Seymour’s famous decomposition theorem for regular matroids states that any totally unimodular (TU) matrix can be constructed through a series of composition operations called k-sums starting from network matrices and their transposes and two compact representation matrices B1, B2 of a certain ten element matroid. Given that B1, B2 are binet matrices we examine the k-sums of network and binet m...

We investigate the relation between fine-grained and coarse-grained distributed computations of a class of problems related to the generic transitive closure problem (TC for short). We choose an intricate systolic algorithm for the TC problem, by Guibas, Kung and Thompson (GKT algorithm for short), as a starting point due to its particularly close relationship to matrix multiplication. The GKT ...

A generalization of the semisimplicity concept for polyadic algebraic structures is proposed. If semisimple can be presented in block diagonal matrix form (resulting Wedderburn decomposition), a general given by block-shift matrices. We combine these forms to get shape nonderived ("double" decomposition two kinds). then introduce polyadization (a "polyadic constructor") according which one cons...

Abstract. This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in wh...

Dynamics of quantum field theory can be formulated by functional equations. To develop a complete functional quantum theory the physical information has to be given by functional operations only. The most important physical information of elementary particle physics is the Ä-matrix. In this paper the functional ^-matrix is constructed for the scattering of relativistic dressed particles, i.e. f...

A KKT matrix, W say, is symmetric and nonsingular, with a leadingˆn׈n block that has a conditional positive definite property and a trailingˆm׈m block that is identically zero, the dimensions of W being (ˆ n+ˆm)×(ˆ n+ˆm). The author requires the inverse matrix H = W −1 explicitly in an iterative algorithm for unconstrained minimization without derivatives, and only one of the firstˆn rows and...

 Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...

Purpose. Development of an automated method for determining the zones rock crushing in collapse order to select rational technologies drilling and blasting operations. Methods. Methods positions nodal internal points coordinate grid blasted collapse, approximation methods, matrix theory, numerical methods technology are used. Findings. An is described. It based on analytical granulometric compo...