In analogy with the classical Kazhdan-Lusztig polynomials for Coxeter groups, Elias, Proudfoot and Wakefield introduced concept of matroids. It is known that both matroid can be considered as special cases Kazhdan-Lusztig-Stanley locally finite posets. framework polynomials, we study inverse functions define We also compute these boolean matroids uniform As an unexpected application obtain a ne...

Let p(x) be a hyperbolic polynomial–like function of the form p(x) = (x − r1)1 · · · (x − rN )N , where m1, . . . ,mN are given positive real numbers and r1 < r2 < · · · < rN . Let x1 < x2 < · · · < xN−1 be the N − 1 critical points of p lying in Ik = (rk, rk+1), k = 1, 2, . . . , N−1. Define the ratios σk = xk−rk rk+1−rk , k = 1, 2, . . . , N−1. We prove that mk mk+···+mN < σk < m1+···+mk m1+·...

A Class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional Bratu's problem are presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Associated boundary f...

in this paper, an effective technique is proposed to determine thenumerical solution of nonlinear volterra-fredholm integralequations (vfies) which is based on interpolation by the hybrid ofradial basis functions (rbfs) including both inverse multiquadrics(imqs), hyperbolic secant (sechs) and strictly positive definitefunctions. zeros of the shifted legendre polynomial are used asthe collocatio...

In the present work, under some di¤erentiability conditions on the potential functions , we …rst reduce the inverse scattering problem (ISP) for the polynomial pencil of the Scroedinger equation to the corresponding ISP for the generalized matrix Scrödinger equation . Then ISP will be solved in analogy of the Marchenko method. We aim to establish an e¤ective algorithm for uniquely reconstructin...

As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l1 or l∞ norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l1 and l∞ norms. It has been proved that the inverse maximum-we...

A necessary and sufficient condition is given for the existence of a polynomial left inverse for a polynomial (FIR) system. Additionally, random systems are defined, and a sufficient condition is given for almost sure existence of a polynomial inverse. The two results extend previous work in single-input, multiple-output systems to the case of multiple input systems and to functions of several ...