In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

Multi-criteria decision making is used in many areas of human activities. Each alternative in multi-criteria decision making problem can be described by a set of criteria. Criteria can be qualitative and quantitative. They usually have different units of measurement and different optimization direction. The normalization aims at obtaining comparable scales of criteria values. The normalization ...

Signomial programming problems with discrete variables (SPD) appear widely in real-life applications, but they are hard to solve. This paper proposes an enhanced logarithmic method to reformulate the SPD problem as a mixed 0-1 linear program (MILP) with a minimum number of binary variables and inequality constraints. Both of the theoretical analysis and numerical results strongly support its su...

Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic behavior of some combinatorially relevant sequences, such as Motzkin and Schröder numbers, sequences of values of some classic orthogonal polynomials, and ma...

We present a proximal point method to solve multiobjective problems based on the scalarization for maps. We build a family of a convex scalar strict representation of a convex map F with respect to the lexicographic order on R and we add a variant of the logarithmquadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced on the quadratic term and ...

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Recently, Ethernet celebrated its twentieth anniversary. Over those years, the processing speed of the attached hosts has increased by several orders of magnitude, to the point where the relative bandwidth of a 10 Mbps Ethernet has fallen from more than adequate to support large enterprise networks (whose utilizations were typically only a few percent, anyway), to marginally fast enough to supp...

In a recent paper [3], Y. Cao and Y. Xu established the Galerkin method for weakly singular Fredholm integral equations that preserves the singularity of the solution. Their Galerkin method provides a numerical solution that is a linear combination of a certain class of basis functions which includes elements that reflect the singularity of the solution. The purpose of this paper is to extend t...