Orthogonal Basis Functions in Discrete-Time Electromagnetics and Their Implementation to Compute the Matrix-Type UTD Transition Function for PEC Wedge Diffractions

2017 ◽  
Vol 65 (2) ◽  
pp. 741-750 ◽  
Author(s):  
Hsi-Tseng Chou
Keyword(s):  
Discrete Time ◽  
Transition Function ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Matrix Type ◽  
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 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.

scholarly journals Orthogonal Functions Solving Linear functional Differential EquationsUsing Chebyshev Polynomial

2008 ◽  
Vol 5 (1) ◽  
pp. 143-148 ◽  
Author(s):  
Baghdad Science Journal
Keyword(s):  
Function Approximation ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Least Square ◽  
Orthogonal Functions ◽  
Functional Differential ◽  
Approximated Evaluation ◽  
Chebyshev Functions

A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

scholarly journals Caracterización en línea de la dinámica temporal de señales para el monitoreo del sistema eléctrico de potencia

2020 ◽  
pp. 26-34
Author(s):  
Francisco Román Lezama-Zárraga ◽  
Jorge de Jesús Chan-González ◽  
Meng Yen Shih ◽  
Roberto Carlos Canto-Canul
Keyword(s):  
Nonlinear Oscillations ◽  
Electrical Power ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Electrical Power System ◽  
Transient Phenomena ◽  
On Line ◽  
Measurement Units ◽  
Dynamic Phenomena

The characterization of dynamic phenomena is essential for monitoring the Electrical Power System subject to disturbances. This article proposes an On-line time systematic approach to analyze and characterize the temporal evolution of transient and nonlinear oscillations in these systems. Two methods are used; the first method is based on a local decomposition of the signal under study into orthogonal basis functions to obtain the dynamics of transient oscillations. Next, a second method is applied to those orthogonal basis functions to obtain analytical signals and characterize the instantaneous amplitude, phase and frequency attributes of the oscillations and determine a physical interpretation of the system’s behavior. The proposed methodology is a time-frequencyenergy analysis which can be applied to the timesynchronized Phasor Measurement Units measurements. The results demonstrate that the proposed methodology provide an accurate characterization of transient phenomena with non-stationary effects.

Proportional intensities and strong ergodicity for Markov processes

1983 ◽  
Vol 20 (01) ◽  
pp. 185-190 ◽  
Author(s):  
Mark Scott ◽  
Dean L. Isaacson
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Homogeneous Markov Process ◽  
Strong Ergodicity ◽  
Transition Functions ◽  
The Matrix ◽  
Intensity Functions ◽  
Time Point

By assuming the proportionality of the intensity functions at each time point for a continuous-time non-homogeneous Markov process, strong ergodicity for the process is determined through strong ergodicity of a related discrete-time Markov process. For processes having proportional intensities, strong ergodicity implies having the limiting matrix L satisfy L · P(s, t) = L, where P(s, t) is the matrix of transition functions.

Orthogonal basis for the Shapovalov form on $U_q(\mathfrak{sl}(n + 1))$

2015 ◽  
Vol 27 (02) ◽  
pp. 1550004 ◽  
Author(s):  
Andrey Mudrov
Keyword(s):  
Lie Algebra ◽  
Cartan Subalgebra ◽  
Verma Module ◽  
Orthogonal Basis ◽  
Enveloping Algebra ◽  
Pbw Basis ◽  
Inverse Form ◽  
Matrix Coefficients ◽  
The Matrix ◽  
Quantized Universal Enveloping Algebra

Let U be either the classical or quantized universal enveloping algebra of the Lie algebra [Formula: see text] extended over the field of fractions of the Cartan subalgebra. We suggest a PBW basis in U over the extended Cartan subalgebra diagonalizing the contravariant Shapovalov form on generic Verma module. The matrix coefficients of the form are calculated and the inverse form is explicitly constructed.

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