A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

In this paper, a new method for estimating the linear regression coefficients approximation is presented based on Z-numbers. In this model, observations are real numbers, regression coefficients and dependent variables (y) have values ​​for Z-numbers. To estimate the coefficients of this model, we first convert the linear regression model based on Z-numbers into two fuzzy linear regression mode...

Let H 0 (t); H 1 (t) be real 2 2 matrix{functions with entries from L 1 (0; 1), H 1 (t) = H 1 (t); H 0 (t) 0. We associate with these data the solution of the Cauchy problem for the diierential system dA(t; z) dt = A(t;z)fzH 0 (t) + H 1 (t)gJ; A(0;z) = 1 2 ; where J = 0 1 ?1 0 : The matrix{function A(z) = A(1;z) is called the monodromy matrix of the corresponding system 5]. More generally, let ...

(1) d/dxX(z) = A{z)X{z), where X(z) is an n x 1 column vector and A(z) is an n x n matrix of singlevalued meromorphic functions in a neighbourhood of the (isolated) singular point 0. Sometimes we write A instead of A(z) but we always consider a matrix of functions with such a notation unless explicitly stated otherwise. Each fundamental solution matrix for (1) can be represented near zero as (2...

We give the infinite-dimensional representation for the ellipticK-operator satisfying the boundary Yang-Baxter equation. By restricting the functional space to finite-dimensional space, we construct the elliptic K-matrix associated to Belavin’s completely Z-symmetric R-matrix. PACS: ¶ arch-ive/9507123 † [email protected] 1 The quantum R-matrix as solutions of the Yang-Baxter equ...

Abstract. We consider the finite binary words Z(n), n ∈ N defined by the following self-similar process: Z(0) := 0, Z(1) := 01, and Z(n+ 1) := Z(n) · Z(n− 1), where the dot · denotes word concatenation, and w the word obtained from w by exchanging the zeros and the ones. Denote by Z(∞) = 01110100 . . . the limiting word of this process, and by z(n) the nth bit of this word. This sequence z is a...

‎in this paper‎, ‎we propose two preconditioned aor iterative methods to solve systems of linear equations whose coefficient matrices are z-matrix‎. ‎these methods can be considered as improvements of two previously presented ones in the literature‎. ‎finally some numerical experiments are given to show the effectiveness of the proposed preconditioners‎.‎

In this paper, we consider the l0 norm minimization problem with linear equation and nonnegativity constraints. By introducing the concept of generalized Z-matrix for a rectangular matrix, we show that this l0 norm minimization with such a kind of measurement matrices and nonnegative observations can be exactly solved via the corresponding lp (0 < p ≤ 1) norm minimization. Moreover, the lower b...

A scaling vector = (1 ; ; r) T is a compactly supported and vector-valued distribution vector that satisses a matrix reenement equation (x) = P P k (2x ? k); where (P k) is a nite matrix sequence. We call P (z) = 1 2 P P k z k the symbol of. A symbol P (z) is said two-scale similar to a polynomial matrix Q(z) if there is an invertible polynomial matrix T (z) that satisses P (z) = T (z 2)Q(z)T ?...