相关论文: Systems of Equations in Elamite Mathematics
In this article, we study some of quadratic equations and their solutions found in the Susa Mathematical Texts (\textbf{SMT}). We show that the Susa scribes used this group of equations in different problems and took a standard approach,…
In this article, we study similarity of triangles in the Susa Mathematical Texts (\textbf{SMT}). We also suggest that the Susa scribes were aware of intercept theory because they used this theorem in solving a complicated system of…
This article studies the application of the Pythagorean theorem in the Susa Mathematical Texts (\textbf{SMT}) and we discuss those texts whose problems and related calculations demonstrate its use. Among these texts, \textbf{SMT No.\,1}…
In this article, we study a particular group of plane figures whose constants are listed in the Susa Mathematical Tablet No.\,3 (\textbf{SMT No.\,3}). We explain possible ways to define these figures and seek to demonstrate that the Susa…
In this article, we study the problems found in the Susa Mathematical Texts No.\,24 and No.\,25 (\textbf{SMT No.\,24} and \textbf{SMT No.\,25}) which concern excavation projects such as canals and holes. We also examine certain Elamite…
This article studies three-dimensional objects and their volumes in Elamite mathematics, particularly those found in the Susa Mathematical Tablet No.\,14 (\textbf{SMT No.\,14}). In our discussion, we identify some basic solids whose volumes…
This paper deals with the existence of solutions for an elliptic system of partial differential equations. The solution method is based on the sub- and super-solutions approach. An application to a stochastic control problem is presented.…
This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software…
We use SMT technology to address a class of problems involving uninterpreted functions and nonlinear real arithmetic. In particular, we focus on problems commonly found in mathematical competitions, such as the International Mathematical…
A system of SU(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz, also called "off shell" Bethe Ansatz. The highest weight property of the solutions is proved. (Part I of a series of…
The simulations of the light scalar mesons on the lattice are presented at the introductory level. The methods for determining the scalar meson masses are described. The problems related to some of these methods are presented and their…
In this paper, we study systems of nonlinear partial differential equations which describe surfaces of constant curvature. From the flatness condition of connection 1-forms, we present a classification of systems of Camassa-Holm-type…
We consider systems of partial differential equations of the form \begin{equation}\nonumber \left\{ \begin{array}{l} u_{xt}=F\left(u,u_x,v,v_x\right),\\ v_{xt}=G\left(u,u_x,v,v_x\right), \end{array} \right. \end{equation} describing…
This paper is to explore a model of the ABS Algorithms dealing with the solution of a class of systems of linear stochastic equations $A\xi=\eta$ when $\eta$ is a $m$-dimensional normal distribution. It is shown that the stepsize $\alpha_i$…
We develop new polynomial methods for studying systems of word equations. We use them to improve some earlier results and to analyze how sizes of systems of word equations satisfying certain independence properties depend on the lengths of…
We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good…
A method to the explict solutions of general systems of algebraic equations is presented via the metric form of affiliated K\"ahler manifolds. The solutions to these systems arise from sets of geodesic second order non-linear differential…
This paper studies systems of linear difference equations on the lattice $\Z^n$ that are invariant under a finite group of symmetries, and shows that there exist solutions to such systems that are also invariant under this group of…
The article highlights the promising ways of providing access to the mathematical software in higher educational institutions. It is emphasized that the cloud computing services implementation is the actual trend of modern ICT pedagogical…
The supersymmetric version of the descent equations following from the Wess-Zumino consistency condition is discussed. A systematic framework in order to solve them is proposed.