Mathematical Physics Research Articles

Exact Solutions of Nonlinear Equations in Mathematical Physics via Negative Power Expansion Method

Exact Solutions of Nonlinear Equations in Mathematical Physics via Negative Power Expansion Method

Theory of a superluminous vacuum quanta as the fabric of Space

Our observations of magneton with Ferrolens shows evidence pointing to such magneton entity, and more evidently in recent results with the synthetic vacuum unipole experiments. Physics formalism ansatz novel model analyses demonstrate how vacuum quanta may have sufficient energy for vacuum genesis, by constructing eigen spinors of zero_point microblackhole Hamiltonian quantum mechanics with Helmholtz decomposition matrix of gradient and rotational tensors, that are characteristic of translational vortex fields. With these mathematical physics processes, we obtain resulting energy fields spatial property partial differential equations characterizing eigen state energetics of zero point vacuum quagmire, as well as eigen state vortex fields of micro black hole, both together making up plasmodial zones within quagmire. Specific eigen spinors Hamiltonian partial differential equations quantifying energy and fields eigen functions. Vacuum that is dipole vacuum may have superposition of complex input of quagmire vortex fields acting to create non–hermitian quantum relativistic physics.

EA3: A softmax algorithm for evidence appraisal aggregation.

Real World Evidence (RWE) and its uses are playing a growing role in medical research and inference. Prominently, the 21st Century Cures Act—approved in 2016 by the US Congress—permits the introduction of RWE for the purpose of risk-benefit assessments of medical interventions. However, appraising the quality of RWE and determining its inferential strength are, more often than not, thorny problems, because evidence production methodologies may suffer from multiple imperfections. The problem arises to aggregate multiple appraised imperfections and perform inference with RWE. In this article, we thus develop an evidence appraisal aggregation algorithm called EA3. Our algorithm employs the softmax function—a generalisation of the logistic function to multiple dimensions—which is popular in several fields: statistics, mathematical physics and artificial intelligence. We prove that EA3 has a number of desirable properties for appraising RWE and we show how the aggregated evidence appraisals computed by EA3 can support causal inferences based on RWE within a Bayesian decision making framework. We also discuss features and limitations of our approach and how to overcome some shortcomings. We conclude with a look ahead at the use of RWE.

SPECIAL SPLINE APPROXIMATION FOR THE SOLUTION OF THE NON-STATIONARY 3-D MASS TRANSFER PROBLEM

In this paper we consider the conservative averaging method (CAM) with special spline approximation for solving the non-stationary 3-D mass transfer problem. The special hyperbolic type spline, which interpolates the middle integral values of piece-wise smooth function is used. With the help of these splines the initial-boundary value problem (IBVP) of mathematical physics in 3-D domain with respect to one coordinate is reduced to problems for system of equations in 2-D domain. This procedure allows reduce also the 2-D problem to a 1-D problem and thus the solution of the approximated problem can be obtained analytically. The accuracy of the approximated solution for the special 1-D IBVP is compared with the exact solution of the studied problem obtained with the Fourier series method. The numerical solution is compared with the spline solution. The above-mentioned method has extensive physical applications, related to mass and heat transfer problems in 3-D domains.

The Geomorphological Factors and Its Implications for The Tidal Energy Installations in Java, Indonesia

This study aims to place the tidal energy installation effectively in Indonesia based on geomorphological factors. The survey method was used to analyze the characteristics of beaches in Indonesia. Mathematical physics model was implemented to find the new formulas based on geomorphological factors. Tides are the result of gravitational attraction and the centrifugal effect, which is the drive In the earth-moon system, tidal generating forces are the resultant forces that cause tides, namely: the earth-moon system (FS) centrifugal force and the moon's gravitational force (FB). FS works in the center of the mass of the earth-moon system whose mass point is located on the 3/4 radius of the earth. The style of tidal generator caused by the moon can be calculated by combining Newton's universal gravitational law .The results of this study consist of F = m ac, where the style of the tidal generator caused by the moon can be calculated by combining newton's universal gravitational law in equation and newton's second law of motion in Equation. The another results is tan = , where the formula takes into account constants (K) based on slopes. The last result is the constants (K) for each land form starting on 0,00 untill 1,00. The north coast of Java is more suitable for tidal energy installations because the land form is dominated by alluvium plains of the quaternary age with a lower risk than the southern region of Java. The effectiveness of tidal energy installation depends on the characteristics of the land form. In alluvial plains, the quaternary age of the alluvial plains is more suitable than the hill form volcanic quaternary, tertiary volcanic, and tertiary holokarst.

Scattering matrix pole expansions for complex wave numbers inR-matrix theory

In this follow-up article to [Shadow poles in the alternative parametrization of R-matrix theory, Ducru (2020)], we establish new results on scattering matrix pole expansions for complex wavenumbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory, and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wavenumbers. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift $\boldsymbol{S}$ and penetration $\boldsymbol{P}$ functions: the legacy Lane \& Thomas "force closure" approach, versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF. In this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and unveil new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii $a_c$. We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix -- cancelling spurious poles and guaranteeing generalized unitarity -- while still being able to close channels below thresholds.

Matematização da Natureza: do século XVI ao XVIII

This work weaves a timeline of the changes suffered in relation to the way of viewing science and mathematics throughout the 16th and 18th centuries. Transitions between Aristotelian science and modern science are addressed. In the interval in question, there were different traditions of thought, the inclusion of numbers in scientific thought, the Baconian experimental tradition, naturalistic beliefs, the so-called scientific revolution and the universalization of mechanical laws, the mathematization of nature and the unification of what we call mathematical physics. From this historical and philosophical overview, it can be seen that science and mathematics have undergone substantial mutations throughout their historical constructions, in order to make nature mathematized.

A linear-algebraic method to compute polynomial PDE conservation laws

We present a method to compute polynomial conservation laws for systems of partial differential equations (PDEs). The method only relies on linear algebraic computations and is complete, in the sense it can find a basis for all polynomial fluxes that yield conservation laws, up to a specified order of derivatives and degree. We compare our method to state-of-the-art algorithms based on the direct approach on a few PDE systems drawn from mathematical physics.

Multiple wave solutions for nonlinear burgers equations using the multiple exp-function method

In this paper, we use the multiple exp-function method to explicity present traveling wave solutions, double-traveling wave (DTW) solutions and triple-traveling wave solutions (TWs) which include one-soliton, double-soliton and triple-soliton solutions for nonlinear partial differential equations (NPDEs) via, the (2+1)-dimensional and (3+1)-dimensional nonlinear Burgers PDEs in mathematical physics. In this work, we build some series of straightforward and new solutions successfully with the help of a computerized symbol computational software package like Maple or Mathematica. We will make some drawings in some cases with specific values for the relevant parameters for each obtained solutions such as the one-traveling wave solutions, double-traveling wave solutions and TWs. This method is efficient and powerful in solving a wide class of NPDEs.

On one class of solutions of the quasilinear matrix differential equations

In the mathematical description of various phenomena and processes that arise in mathematical physics, electrical engineering, economics, one has to deal with matrix differential equations. Therefore, these equations are relevant both for mathematicians and for specialists in other areas of natural science. Many studies are devoted to them, in which the solvability of matrix equations in various function spaces, boundary value problems for matrix differential equations, and other problems were investigated. In this article, a quasilinear matrix equation is considered, the coefficients of which can be represented in the form of absolutely and uniformly converging Fourier series with coefficients and frequency slowly varying in a certain sense. The problem is posed of obtaining sufficient conditions for the existence of particular solutions of a similar structure for the equation under consideration. For this purpose, the corresponding linear equation is considered first. It is written down in component-wise form, and, based on the assumptions made, the existence of the only particular solution of the specified structure is proved. Then, using the method of successive approximations and the principle of contracting mappings, the existence of a unique particular solution of the indicated structure for the original quasilinear equation are proved.

Singularity Universe or Parallel Universes? – MSP Theory (Multiple Singular and Parallel Theory)

This paper analyzes the issue of the singularity universe and parallel universes. Multiple universes exist, but not inside one to another, as presented in the work “Is It Plausible to Have Universes Inside Universes - The Interuniversal Numbers”. The interuniversal numbers show that every universe has a singularity structure, but parallel cases. The parallel cases are deactivated forms. This means that making time travel causes changes to all the space-time patterns. Then, it is not plausible to go to another point of space-time and this to happen to multiple universes. The parallel universes are different cases of the same universe and then we live a different case of reality. The reason for this is the singularity. Without singularity, it is not plausible to have multiple universes. But, parallel universes are inactive cases of the current universe, and the only way to break them is by following the way described in the paper “Time travel - According to Mathematical Axiomatic Physics”.

Improved Numerical Computation to Solve Lane-Emden type Equations

Lane-Emden equation is also of fundamental importance in mathematical physics, celestial mechanics,and computer science. It can be used to describe stellar structures, equilibrium density distribution in polytrophicisothermal gas, thermal behavior in mutual attraction of its molecules. An improved numerical method is developed for solving Lane-Emden type differential equations. The method is based on power series solutions of differential equations and Maclaurin series expansion. A python program is written to carry out numerical calculations. Five examples are solved and shown in this paper, the solutions obtained by the program are compared with the exact solutions of differential equation, an excellent agreement is found between them. The present method improves runtime.

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Exact solutions to nonlinear differential equations play an undeniable role in various branches of science. These solutions are often used as reliable tools in describing the various quantitative and qualitative features of nonlinear phenomena observed in many fields of mathematical physics and nonlinear sciences. In this paper, the generalized exponential rational function method and the extended sinh-Gordon equation expansion method are applied to obtain approximate analytical solutions to the space-time conformable coupled Cahn–Allen equation, the space-time conformable coupled Burgers equation, and the space-time conformable Fokas equation. Novel approximate exact solutions are obtained. The conformable derivative is considered to obtain the approximate analytical solutions under constraint conditions. Numerical simulations obtained by the proposed methods indicate that the approaches are very effective. Both techniques employed in this paper have the potential to be used in solving other models in mathematics and physics.

Optimal constants in non-commutative Hölder inequality for quasi-norms

We resolve an open problem due to B. Simon [Trace ideals and their applications, Cambridge University Press, Cambridge–New York, 1979; Trace ideals and their applications, American Mathematical Society, Providence, RI, 2005] concerning optimal constants in Hölder inequality for certain quasi-normed principal ideals of importance in Mathematical Physics and Noncommutative Geometry.

Mathematical modeling of filling the CCM mold with liquid metal during its supply from a rotating submersible nozzle

Experimental studies of the flow of liquid metal in CCM mold are long, complex and labor consuming process. Therefore, mathematical modeling by numerical methods is increasingly used for this purpose. The article considers a new technology for liquid metal supply into a mold. The authors present original patented design of the device, consisting of direct-flow and rotating bottom nozzles. The main results of investigations of the melt flow in the mold are considered. The objects of research were hydrodynamic and heat flows of liquid metal at new process of steel casting into a CCM mold of rectangular section. The result is spatial mathematical model describing flows and temperatures of liquid metal in the mold. To simulate the processes occurring during metal flow in the mold, special software was designed. Theoretical calculations are based on fundamental equations of hydrodynamics, equations of mathematical physics (equation of heat conduction taking into account mass transfer) and proven numerical method. The area under study was divided into elements of finite dimensions; for each element, resulting system of equations was written in difference form. The results are fields of velocities and temperatures of metal flow in the mold volume. A calculation program was compiled based on developed numerical schemes and algorithms. An example of calculation of steel casting into a mold of rectangular cross-section, and flow diagrams of liquid metal along various sections of the mold are given. Vector flows of liquid metal in different sections of the mold are clearly presented at different angles of rotation of the deep-bottom nozzle. The authors have identified the areas of intense turbulence. Metal flows of the described technological process were compared with traditional metal supply through a fixed bottom nozzle.

Dynamical structures of exact soliton solutions to Burgers’ equation via the bilinear approach

The Cole–Hopf transformation is used to search for exact multiple wave solutions of Burgers’ equation. Particularly, solitary wave solutions and their interaction solutions are explicitly given, and a fission phenomenon is found, which is tough to be found by other traditional methods. Different solutions are presented with different combinations of elementary functions and a necessary condition for fission is proposed. Based on the bilinear formalism and with the aid of symbolic computation, we also determine two classes of rational solutions, rogue wave solutions and rogue–kink wave solutions, using various ansätze. To exhibit dynamics, we make diverse graphical analyses for the presented solutions, which show that the solutions are reliable in both mathematical physics and engineering.

Numerical simulation for coupled nonlinear Schrödinger–Korteweg–de Vries and Maccari systems of equations

The primary goal of this paper is to seek solutions to the coupled nonlinear partial differential equations (CNPDEs) by the use of q-homotopy analysis transform method (q-HATM). The CNPDEs considered are the coupled nonlinear Schrödinger–Korteweg–de Vries (CNLS-KdV) and the coupled nonlinear Maccari (CNLM) systems. As a basis for explaining the interactive wave propagation of electromagnetic waves in plasma physics, Langmuir waves and dust-acoustic waves, the CNLS-KdV model has emerged as a model for defining various types of wave phenomena in mathematical physics, and so forth. The CNLM model is a nonlinear system that explains the dynamics of isolated waves, restricted in a small part of space, in several fields like nonlinear optics, hydrodynamic and plasma physics. We construct the solutions (bright soliton) of these models through q-HATM and present the numerical simulation in form of plots and tables. The solutions obtained by the suggested approach are provided in a refined converging series. The outcomes confirm that the proposed solutions procedure is highly methodological, accurate and easy to study CNPDEs.

Investigation of Exact Solutions of some Nonlinear Evolution Equations via an Analytical Approach

This study investigates exact analytical solutions of some nonlinear partial differential equations arising in mathematical physics. To this reason, the Kudryashov-Sinelshchikov equation, the ZK-BBM equation and the Gardner equation have been considered. With the implementation of the trial solution algorithm, solitary wave, bright, dark and periodic exact traveling wave solutions of the considered equations have been attained. The solutions have been checked and graphs have been given via package programs to see the behavior of the waves.

Distinct solutions of nonlinear space–time fractional evolution equations appearing in mathematical physics via a new technique

Abstract In this paper, we furnished novel and different traveling wave solutions to the nonlinear space–time fractional Klein–Gordon (KG) equation and the nonlinear space–time fractional symmetric regularized long wave (SRLW) equation. The considered equations are turned into ordinary differential equations with the aid of fractional composite transformation in the sense of conformable fractional derivative and then the proposed improved tanh method along with Riccati equation is employed. Consequently, fresh and further general solutions in the shape of kink, bell, cuspon, compacton, periodic etc. are successfully obtained, which are compared with those in the literature. Further, it is important to point out that some of our solutions is in good harmony for a special case with already published results which in turn validates our other solutions. The comparison ensures the novelty of the proposed technique which might be taken into account for further research in future.

Super fiber bundles, connection forms, and parallel transport

The present work provides a mathematically rigorous account on super fiber bundle theory, connection forms, and their parallel transport, which ties together various approaches. We begin with a detailed introduction to super fiber bundles. We then introduce the concept of so-called relative supermanifolds as well as bundles and connections defined in these categories. Studying these objects turns out to be of utmost importance in order to, among other things, model anticommuting classical fermionic fields in mathematical physics. We then construct the parallel transport map corresponding to such connections and compare the results with those found by other means in the mathematical literature. Finally, applications of these methods to supergravity will be discussed, such as the Cartan geometric formulation of Poincaré supergravity as well as the description of Killing vector fields and Killing spinors of super Riemannian manifolds arising from metric reductive super Cartan geometries.