Matrix development of the calculus of relations

1948 ◽  
Vol 13 (4) ◽  
pp. 193-203 ◽  
Author(s):  
Irving M. Copilowish
Keyword(s):  
Present Approach ◽  
Matrix Approach ◽  
Matrix Notation ◽  
The Matrix ◽  
Elementary Calculus

In his very interesting address On the calculus of refations, Professor Tarski discussed alternative bases for that calculus. He was there interested in “…different methods of setting up the foundations of this elementary calculus in a rigorously deductive way…” and so did not discuss the method of developing the calculus of relations with which this paper is concerned. Our purpose here is to show how the use of matrix notation for relations permits an algorithmic rather than a postulational-deductive development of the calculus of relations. One limitation of the present approach is to be admitted at the very outset: to enjoy the full benefits of the matrix approach, we are obliged to confine our investigations to Universes of Discourse which are finite. The reason for this restriction will become apparent presently.

Complex Chi-Squares: Matrix Notation and Calculation

1972 ◽  
Vol 30 (3) ◽  
pp. 743-746 ◽  
Author(s):  
Edward F. Gocka
Keyword(s):  
Computational Algorithms ◽  
Behavioral Sciences ◽  
Matrix Notation ◽  
Standard Formula ◽  
The Matrix ◽  
Matrix Formula

A matrix formula available for the calculation of complex chi-squares allows several computational variations, each of which requires fewer steps than the standard formula. However, neither the matrix formula nor the associated computational algorithms have been given adequate exposure in statistical texts for the behavioral sciences. This paper reintroduces the formula, expands the notation, and shows how several computational variations can be derived.

scholarly journals Anisotropic Metamaterials Filled Rectangular Metallic Waveguides Propagation Study and Analysis

2021 ◽  
pp. 34-43
Author(s):  
Nizar Tahri
Keyword(s):  
Control Strategy ◽  
Orthonormal Basis ◽  
Matrix Approach ◽  
Transmission Coefficients ◽  
Anisotropic Metamaterials ◽  
Waveguide Filters ◽  
S Matrix ◽  
The Matrix ◽  
The Galerkin Method ◽  
Transverse Fields

In this paper, we propose a novel generalized S-matrix characterization approach. The goal is to keep track of all observed discontinuities as efficiently as possible. In terms of reflection value, the proposed control strategy is based on transmission coefficients and one-axis rectangular guides. We successfully manipulate metal rectangular waveguide filters with both geometrical and physical discontinuity. Lossless discontinuity is depicted as a periodic structure that contains Metamaterials. The modal development of transverse fields provides the basis for the generalized S-matrix approach. The approach works by breaking down electromagnetic fields for each of the guides that make up the discontinuity on an orthonormal basis. When the Galerkin method is used, the matrix of diffraction of the junction is obtained directly.

scholarly journals The Lynden-Bell bar formation mechanism in simple and realistic galactic models

2020 ◽  
Vol 498 (3) ◽  
pp. 3368-3373
Author(s):  
E V Polyachenko ◽  
I G Shukhman
Keyword(s):  
Perturbation Theory ◽  
Angular Momentum ◽  
Formation Mechanism ◽  
Linear Perturbation ◽  
Matrix Approach ◽  
Precession Rate ◽  
Secular Evolution ◽  
The Matrix ◽  
Linear Perturbation Theory ◽  
Bar Formation

ABSTRACT Using the canonical Hamilton–Jacobi approach we study the Lynden-Bell concept of bar formation based on the idea of orbital trapping parallel to the long or short axes of the oval potential distortion. The concept considered a single parameter – a sign of the derivative of the precession rate over angular momentum, determining the orientation of the trapped orbits. We derived a perturbation Hamiltonian that includes two more parameters characterizing the background disc and the perturbation, which are just as important as the earlier known one. This allows us to link the concept with the matrix approach in linear perturbation theory, the theory of weak bars, and explain some features of the non-linear secular evolution observed in N-body simulations.

Synthesis of an Eight-Link Mechanism for Varieties of Motion Programs

1973 ◽  
Vol 95 (3) ◽  
pp. 744-750 ◽  
Author(s):  
S. Hamid ◽  
A. H. Soni
Keyword(s):  
Numerical Approach ◽  
Matrix Approach ◽  
Synthesis Technique ◽  
Link Mechanism ◽  
The Matrix

Using the matrix approach, synthesis equations are derived for eight types of synthesis problems for an eight-link mechanism having five links in each of its three loops. A numerical approach due to Marquardt is applied to illustrate the synthesis technique for the varieties of motion programs.

A Discrete Element Method for the Analysis of Plane Elasto-Plastic Stress Problems

1966 ◽  
Vol 17 (1) ◽  
pp. 83-104 ◽  
Author(s):  
G. G. Pope
Keyword(s):  
Discrete Element Method ◽  
Plane Stress ◽  
Discrete Element ◽  
Stress Strain ◽  
Numerical Examples ◽  
Matrix Notation ◽  
The Matrix ◽  
Triangular Elements ◽  
Plastic Stress ◽  
Element Method

SummaryA procedure is developed for the analysis of plane stress problems when yielding occurs locally. The region is divided into triangular elements and the deformation is analysed on a step-by-step basis, using the matrix notation developed by Argyris. The simple expressions which are derived for the element properties are applicable with any stress-strain relations which are stable and time-independent. Simple numerical examples are given.

The Matrix Approach to Industrial Policy

2006 ◽  
Vol 20 (5) ◽  
pp. 573-601 ◽  
Author(s):  
Karl Aiginger ◽  
Susanne Sieber
Keyword(s):  
Industrial Policy ◽  
Matrix Approach ◽  
The Matrix
Sign in / Sign up

Export Citation Format

Share Document