The aim of this contribution is to characterize the set feasible initial conditions on a diagonal line in order compute solutions 2D discrete state-space system (defined over Z2) half-plane grid. This characterization given terms matrices for state updating.

A square matrix is called line-sum-symmetric if the sum of elements in each of its rows equals the sum of elements in the corresponding column. Let A be an n x n nonnegative matrix and let X and Y be n x n diagonal matrices having positive diagonal elements. Then the matrices XA, XAXand XA Yare called a row-scaling, a similarity-scaling and an equivalence-scaling of A. The purpose of this paper...

There are many applications related to singly linearly constrained quadratic programs subjected to upper and lower bounds. In this paper, a new algorithm based on secant approximation is provided for the case in which the Hessian matrix is diagonal and positive definite. To deal with the general case where the Hessian is not diagonal, a new efficient projected gradient algorithm is proposed. Th...

The Catalan number has a lot of interpretations and one of them is the number of Dyck paths. A Dyck path is a lattice path from (0, 0) to (n, n) which is below the diagonal line y = x. One way to generalize the definition of Dyck path is to change the end point of Dyck path, i.e. we define (generalized) Dyck path to be a lattice path from (0, 0) to (m, n) ∈ N2 which is below the diagonal line y...

The multivariable tracking accuracy on an automotive vibration test rig can be improved by extending the current industrial off-line iterative feedforward procedure with a real time feedback controller. This paper tests and validates three different MIMO-control schemes on an industrial test rig. First decentralized (or diagonal) control is used, which is a combination of independently designed...

Fast collisionless magnetic reconnection implies fast energy conversion. The main form of conversion in concerns bulk ion acceleration with resulting jets. Based on theoretical analysis and MMS data, we examine the kinetic imprints context rates. analyze observations include beams toward X-line distorted velocity distributions lead to a bipolar reversal an off-diagonal element pressure tensor a...

We consider in the unidirectional approximation the propagation of an ultra short electromagnetic pulse in a resonant medium consisting of molecules characterized by a transition operator with both diagonal and non-diagonal matrix elements. We find the zero-curvature representation of the reduced Maxwell-Bloch equations in the sharp line limit. This can be used to develop the inverse scattering...

In this paper we study Banakh’s quarter-stratifiability among generalized ordered (GO)-spaces. All quarterstratifiable GO-spaces have a σ-closed-discrete dense set and therefore are perfect, and have a Gδ-diagonal. We characterize quarter-stratifiability among GO-spaces and show that, unlike the situation in general topological spaces, quarter-stratifiability is a hereditary property in GO-spac...

Impaired balance is common post stroke and can be assessed by means of force-platforms measuring center of pressure (COP) displacements during static standing, or more dynamically during lateral maximum weight shift (MWS). However, activities of daily life also include diagonal MWS and since force platforms are nowadays commercially available, investigating lateral and diagonal MWS in a clinica...