systems in nanodis...

We offer a technique for visualizing (and locating) objects in N > 3-dimensional space-for a human being. We hope that our new cartesian coordinate system will be of use for the entire span of the human race. Just as Einstein referenced, at least implicitly, Newton in his theory of special/general relativity in his use of the concept of velocity i...

Las Redes Sociales son una parte fundamental de la sociedad actual. Son fuente de conocimiento que nutren a la enseñanza formal, permitiendo encontrar recursos que poder utilizar y crear en el aula. El propósito de este trabajo es mostrar el alcance que el uso de videos educativos interdisciplinares en las áreas de Música, Educación Física y Matemá...

New types of truncated M-fractional wave solitons to the simplified Modified Camassa–Holm model, a mathematical physics model, are obtained. This model is used to explain the unidirectional propagation of shallow water waves. The required solutions are obtained by utilizing the simplest equation, the Sardar subequation, and the generalized Kudryash...

Zero and infinity are among the most intriguing and paradoxical concepts in mathematics, serving as cornerstones for numerical systems and theoretical frameworks. Their meanings, however, are deeply relational, dependent on the contexts in which they arise. Zero symbolizes absence, while infinity represents boundlessness, yet neither exists indepen...

This paper presents a comprehensive analysis of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1+1)$$\end{document}-dimensional Klein-Gordan equation which plays...

In this paper, the thin-film ferroelectric material equation which enables a propagation of solitary polarization in thin-film ferroelectric materials, and it also can be described using the nonlinear evolution equations. Ferroelectrics are dielectric materials explain wave propagation nonlinear behaviors. Thin films made from the ferroelectric mat...

In this work, we present various novelty methods by employing the fractional differential quadrature technique to solve the time and space fractional nonlinear Benjamin–Bona–Mahony equation and the Benjamin–Bona–Mahony–Burger equation. The novelty of these methods is based on the generalized Caputo sense, classical differential quadrature method, a...

While the evaluation of multimodal English-centric models is an active area of research with numerous benchmarks, there is a profound lack of benchmarks or evaluation suites for low- and mid-resource languages. We introduce ZNO-Vision, a comprehensive multimodal Ukrainian-centric benchmark derived from standardized university entrance examination (...

The purpose of this work is to study the limit behaviour of trajectory attractors for some equations and systems from mathematical physics depending on a small parameter when this small parameter approaches zero. The main attention is given to the cases when, for the limit equation, the uniqueness theorem for a solution of the corresponding initial...

The minimal operators generated by overdetermined boundary value problems for differential equations are extremely important in the description of regular boundary value problems for differential equations, and are also widely used in the study of local properties of solutions. The study of overdetermined boundary value problems is closely related...

For the first time, the general nonlinear Schrödinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class of related nonlinear partial differential equations that are often used in various areas of theoretical physics...

In this study, we introduce an efficient analysis of a new equation, termed the time-fractional q -deformed tanh-Gordon equation (TGE), which is the fractional form of the q -deformed TGE that was recently introduced by Ali and Alharbi. This equation represents a significant advancement in the field of mathematical physics, which is due to its appl...

Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in differential geometry. In this lecture notes, we will introduce the essential objects and techniques in symplectic geomet...

In this paper we give a brief overview of the present state of belief research done in Finland. The Finnish research on mathematical beliefs has recently flourished because of three different sources of funding provided by the Academy of Finland: 1) a national graduate school for mathematics, physics, and chemistry teachers, 2) a series of internat...

Wistedt, I. (1996). Gender-inclusive Higher Education in Mathematics, Physics and Technology. Five Swedish Development Projects. Stockholm: Högskoleverket. (75 sidor)

Complex physical occurrences currently need the use of nonlinear fractional partial differential equations. This paper provides a new approach to using the conformable derivative of Atangana to achieve exact travelling wave solutions to the space time-fractional Phi-4 problem. Our method enables a more profound comprehension of complex mathematical...

We prove the existence of an algebraic plane curve of equation $P(x,y)=0$, with prescribed asymptotic behaviors at punctures, and with the Boutroux property, namely, periods have vanishing real part, i.e, $\Re(\int_\gamma y dx)=0$ for every closed loop $\gamma$. This has applications in the Riemann-Hilbert problem, in random matrix theory, in spect...

Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state and its application to unbounded operators remains unclear. Here, we present a general theory for error estimation, including higher-order product for...

The significant characteristics of Associate Laguerre polynomials (ALPs) have noteworthy applications in the fields of complex analysis and mathematical physics. The present article mainly focuses on the inclusion relationships of ALPs and various analytic domains. Starting with the investigation of admissibility conditions of the analytic function...

The study focuses on the fractional complex order plant model, which has gained popularity in applied mathematics, physics, and control systems. A significant contribution of this research lies in discussing the physical phenomena associated with complex plant models and their impact on system stability and robustness. The main purpose of the metho...

The method proposed here represents an alternative way of combining symplectic geometry with the theory of differential forms within a Riemannian structure, in order to provide new insights in complex physical processes due to the common underlying mathematical formalism. The interplay between symplectic and Riemannian geometries is pursued as far...

Este trabalho apresenta resultados inéditos de investigações geofísicas de alta resolução realizadas no estuário do rio Oiapoque, na fronteira do Brasil com a Guiana Francesa, com o intuito de entenderas superfícies sísmicas e o padrão de preenchimento sedimentar. Os levantados foram realizados em maio de 2018, pelo Projeto SEAM (CNPq xxxx) utiliza...

Ein zentrales Problem des Mathematikunterrichts weltweit dürfte der unzureichende Einsatz adaptiver (Modellierungs-)Aufgaben sein. Oft müssen alle Lernenden einer Klasse an denselben Aufgaben mit einheitlichem Anforderungsniveau arbeiten. Dabei werden die Leistungsstarken oft unter- und die Leistungsschwachen häufig überfordert. Wir zeigen am Beisp...

Conformal blocks of the Virasoro algebra have a Coulomb-gas representation as Dotsenko-Fateev integrals over the positions of screening charges. In q-deformed Virasoro, the conformal blocks on a sphere with an arbitrary number of punctures are manifestly the same, when written in Dotsenko-Fateev representation, as the partition functions of a class...

It is established that the standard metrology SI-2019 cannot provide a quantitative assessment of the metric units of the Standard Physical Model with a relative accuracy better than 1/10^12 due to the logically contradictory fixation of the constant "Speed of light" as an integer value of 299792458 m/s. It is shown that the position vector-tensor-...

Since the late Ming Dynasty, Western missionaries have gradually set foot in China, among which Ba Fanji, Michele Ruggieri, Matteo Ricci and so on are representatives. In the cultural exchange and integration between China and the West, many advanced natural sciences were introduced to China by missionaries, such as astronomy, geography, mathematic...

The article is devoted to the existence of solutions of a certain quadratic integral equation in H 2 (R d), d = 2, 3. The theory of quadratic integral equations has many important applications in the mathematical physics, economics, biology. It is crucial for describing the real world problems. The proof of the existence of solutions relies on a fi...

The time-fractional Emden-Fowler model is an interesting mathematical model because it is widely used and important in mathematics and applied sciences. The current investigation compiles the Elzaki transform homotopy perturbation method (ET-HPM) and the Laplace transform homotopy perturbation method (LT-HPM) for the analytical solution of the cons...

Within the framework of AdS/CFT correspondence we considered large N limits of conformal field theories in d dimensions which described in terms of supergravity on the product of AdS space with a compact manifold. An important example of such correspondence is equivalence between N = 4 super Yang-Mills theory in four dimensions and Type IIB superst...

This study compares performance of three data clustering algorithms: K-Means, K-Medians, and K-Mode. Using correlation analysis, key variables with the highest interrelationships were identified and then used to determine the optimal number of clusters through the Elbow method. Once the optimal cluster count was established, the clustering was cond...

The Point of Oblivion is an emergent theoretical concept that suggests a critical state where the combined influence of all factors responsible for the existence of matter and energy converges to zero. This state, mathematically represented as ∑ = 0, has implications that extend across multiple domains, including quantum mechanics, cosmology, and i...

Machine learning (ML) has emerged as a powerful tool in mathematical research in recent years. This paper applies ML techniques to the study of quivers--a type of directed multigraph with significant relevance in algebra, combinatorics, computer science, and mathematical physics. Specifically, we focus on the challenging problem of determining the...

This paper employs the generalized projective Riccati equation method and the Sardar sub-equation technique to extract the solitary wave solutions of the nonlinear (2+1)-dimensional Coupled Riemann wave equations, which describes the electrostatic and magneto-sound waves in plasma, ion cyclotron waves, tidal and tsunami waves, homogeneous and stati...

This paper addresses the extension of Martinez-Kaabar (MK) fractal-fractional calculus (for simplicity, in this research work, it is referred to as MK calculus) to the field of integral transformations , with applications to some solutions to integral equations. A new notion of Laplace transformation , named MK Laplace transformation, is proposed,...

O objetivo deste trabalho e desenvolver idéias sobre como representar os resultados experimentais obtidos a partir do espalhamento da luz numa bolha de sabão conhecida como bolha de Reuleaux, utilizando a inspiração geométrica dos padroes de Moiré para representar padroes ópticos de discos de Airy e as ferramentas da Física-Matemática como funções...

Graphical representations of data are common in many disciplines. Previous research has found that physics students appear to have better graph comprehension skills than students from social science disciplines, regardless of the task context. However, the graph comprehension skills of physics students have not yet been compared with (veterinary) m...

Based on the understanding of relativity and quantum mechanics, this paper demonstrates that gravity is the result of spatial shape and dimension changes. The concept of space as dimension is expounded, and the difference between gravitational field space and material space is distinguished. The reason why the photon moves in space at a constant sp...

Une tendance se développe depuis quelques années dans/ 'Éducation nationale française, la mise en place de classes appelées classes européennes et dites un peu abusivement classes "bilingues". Certaines matières sont enseignées, pour la totalité de l'emploi du temps ou une partie seulement, dans une langue étrangère: elles peuvent à ce titre être r...

This paper aims to investigate appropriate mathematical models devoted to the optimization of some cleaning processes related to pharmaceutical contaminant removal. In our recent works, we found the rehabilitation of the existing cleaning plants as a viable solution for the removal of this type of micropollutants from waters by introducing efficien...

Neste artigo, analisou-se a associação entre o nível socioeconômico dos licenciandos em Biologia, Física, Matemática e Química e o desempenho em itens envolvendo o tema da desigualdade social na prova do Enade de 2021. Aventou-se como hipótese que a vulnerabilidade econômica poderia contribuir para uma compreensão privilegiada dos problemas apresen...

El problema de la caja bidimensional se aborda con ecuaciones diferenciales parciales elípticas para relacionar la existencia o no de estados ligados con el acoplamiento de la misma ecuación en diferencias parciales. Las EDP son cruciales para entender la naturaleza subyacente y sus implicaciones en el mundo cuántico. La estrategia matemática model...

The article changes the foundation of theoretical and mathematical physics by abandoning the principle of stationary action. It is shown that the use of the principle of stationary action in the theory of electromagnetism at the beginning of the 20th century led to the loss of uniqueness and to the loss of localization of electromagnetic energy tho...

With the assistance of emblematic calculation programming, the current paper explores the specific voyaging wave arrangements from the general (2+1)- layered nonlinear development conditions by utilizing the advanced exp⁡(-φ(ξ))-expansion with time-partial boundaries. As a result, the used technique is effectively utilized and recently created some...

A general structure-preserving method is proposed for a class of Marcus stochastic Hamiltonian systems driven by additive Lévy noise. The convergence of the symplectic Euler scheme for this systems is investigated by Generalized Milstein Theorem. Realizable numerical implementation of this scheme is also provided in details. Numerical experiments a...

Este estudio se centra en la resolución de problemas utilizando Operadores Matemáticos aplicados a la Teoría de Schrödinger en la mecánica cuántica, con un enfoque por competencias para estudiantes de quinto año de la carrera Física-Matemática en la UNAN-Managua/CUR Estelí. El objetivo principal fue validar la eficacia de actividades didácticas que...

The paper considers the generalized hypergeometric function F23, which is important in various fields of mathematics, physics, and economics. The method is used, according to which the domains of the analytical continuation of the special functions are the domains of convergence of their expansions into a special family of functions, namely branche...

In this work, we establish a novel approach to the foundations of relativistic quantum theory, which is based on generalizing the quantum-mechanical Born rule for determining particle position probabilities to curved spacetime. A principal motivator for this research has been to overcome internal mathematical problems of relativistic quantum field...

The study of Real Numbers (R) is a fundamental pillar of Mathematical Analysis, serving as the cornerstone for a broad spectrum of Mathematical principles and practical applications. Real Numbers are examined both in theory and in practice, impacting fields like pure Mathematics, physics, engineering, and economics. This paper thoroughly explores R...

In this paper we get the existence of nodal solutions and we will study some bifurcation properties for the following class of nonlocal problems where \(N\ge 3\), \(c>0\), \(g: \mathbb {R}^N\times \mathbb {R} \rightarrow \mathbb {R}\) is a \(C^1-\)function, \(\Delta \) is the euclidean Laplacian and the linear operator \(e^{-c\Delta }\) is defined...

In the work, using the Carleman function, an unknown function is restored from the Cauchy data on a part of the boundary of the domain. If the Carleman function is constructed, then using Green’s formula, one can find a regularized solution in an explicit form. It is shown that the efficient construction of the Carleman function is equivalent to th...

It is established that the fundamental metric constant "Speed of light" and all associated with it metric units of the Standard Physical Model can be initially described purely qualitatively, designated symbolically and processed analytically-in logical judgments expressed by definitions, terms, letters, figures and other signs of natural and artif...

In this study, we investigate the (3+1) q-deformed tanh-Gordon equation due to its importance in the context of mathematical physics. It describes solitonic solutions in quantum field theory; it can sometimes be used in condensed matter physics to describe interactions between particles in magnetic materials or superconductors; it can model light p...

The present essay aims to address the relationship between the theory of biological evolution (which has its origin in Darwinism) and the mathematical physics of entropy, fundamental in thermodynamic physics. The objective is to try to examine some of the assumptions of Darwin's theory of evolution in the light of the hypothesis that life on Earth...

The space–time fractional Kraenkel–Manna–Merle system (FKMMS) is a mathematical physics system that is particularly established to outline the transmission of nonlinear short waves in ferromagnetic materials considering the impact of a zero conductivity external field. Motivated by this application, the current investigation seeks to thoroughly exa...

Fractal analysis is a mathematical approach employed to study and describe complex patterns and structures across various disciplines, including mathematics, physics, computer science, biology and finance. Introduced by mathematician Benoit Mandelbrot in the 1970s, fractals are intricate, self-similar patterns that repeat at different scales, exhib...

This article reflects on the life and mathematical contributions of Pierre Cartier, a distinguished figure in 20th- and 21st-century mathematics. As a key member of the Bourbaki collective, Cartier played a pivotal role in the formalization and modernization of mathematics. His work spanned fields such as algebraic geometry, representation theory,...

The theory of ill-posed problems is a direction of mathematics which has developed intensively in the last two decades and is connected with the most varied applied problems: interpretation of readings of many physical instruments and of geophysical, geological, and astronomical observations, optimization of control, management and planning, synthe...

In this work, we apply the Riccati-Bernoulli (RB) sub-ODE approach to provide some vital solitary wave solutions for the nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the Klein-Gordan (KG) equation. The solutions that are provided here are helpful in describing several physical phenomena in inharmonic crystals, cold plasma...

This article investigates the construction of new traveling wave solutions for the conformable fractional Klein–Gordon equation, which is a well-known mathematical and physical model that can be used to explain spinless pion and de Broglie waves. In order to accomplish this task, a classic and effective analysis method, namely, the extended tanh–co...

Based on a systematic analysis of the structure and dynamics of water resource usage in the catchment area of the Tobyl River basin, the dynamics of the formation of geoecological conditions of water use in the economic sectors within the Kostanay region of the Republic of Kazakhstan were studied. The analysis revealed a significant load from retur...

On 6 June 2024, we had the privilege of visiting Professor Chang-Pu Sun at the China Academy of Engineering Physics [...]

This design‐based research project explored how various design features of AR‐based learning environments (ARLE) influence students' mathematics self‐efficacy and learning of kinematics. Specifically, five ARLEs with different design features were developed and implemented with 136 seventh‐grade students in two rounds. Data were gathered from pre‐...

In this paper, the final stage of the Petrov classification is carried out. As it is known, the Killing vector fields specify infinitesimal transformations of the group of motions of space V4. In the case where the group of motions G3 acts in a simply transitive way in the homogeneous space V4, the geometry of the non-isotropic hypersurface is dete...

In this paper, abundant analytical solutions of the damped (2 + 1)-dimensional nonlinear Schrödinger equation are achieved by taking advantage of the extended systematic method. By considering various values of parameters, dynamic behaviors of bright, dark soliton, period wave, and kink solitary solutions are displayed with different amplitudes and...

This study discusses the existence of tracking N-dimensional Brownian nanoparticle in an interactive medium, where this tracking is based on Brownian motion analysis. A group of N nanosensors begin the tracking process at the origin of N dimensional space, where the nanosensors serve an important role in detecting and monitoring this nanoparticle....

Systems with predetermined Lyapunov functions play an important role in many areas of applied mathematics, physics and engineering: dynamic optimization methods (objective functions and their modifications), machine learning (loss functions), thermodynamics and kinetics (free energy and other thermodynamic potentials), adaptive control (various obj...

In this paper, we study the Camassa–Holm type equation, which has applications in mathematical physics and engineering. Its applications extend across disciplines, contributing to our understanding of complex systems and helping to develop innovative solutions in diverse areas of research. Our main aim is to construct closed-form solutions of the e...

In this article, exact solutions of the Biswas–Arshed equation are obtained using the extended Weierstrass transformation method (EWTM). This method is widely used in solid-state physics, electrodynamics, and mathematical physics, and it yields exact solution functions involving trigonometric, rational trigonometric, Weierstrass elliptic, wave, and...

Evaluating a real-valued expression to high precision is a key building block in computational mathematics, physics, and numerics. A typical implementation uses a uniform precision for each operation, and doubles that precision until the real result can be bounded to some sufficiently narrow interval. However, this is wasteful: usually only a few o...

This study undertakes a comprehensive analytical and numerical investigation of the nonlinear Kairat model, a significant evolution equation that governs a wide range of physical phenomena, including shallow water waves, plasma physics, and optical fibers. The Kairat model effectively describes the propagation of nonlinear waves in shallow water, c...

In this paper, we apply the powerful sine-Gordon expansion method (SGEM), along with a computational program, to construct some new traveling wave soliton solutions for two models, including the higher-order nonlinear Boussinesq dynamical wave equation, which is a well-known nonlinear evolution model in mathematical physics, and the (1+1)-dimension...

In this paper, we discussed Reduced Differential Transform Method (RDTM) for solving fractional order partial differential equations. In this study, we find analytic approximate solutions of initial value problems of one dimensional homogeneous time fractional Cahn-Hilliard equation by reduced differential transform method. The result of same fract...

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The concept of the empty set and its relation to the construction of natural numbers has profound implications in mathematics, physics, and philosophy. In this paper, we explore von Neumann's construction of natural numbers, particularly the fundamental relation 1 = {0}, and delve into its philosophical and physical implications. We draw parallels...