Recently, Kenyon and Wilson introduced a certain matrix M in order to compute pairing probabilities of what they call the double-dimer model. They showed that the absolute value of each entry of the inverse matrix M−1 is equal to the number of certain Dyck tilings of a skew shape. They conjectured two formulas on the sum of the absolute values of the entries in a row or a column of M−1. In this...

In this note we exploit the knowledge embodied in innnitesi-mal generators of Markov processes to compute eeciently and economically the transient solution of continuous time Markov processes. We consider the Krylov subspace approximation method which has been analysed by Y. Saad for solving linear diierential equations. We place special emphasis on error bounds and stepsize control. We discuss...

On a vu qu’on pouvait réécrire (BP) comme un problème de programmation linéaire et que donc on pouvait implémenter cette procédure de manière efficace même en grandes dimensions N . D’un point de vue théorique, on a montré que si une matrice de mesure A ∈ Rm×N permettait la reconstruction de n’importe quel signal de Σs par Basis Pursuit alors nécessairement m & s log(eN/s), càd on doit avoir au...

‎This paper obtains the exact solutions of the wave equation as a second-order partial differential equation (PDE)‎. ‎We are going to calculate polynomial and non-polynomial exact solutions by using Lie point symmetry‎. ‎We demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎A generalized procedure for polynomial solution is pr...

abstract. suppose g is an nvertex and medge simple graph with edge set e(g). an integervalued function f: e(g) → z is called a flow. tutte was introduced the flow polynomial f(g, λ) as a polynomial in an indeterminate λ with integer coefficients by f(g,λ) in this paper the flow polynomial of some dendrimers are computed.

the wiener index is a graph invariant that has found extensive application in chemistry. inaddition to that a generating function, which was called the wiener polynomial, who’sderivate is a q-analog of the wiener index was defined. in an article, sagan, yeh and zhang in[the wiener polynomial of a graph, int. j. quantun chem., 60 (1996), 959969] attainedwhat graph operations do to the wiener po...

The analytical least-squares method has been generalized and extended for designing 16 types of two-dimensional FIR filters with quadrantally symmetric or antisymmetric frequency responses. By means of a closed-form transformation matrix, this fast design method can determine the filter’s coefficients very effectively without a recourse to an iterative optimization technique or matrix inversion...

We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner approximation algorithm, that in many case estimates exact bounds. To our knowledge, this is the first algorithm that is able to guarantee exactness. We illus...