## Publications (16)0 Total impact

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**ABSTRACT:**Some boundary value problems for the Cauchy-Riemann equation with non-local boundary conditions in several regions of plane have been investigated and solved by authors. In this paper، by making use of fundamental solutions of Cauchy-Riemann equations and by presenting analytic solutions to the above-mentioned boundary value problems، we try to present an analytic expression for the solution of Cauchy-Riemann equation in the first semi-quarterQuarterly Journal of Science Tarbiat Moallem University. 12/2010; 9(1):29-40. - [Show abstract] [Hide abstract]

**ABSTRACT:**Mixed problems on the unit balls have special complexity. By using a new method we shall give some suﬃcient conditions for existence of solutions of the Feﬀerman’s problem B ([4])Mathematica Moravica. 01/2009; 13(1):13–24. - [Show abstract] [Hide abstract]

**ABSTRACT:**Two dimensional steady-state system of Navier-Stokes equations is considered in this paper. This Navier-Stokes system with three equations and three unknown functions is changed into a system of ﬁrst order diﬀerential equations with four equation and four unknown functions by a suitable change of variable. Then the resulting system is reduced to a new system which consist of two inhomogenuous Cauchy-Riemann equations. Next, necessary conditions are obtained by using of fundamental solution of the Cauchy-Riemann equation. Finally, by using of these necessary conditions, we show that this boundary value problem can be reduced to a system of second kind of Fredholm integral equations which their kernel shoving no singularities. Moreover, these necessary conditions give analytical expressions for the boundary values of the unknown functions of the Navier-Stokes system. At the end, we can construct a numerical scheme for an approximate solution of this system by using of boundary values of unknown functins.Southeast Asian Bulletin of Mathematics 01/2009; 33. - [Show abstract] [Hide abstract]

**ABSTRACT:**The Cauchy-Riemann equation has an important role in the com- plex theory and boundary value problems. In this paper, we consider this equation with a non-local boundary condition in the first quarter. We give an analytic solution for this boundary value problem by making use of analytic continuation in complex theory.International Journal of Pure and Applied Mathematics. 01/2008; 46(2):245-249. - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we first define paradoxes and their sources and how they came to existence. Then we classify the dierent type of paradoxes, describe and explain them and will show that fundamental paradoxes (non-removable) exist in mathematical theories inherently. But removable paradoxes are the result of two kinds of mistakes, one is intentional and second is accidental which made by men or mathematicians. Following that, some removable paradoxes will be shown which is resulted from formulizationism and activizationism trends in new age mathematicians. Those which their entrance in mathematics based on somebodies whose their empirical basis and intuitive thought with fundamental concept of mathematics were not so deep. In the main part of the paper we state and describe some fundamental pa- rameters in mathematics which are the main cases of historical crisis in math- ematics and resulted dierent branches in mathematics and other sciences andMathematical Sciences Quarterly Journal. 01/2007; 1(1). -
##### Article: On Feﬀerman’s Non-existence Problems

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**ABSTRACT:**Feﬀerman has propounded four open Cauchy problems A, B, C and D in Navier-Stokes equations. The problems A and B refer to suﬃcient condition for the existence of solutions, and the problems C and D to the ones for the non-existence of solutions. Here, we shall answer to the problems C and D.Mathematica Moravica. 01/2007; 11:1-7. - Journal of Mathematical Sciences. 01/2007; 1(1).
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**ABSTRACT:**Linear and Non-linear diﬀerence equations are appeared in many ﬁelds of applied mathematics, engineering and physical problems such as natural phenomena, social and economical systems which have essentially discrete elements. In this paper by making use of invariant functions for discrete derivatives [6], we present an analytical method to solve the general form of the n-th order non-homogenous linear diﬀerence equations and some non-linear diﬀerence equations.International Mathematical Forum. 01/2007; 2(11-2):, 533 - 542. - [Show abstract] [Hide abstract]

**ABSTRACT:**Laplace equation and Cauchy-Riemann equations have important role in complex analysis theory and boundary value problems. We know that the real and imaginary parts of Cauchy-Riemann equation are the solutions of Laplace equation. In other words, these functions are har- monic functions. In this paper, we show that there is a similar relation between lin- earized Benjamin-Ono equation and Schrodinger equations. In other words, we can write the solution of linearized Benjamin-Ono equation by real and imaginary parts of Schrodinger equation.01/2007; - [Show abstract] [Hide abstract]

**ABSTRACT:**Navier-Stokes equations are appeared in many engineering and physical problems. According to the non-linearity of these equations solving methods are often numerical. In this paper a theoretical method is presented for investigation and solving of three dimensional steady state Navier-Stokes equations. According to this method, Navier-Stokes system of equations is reduced to the second kind of Fredholm integral equations whith weakly kind singularities in the integral expressions. For this at first, divergence of equation (continuity equation) is reduced to a system of Cauchy-Riemann equations. Next, the three Navier-Stokes equations are reduced to the divergence form of equations. Finally, by making use of fundamental solutions of Cauchy-Riemann equations, the resulted equation will be reduced to the second kind of Fredholm integral equations. So, numerical methods are applicable after this reduction.International Journal of Differential Equations and Applications. 01/2005; 10(2):135-145. - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper is for the investigation and writing of asymptotic expansions of periodic solutions of a singular perturbation problem which includes a nonlinear dynamical system. One of the equations of this system includes small parameter e. Supposing that boundary layers are formed at the both of boundary points of the interval (0, ?). We calculate the asymptotic expansions of outer solution (solution which outside boundary layer) and also two inner solutions (solutions which inside boundary layer). Then by making use of arbitrary constants in the general solutions of differential equations, periodic conditions and matching conditions are imposed. Finally the outer solution and the two inner solutions are connected by these conditions in order to obtaining a global solutionSoutheast Asian Bulletin of Mathematics 05/2004; 28(1):41-57. - [Show abstract] [Hide abstract]

**ABSTRACT:**In the classic theory of complex analysis, if an analytic function was given on a non-zero measure subset of IR� or on a zero measure subset of IR�, then this analytic function can be determined on the whole of its analytic domain. In this paper, we want to determine the value of analytic function at the inside of its analytic domain, when its values were only given on the boundary of its domain. To do this, we solve the Cauchy-Riemann differential equation with special kind of boundary conditionsSoutheast Asian Bulletin of Mathematics 05/2004; 28(1):33. - [Show abstract] [Hide abstract]

**ABSTRACT:**Linear and Non-linear difference equations are appeared in many fields of applied mathematics, engineering and physical problems such as natural phenomena, social and economical systems which have essen- tially discrete elements. In this paper by making use of invariant functions for discrete deriva- tives (6), we present an analytical method to solve the general form of the n-th order non-homogenous linear difference equations and some non-linear difference equations. - [Show abstract] [Hide abstract]

**ABSTRACT:**There are some physical phenomena and engineering problems whose math- ematical models appear as difference equations with variable coefficients. In this paper, at first we define the concept of discrete multiplicative derivative and discrete multiplicative integration, then the invariant function with respect to this derivative is introduced. Next differential equations with this type of derivative are considered. In the final section, we consider some initial and boundary value problems which include difference equations with variable coefficients. At the end, by making use of linear algebra and numerical differentiation and discrete multiplicative integration, we present an analytic-numerical method for solving these differ- ence equations. - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, at first we define the concept of additive and multiplicative discrete differentiations. Then, by considering these definitions of derivatives, the invariant functions with respect to additive and multiplicative derivatives are introduced respectively. Next, the differential equations with these kinds of derivatives are considered. In the main sections, some boundary value and initial value problems in- cluding these differential equations are investigated and solved. In the second forthcoming part of this paper additive and multiplicative discrete integration are defined and considered. Finally by making use of solutions of these dif- ferential equations, the solutions of some nonlinear difference equations are found. - [Show abstract] [Hide abstract]

**ABSTRACT:**Mixed problems are changed to boundary value prob-lems by making used of Laplace transform. In classical boundary value problems, boundary conditions are local, but boundary con-ditions could be global ([2, 3, 11]). Every boundary value problem depends on a potential method in mathematical-physics theory. Of course, one couldn't solve some many problems by potential methods. We shall give a method in which one could reduce every boundary value problem to the second kind Fredholm in-tegral equations and then solve it. In fact, we could obtain solu-tion of every local, non-local or global boundary value problem by this method. Finally, we shall give some sufficient conditions for existence of solutions of the Fefferman's problem A ([4]).

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