On the Maximally Overdetermined System of Linear Differential Equations, I*
نویسندگان
چکیده
The purpose of this paper is to present finiteness theorems and several properties of cohomologies of holomorphic solution sheaves of maximally overdetermined systems of linear differential equations. The proof relies on the finiteness theorem for elliptic systems due to T. Kawai [4], as an analytic tool, and on the theory of stratifications of analytic sets introduced by H. Whitney [8] and [9] ,as a geometric tool. Our goal is the following theorem.
منابع مشابه
A Chebyshev functions method for solving linear and nonlinear fractional differential equations based on Hilfer fractional derivative
The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...
متن کاملTransformations of Ordinary Differential Equations via Darboux Transformation Technique
A new approach for obtaining the transformations of solutions of nonlinear ordinary differential equations representable as the compatibility condition of the overdetermined linear systems is proposed. The corresponding transformations of the solutions of the overdetermined linear systems are derived in the frameworks of the Darboux transformation technique.
متن کاملPositive solution of non-square fully Fuzzy linear system of equation in general form using least square method
In this paper, we propose the least-squares method for computing the positive solution of a $mtimes n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of ...
متن کاملApplication of the linear Differential Equations on the Plane and Elements of Nonlinear Systems, In Economics
In recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. These two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. In this paper I will consider the linear differential equations on the plane (phase diagram) and elements of nonl...
متن کاملOn the convergence of the homotopy analysis method to solve the system of partial differential equations
One of the efficient and powerful schemes to solve linear and nonlinear equations is homotopy analysis method (HAM). In this work, we obtain the approximate solution of a system of partial differential equations (PDEs) by means of HAM. For this purpose, we develop the concept of HAM for a system of PDEs as a matrix form. Then, we prove the convergence theorem and apply the proposed method to fi...
متن کامل