In this note, we show how optimal or approximate weighted independent sets in k-partite graphs may yield to a good approximate weighted independent set in general graphs. Precisely, optimal solutions in bipartite graphs do yield to a 2 ∆(G) approximation and, more generally, ρ-approximate solutions in k-partite graphs yield to a k ∆(G)ρ-approximation in general graphs.

Approximation of solutions of integral equations by networks with kernel units is investigated theoretically. There are derived upper bounds on speed of decrease of errors in approximation of solutions of Fredholm integral equations by kernel networks with increasing numbers of units. The estimates are obtained for Gaussian and degenerate kernels.

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

In order to improve the approximation of spatial derivatives without meshes, a set of meshfree numerical schemes for derivative terms is developed, which is compatible with the coordinates of Cartesian, cylindrical, and spherical. Based on the comparisons between numerical and theoretical solutions, errors and convergences are assessed by a posteriori method, which shows that the approximations...

A multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem ...

In this note, we show how optimal or approximate weighted independent sets in k-partite graphs may yield to a good approximate weighted independent set in general graphs. Precisely, optimal solutions in bipartite graphs do yield to a 2 ∆(G) approximation and, more generally, ρ-approximate solutions in k-partite graphs yield to a k ∆(G)ρ-approximation in general graphs.

Stochastic solutions are obtained for the Maxwell-Vlasov equation in the approximation where magnetic field fluctuations are neglected and the electrostatic potential is used to compute the electric field. This is a reasonable approximation for plasmas in a strong external magnetic field. Both Fourier and configuration space solutions are constructed. PACS: 52.25Dg, 02.50Ey

We study existence and approximation of solutions of some Neumann boundary-value problems in the presence of an upper solution β and a lower solution α in the reversed order (α ≥ β). We use the method of quasilinearization for the existence and approximation of solutions. We also discuss quadratic convergence of the sequence of approximants.