Absact This paper deals with the study of test sets of the knapsack problem and simultaneous diophantine approximation. The Graver test set of the knapsack problem can be derived from minimal integral solutions of linear diophantine equations. We present best possible inequalities that must be satisfied by all minimal integral solutions of a linear diophantine equation and prove that for the co...

This paper deals with the study of test sets of the knapsack problem and simultaneous diophantine approximation. The Graver test set of the knapsack problem can be derived from minimal integral solutions of linear diophantine equations. We present best possible inequalities that must be satisfied by all minimal integral solutions of a linear diophantine equation and prove that for the correspon...

In this paper, we use the continuous Legendre wavelets on the interval [0,1] constructed by Razzaghi M. and Yousefi S. [6] to solve the linear second kind integral equations. We use quadrature formula for the calculation of the products of any functions, which are required in the approximation for the integral equations. Then we reduced the integral equation to the solution of linear algebraic ...

‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

In this paper, recent development of the dual BEM in acoustic problem is presented. The role of hypersingular integral equation in the dual BEM for the problems with a degenerate boundary is examined. First, the dual integral formulation is proposed. Based on the formulation, we develop four methods ± the complex-valued dual BEM, the real-part dual BEM, the real-valued dual MRM, and the complet...

We describe how Borel summability of divergent asymptotic expansion can be expanded and applied to nonlinear partial differential equations (PDEs). While Borel summation does not apply for nonanalytic initial data, the present approach generates an integral equation applicable to much more general data. We apply these concepts to the 3-D Navier-Stokes system and show how the integral equation a...

This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

in this paper, the dual area vector of a closed dual spherical curve is kinematically generatedand the dual steineer vector of a motion are extensively studied by the methods of differential geometry.jacobi’s theorems, known for real curves, are investigated for closed dual curves. the closed trajectorysurfaces generated by an oriented line are fixed in a moving rigid body in ir3 , in which the...