In this work we present a method, based on the use of Bernstein polynomials, for the numerical resolution of some boundary values problems. The computations have not need of particular approximations of derivatives, such as finite differences, or particular techniques, such as finite elements. Also, the method doesn’t require the use of matrices, as in resolution of linear algebraic systems, no...

The security framework in Ad-hoc Networks (ANET) continues to attract the attention of researchers, although significant work has been accomplished already. Researchers last couple years have shown quite an improvement Identity Dependent Cryptography (IDC). Security ANET is hard attain due vulnerability links (Wireless). IDC encompasses Polynomial Interpolations (PI) such as Lagrange, curve-fit...

This paper deals with the problem of graph matching or network alignment for Erd?s–Rényi graphs, which can be viewed as a noisy average-case version isomorphism problem. Let G and $$G'$$ G(n, p) graphs marginally, identified their adjacency matrices. Assume that are correlated such $${\mathbb {E}}[G_{ij} G'_{ij}] = p(1-\alpha )$$ . For permutation $$\pi $$ representing latent between vertices ,...

It has been recently proved that a variety of associative PI-superalgebras with graded involution finite basic rank over field characteristic zero is minimal fixed ⁎-graded exponent if, and only it generated by subalgebra an upper block triangular matrix algebra, A:=UTZ2⁎(A1,…,Am), equipped suitable elementary Z2-grading involution. Here we give necessary sufficient conditions so IdZ2⁎(A) facto...

Techniques from algebraic geometry, in particular the hard Lefschetz theorem, are used to show that certain finite partially ordered sets O x derived from a class of algebraic varieties X have the k-Sperner property for all k. This in effect means that there is a simple description of the cardinality of the largest subset of C) x containing no (k + 1)-element chain. We analyze, in some detail, ...

f~rmed by an algorith m (detailed below) under which th e degrees no, nl , ... nt of the Pi (x) decrease monotonically. We denote degree drop by d i = ni nj _ 1 ~ 1; we distinguish the lead ing and maximum coefficien t magnitudes of the Pi (x) by Ci = I p\/) I and gi ~ I pI!') I; we deno te the norms of the P;(x) by ej = (~(p\,:»2) 1/2; and we distinguish the degree of the initia l Po(x) by N =...

let $g$ be a simple graph of order $n$‎. ‎we consider the‎ ‎independence polynomial and the domination polynomial of a graph‎ ‎$g$‎. ‎the value of a graph polynomial at a specific point can give‎ ‎sometimes a very surprising information about the structure of the‎ ‎graph‎. ‎in this paper we investigate independence and domination‎ ‎polynomial at $-1$ and $1$‎.

We prove that a polynomial mapping $$f:{{\mathbb {K}}^{n}}\rightarrow {\mathbb {K}}^{p}$$ , where $${\mathbb {K}}=\mathbb {R}$$ or $$\mathbb {C}$$ attains Lipschitz trivial value $$\mathbf{c}$$ if and only there exist $$g:{\mathbb {K}}^m \rightarrow for which the is regular of properness, linear surjective projection $$\pi :{{\mathbb {K}}^m$$ such $$f = g\circ \pi $$ . The integer m {K}}$$ -cod...

| In this paper, a new class of higher-order feedforward neural networks, called ridge polynomial networks (RPN) is formulated. The new networks are shown to uniformly approximate any continuous function on a compact set in multidimensional input space with any degree of accuracy. Moreover, these networks have an eecient and regular architecture as compared to ordinary higher-order feedforward ...