This document describes one possible implementation of a matrix class and matrix multiplication using the data-parallel SIMD types introduced in [N4184]. The example shows the basic use of SIMD types for manual transformation of a loop over scalars to a loop with increased stride using SIMD vector loads and stores and SIMD operations in the loop body.

Orthogonal eigenstructure control is a novel active control method for vibration suppression in multi-input multi-output linear systems. This method is based on finding an output feedback control gain matrix in such a way that the closed-loop eigenvectors are almost orthogonal to the open-loop ones. Singular value decomposition is used to find the matrix, which spans the null space of the close...

Abstract. A method of constructing n × n matrix solutions(with n matrix elements) of Temperley-Lieb algebra relation is presented in this paper. The single loop of these solutions are d = √ n. Especially, a 9×9−matrix solution with single loop d= √ 3 is discussed in detail. An unitary Yang-Baxter R̆(θ, q1, q2) matrix is obtained via the Yang-Baxterization process. The entanglement property and g...

The loop equation for the complex one-matrix model with a multi-cut structure is derived and solved in the planar limit. An iterative scheme for higher genus contributions to the free energy and the multi-loop correlators is presented for the two-cut model, where explicit results are given up to and including genus two. The double-scaling limit is analyzed and the relation to the one-cut soluti...

This manuscript will provide a step by step method on how a graph theory and topology can be utilized to construct a Z-loop matrix for the study of faulted 3 phase power systems. The growing demand for reliable electrical power supply has forced the pace developments in electrical power system analysis using computer. In this, power system analysis plays a significant role for the analysis of f...

We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zero-simple semigroups for which the loop problem is context-free. We also establish some results concerning loop problems for subsemigroups and Rees quotients.

Orthogonal eigenstructure control is a novel control method that can be used for vibration suppression in flexible structures. The method described in this study does not need defining the desired locations of the closed-loop poles or predetermining the closed-loop eigenvectors. The method, which is applicable to linear multi-input multi-output systems, determines an output feedback control gai...

Wewill discuss how to generate integrable couplings from zero curvature equations associated with matrix spectral problems. The key elements are matrix loop algebras consisting of block matrices with blocks of the same size or different sizes. Hamiltonian structures are furnished by applying the variational identity defined over semi-direct sums of Lie algebras. Illustrative examples include in...