We present and compare various approaches to a classical selection problem on Graphics Processing Units (GPUs). The selection problem consists in selecting the k-th smallest element from an array of size n, called k-th order statistic. We focus on calculating the median of a sample, the n/2-th order statistic. We introduce a new method based on minimization of a convex function, and show its nu...

Obtainment of exact value or high lower bound on the r-th order nonlinearity of Boolean function is a very complicated problem (especial if r > 1). In a number of papers lower bounds on the r-th order nonlinearity of Boolean function via its algebraic immunity were obtain for different r. This bounds is rather high for function with maximum near maximum possible algebraic immunity. In this pape...

We are concerned with the asymptotic behavior of solutions of an nth order linear dynamic equation on a time scale in terms of Taylor monomials. In particular, we describe the asymptotic behavior of the so-called (first) principal solution in terms of the Taylor monomial of degree n−1. Several interesting properties of the Taylor monomials are established so that we can prove our main results.

In this paper, we theoretically prove a set of fundamental conditions pertaining discrete velocity sets and corresponding weights. These conditions provide sufficient conditions for a priori formulation of lattice Boltzmann models that automatically admit correct hydrodynamic moments up to any given N-th order.

The method of symmetric polynomials (MSP) was developed for computation analytical functions of matrices, in particular, integer powers of matrix. MSP does not require for its realization finding eigenvalues of the matrix. A new type of recurrence relations for symmetric polynomials of order n is found. Algorithm for the numerical calculation of high powers of the matrix is proposed.This comput...