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A two-sided inverse of the differential operator for the unbounded system of elliptic equations on Lipshitz domains was obtained. It was based on a special convolution of sequences. The Dirichlet and Neumann problems for the unbounded systems were reduced to the systems of Fredholm integral equations of either the first kind or the second kind. All equations in integral systems distinguish only by...
A system with infinite quantity of the boundary integral equations which is equivalent to the Dirichlet problem for some triangular system of elliptical equations and its weak formulation has been considered. A recurrent algorithm for solving such systems has been constructed. It involves finding the components of the solution using the boundary elements method step-by-step. The convergence orders...
This paper presents an improved multi-object segmentation algorithm. First, a critical look is focused on utilizing vector calculus operator and combinational operator to rewrite Dirichlet integral into a matrix form, and boundary condition is defined to obtain the needed harmonic function, from which a set of probabilistic values for each pixel are calculated and the maximum is used to label the...
The Dirichlet problem for the 2-D Helmholtz equation in an exterior domain bounded by closed curves and open arcs is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind and index zero, which is uniquely solvable. It means, that the solution can be computed by standard codes.
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