A New Approach to Matrix Theory or Many Facets of the Matrix Decomposition Theorem

1975 ◽  
pp. 133-139 ◽  
Author(s):  
Alladi Ramakrishnan ◽  
R. Jagannathan
Keyword(s):  
Matrix Theory ◽  
Matrix Decomposition ◽  
Decomposition Theorem ◽  
New Approach ◽  
The Matrix

scholarly journals Partial Component Consensus of Discrete-Time Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Wenjun Hu ◽  
Gang Zhang ◽  
Zhongjun Ma ◽  
Binbin Wu
Keyword(s):  
Multiagent Systems ◽  
Discrete Time ◽  
Matrix Theory ◽  
Pinning Control ◽  
Directed Network ◽  
Strong Function ◽  
Partial Stability ◽  
Partial Component ◽  
The Matrix ◽  
Error System

The multiagent system has the advantages of simple structure, strong function, and cost saving, which has received wide attention from different fields. Consensus is the most basic problem in multiagent systems. In this paper, firstly, the problem of partial component consensus in the first-order linear discrete-time multiagent systems with the directed network topology is discussed. Via designing an appropriate pinning control protocol, the corresponding error system is analyzed by using the matrix theory and the partial stability theory. Secondly, a sufficient condition is given to realize partial component consensus in multiagent systems. Finally, the numerical simulations are given to illustrate the theoretical results.

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals MATRIX THEORY, HILBERT SCHEME AND INTEGRABLE SYSTEM

1998 ◽  
Vol 13 (34) ◽  
pp. 2731-2742 ◽  
Author(s):  
YUTAKA MATSUO
Keyword(s):  
Hilbert Scheme ◽  
Matrix Theory ◽  
Fock Space ◽  
Homology Class ◽  
Orthogonal Basis ◽  
Inner Product ◽  
Virasoro Symmetry ◽  
Hilbert Scheme Of Points ◽  
The Matrix ◽  
Boson Fock Space

We give a reinterpretation of the matrix theory discussed by Moore, Nekrasov and Shatashivili (MNS) in terms of the second quantized operators which describes the homology class of the Hilbert scheme of points on surfaces. It naturally relates the contribution from each pole to the inner product of orthogonal basis of free boson Fock space. These bases can be related to the eigenfunctions of Calogero–Sutherland (CS) equation and the deformation parameter of MNS is identified with coupling of CS system. We discuss the structure of Virasoro symmetry in this model.

The Influence of Cu and Cr on the Matrix Decomposition of Quenched AlZnMg Alloy

1991 ◽  
Vol 124 (1) ◽  
pp. K11-K14 ◽  
Author(s):  
C. Dos Santos Lourenço ◽  
M. Cilense ◽  
W. Garlipp
Keyword(s):  
Matrix Decomposition ◽  
Mg Alloy ◽  
The Matrix

Identifying graph clusters using variational inference and links to covariance parametrization

2009 ◽  
Vol 367 (1906) ◽  
pp. 4407-4426
Author(s):  
David Barber
Keyword(s):  
Mean Field ◽  
Matrix Decomposition ◽  
Difficult Problem ◽  
Positive Definite ◽  
Variational Inference ◽  
Field Theories ◽  
Variational Approximation ◽  
Positive Definite Matrices ◽  
The Matrix ◽  
Non Gaussian

Finding clusters of well-connected nodes in a graph is a problem common to many domains, including social networks, the Internet and bioinformatics. From a computational viewpoint, finding these clusters or graph communities is a difficult problem. We use a clique matrix decomposition based on a statistical description that encourages clusters to be well connected and few in number. The formal intractability of inferring the clusters is addressed using a variational approximation inspired by mean-field theories in statistical mechanics. Clique matrices also play a natural role in parametrizing positive definite matrices under zero constraints on elements of the matrix. We show that clique matrices can parametrize all positive definite matrices restricted according to a decomposable graph and form a structured factor analysis approximation in the non-decomposable case. Extensions to conjugate Bayesian covariance priors and more general non-Gaussian independence models are briefly discussed.

scholarly journals Development of High-Performance SiCp/Al-Si Composites by Equal Channel Angular Pressing

Metals ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 738 ◽  
Author(s):  
Qiong Xu ◽  
Aibin Ma ◽  
Junjie Wang ◽  
Jiapeng Sun ◽  
Jinghua Jiang ◽  
...  
Keyword(s):  
Wear Resistance ◽  
Equal Channel Angular Pressing ◽  
High Performance ◽  
Adhesive Wear ◽  
Processing Route ◽  
Matrix Composites ◽  
New Approach ◽  
Angular Pressing ◽  
The Matrix ◽  
Industry Applications

Relatively low compactness and unsatisfactory uniformity of reinforced particles severely restrict the performance and widespread industry applications of the powder metallurgy (PM) metal matrix composites (MMCs). Here, we developed a combined processing route of PM and equal channel angular pressing (ECAP) to enhance the mechanical properties and wear resistance of the SiCp/Al-Si composite. The results indicate that ECAP significantly refined the matrix grains, eliminated pores and promoted the uniformity of the reinforcement particles. After 8p-ECAP, the SiCp/Al-Si composite consisted of ultrafine Al matrix grains (600 nm) modified by uniformly-dispersed Si and SiCp particles, and the composite relative density approached 100%. The hardness and wear resistance of the 8p-ECAP SiCp/Al-Si composite were markedly improved compared to the PM composite. More ECAP passes continued a trend of improvement for the wear resistance and hardness. Moreover, while abrasion and delamination dominated the wear of PM composites, less severe adhesive wear and fatigue mechanisms played more important roles in the wear of PM-ECAP composites. This study demonstrates a new approach to designing wear-resistant Al-MMCs and is readily applicable to other Al-MMCs.

Sign in / Sign up

Export Citation Format

Share Document