We consider the dissipative singular q-Sturm-Liouville operators acting in Hilbert space L2 w,q(R+), that extensions of a minimal symmetric operator with deficiency indices (2, 2) (in limit-circle case).We construct self-adjoint dilation and its incoming outgoing spectral representations, which make it possible to determine scattering matrix terms Weyl-Titchmarsh function operator. also functio...

Abs t rad -Th i s paper presents all controllers for the general ~'® control problem (with no assumptions on the plant matrices). Necessary and sufficient conditions for the existence of an ~® controller of any order are given in terms of three Linear Matrix Inequalities (LMIs). Our existence conditions are equivalent to Scherer's results, but with a more elementary derivation. Furthermore, we ...

in this paper we introduce the root of a fuzzy number, and we present aniterative method to nd it, numerically. we present an algorithm to generatea sequence that can be converged to n-th root of a fuzzy number.

In [1], Dazheng studies Fibonacci matrices, namely matrices M such that every entry of every positive power of M is either 0 or plus or minus a Fibonacci number. He gives 40 such four-byfour matrices. In the following, we give an interpretation of these matrices, from which we give simpler proofs of several of his theorems. We also determine all two-by-two Fibonacci matrices. Let £ = e be a pri...

B.Ya. Ryabko, " Data compression by means of a book stack, Probl. Abstract-Two of the algebraic constructions for Costas arrays, designated as T4 and C,, are described in detail, and necessary and sufficient conditions are given for the sizes of Costas arrays for which these constructions occur. These constructions depend on the existence of primitive roots satisfying certain equations in finit...

We propose a geometric approach to the BRST-symmetries of the Lagrangian of a topological quantum field theory on a four dimensional manifold based on the formalism of superconnections. Making use of a graded q-differential algebra, where q is a primitive N -th root of unity, we also propose a notion of ZN -connection which is a generalization of a superconnection. In our approach the Lagrangia...

We present in this paper a canonical form for the elements in the ring of continuous piecewise polynomial functions. This new representation is based on the use of a particular class of functions {Ci(P ) : P ∈ Q[x], i = 0, . . . , deg(P )} defined by Ci(P )(x) = { 0 if x ≤ α P (x) if x ≥ α where α is the i-th real root of the polynomial P . These functions will allow us to represent and manipul...

In this paper we show that the multicast problem in trees can be expressed in term of arranging rows and columns of boolean matrices Given a p q matrix M with entries the shadow of M is de ned as a boolean vector x of q entries such that xi if and only if there is no entry in the ith column of M and xi otherwise The shadow x can also be seen as the binary expression of the integer x Pq i xi q i...

The Q-state Potts model can be extended to noninteger and even complex Q by expressing the partition function in the Fortuin-Kasteleyn (F-K) representation. In the F-K representation the partition function Z(Q,a) is a polynomial in Q and v=a-1 (a=e(betaJ)) and the coefficients of this polynomial, Phi(b,c), are the number of graphs on the lattice consisting of b bonds and c connected clusters. W...

Recently, Guo and Lin [SIAM J. Matrix Anal. Appl., 31 (2010), 2784–2801] proposed an efficient numerical method to solve the palindromic quadratic eigenvalue problem (PQEP) . 2ATC QCA/ ́ D 0 arising from the vibration analysis of high speed trains, where A; Q 2 C n have special structures: both Q and A are, among others, m m block matrices with each block being k k (thus, n D mk), and moreover, ...