Let F be an infinite field with characteristic different from two. For a graph G = (V,E) with V = {1, . . . , n}, let S(G;F) be the set of all symmetric n × n matrices A = [ai,j ] over F with ai,j 6= 0, i 6= j if and only if ij ∈ E. We show that if G is the complement of a partial k-tree and m ≥ k + 2, then for all nonsingular symmetric m ×m matrices K over F, there exists an m× n matrix U such...

Recently, some authors proposed the use of symmetric weightsfor computing the elements of cross-efficiency matrix. In spite ofthe fact that the proposed method decreases the number of zeroweights, a large number of zero weights may still exist among inputand output symmetric weights. To decrease the number of input andoutput symmetric weights, this paper improves the proposed secondarygoal mode...

For a real matrix A whose spectrum avoids the imaginary axis, it is shown that the three following, seemingly independent problems, are in fact equivalent. • Characterizing the set of real symmetric solutions of the algebraic Lyapunov inclusion associated with A. • The image of all Nevalinna-Pick interpolations associated with the spectrum of A. • The structure of the Convex Invertible Cone gen...

In this article, we introduce ST decomposition procedure to solve fully fuzzy linear systems. This paper mainly to discuss a decomposition of non singular fuzzy matrix, Symmetric times triangular(ST) decomposition. Every non singular fuzzy matrix can be represented as a product of symmetric matrix S and triangular matrix T in the form of trapezoidal fuzzy number matrices. By this method, we obt...

In wave chaotic scattering, statistical fluctuations of the scattering matrix S and the impedance matrix Z depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. This paper considers the impedance and scattering variance ratios, Xi(z) and Xi(s), where Xi(z) = Var[Z(ij)]/{Var[Z(ii)]Var[Z(jj)]}1/2, Xi(s) = Var[S(ij)]/{Var[S(ii)]Var[S(...

We propose an eigenvalue contractor for symmetric matrices. Given a symmetric interval matrix A and an interval approximation of its eigenvalue sets λ1, . . . ,λn the contractor reduces the entries of A S such that no matrix with eigenvalues in λ1, . . . ,λn is omitted. Our contractor is based on sequentially reducing the entries of A. We discuss properties of the method and demonstrate its per...

At CHES 2006, a DPA countermeasure based on the Fourier Transform was published. This generic countermeasure aims at protecting from DPA any S-box calculation used in symmetric cryptosystems implementations. In this paper, we show that this countermeasure has a flaw and that it can be broken by first order DPA. Moreover, we have successfully put into practice our attack on two different S-box i...

In cryptography, a Substitution box (S-box) is one of the basic components of a symmetric key cryptography. Generally, it transforms a number of m input bits into n output bits. In this paper, there are presented the cryptographic properties of S-boxes and it is introduced a knowledge-based schema for building S-boxes.

afael Navarro nstituto de Ciencia de Materiales de Aragón ICMA onsejo Superior de Investigaciones Científicas-Universidad de Zaragoza, Facultad de Ciencias laza San Francisco s/n 0 009 Zaragoza, Spain -mail: [email protected] Abstract. A theoretical framework to formulate and solve the problem of obtaining the objective refraction of an eye from aberrometric data is presented. Matrix formalism...

In this paper, we show that a matrix A in Mn(C) that has n coneigenvectors, where coneigenvaluesassociated with them are distinct, is condiagonalizable. And also show that if allconeigenvalues of conjugate-normal matrix A be real, then it is symmetric.