This paper presents the new approach to the formation of the gas turbine engine diagnostic matrix employing A.Tikhonov’s regularization method and taking into account the compressor properties shift under the condition of engine air-gas channel alteration. This method allows eliminating the certain inadequacy of the diagnostic matrices in some cases and removes the restrictions on their impleme...

This paper shows that Cayley Transforms, which map Orthogonal and SkewSymmetric matrices, may be considered the extension to matrix field of the complex conformal mapping function f1(z) = 1− z 1 + x . Then, by using a set of real matrices which are, simultaneously, Orthogonal and Symmetric (the Ortho−Sym matrices), it similarly shows how to extend two complex conformal mapping functions (namely...

Let g(z, x) denote the diagonal Green's matrix of a self-adjoint m × m matrix-valued Schrödinger operator H = − d 2 dx 2 Im + Q(x) in L 2 (R) m , m ∈ N. One of the principal results proven in this paper states that for a fixed x 0 ∈ R and all z ∈ C + , g(z, x 0) and g ′ (z, x 0) uniquely determine the matrix-valued m × m potential Q(x) for a.e. x ∈ R. We also prove the following local version o...

Let g(z; x) denote the diagonal Green's matrix of a self-adjoint m m matrix-valued Schrr odinger operator H = ? d 2 dx 2 Im + Q(x) in L 2 (R) m , m 2 N. One of the principal results proven in this paper states that for a xed x 0 2 R and all z 2 C + , g(z; x 0) and g 0 (z; x 0) uniquely determine the matrix-valued m m potential Q(x) for a.e. x 2 R. We also prove the following local version of th...

In this paper, we present a sufficient condition for the universal rigidity of a generic bar framework G(p) in terms of the Gale matrix Z corresponding to G(p). We also establish a relationship between the stress matrix S and the Gale matrix Z for bar frameworks. This allows us to translate back and forth between S and Z in recently obtained results concerning universal rigidity, global rigidit...

Abstract. This paper shows that the matrix fraction description, given by a pair {A(z) B(z)} of matrix polynomials of z, for a linear time-invariant system may not be unique even if A(z) is monic, A(z) and B(z) have no common left factor, and the matrix coefficients corresponding to the highestorder terms of A(z) and B(z) are full row rank. The orders of all possible matrix fraction description...

We give a framework for formal orthogonal polynomials with respect to an arbitrary moment matrix. When the moment matrix is Hankel, this simplifies to the classical framework. The relation with Padé approximation and with Krylov subspace methods is given. 1 Formal block orthogonal polynomials We consider a linear functional defined on the space of polynomials in two variables, defined by the mo...

A 0-1 matrix is d-disjunct if no column is covered by the union of any d other columns. A 0-1 matrix is (d; z)-disjunct if for any column C and any d other columns, there exist at least z rows such that each of them has value 1 at column C and value 0 at all the other d columns. Let t (d, n) and t (d, n; z) denote the minimum number of rows required by a d-disjunct matrix and a (d; z)-disjunct ...