Weighted membership based on matrix relation

2017 ◽  
Vol 41 (15) ◽  
pp. 5761-5769 ◽  
Author(s):  
Assem Elshenawy ◽  
M. Kamel EL-Sayed ◽  
E. Elsodany
Keyword(s):  
Matrix Relation

Matrix relation algebras

2002 ◽  
Vol 48 (3) ◽  
pp. 273-299 ◽  
Author(s):  
M. El Bachraoui ◽  
M. Van de Vel
Keyword(s):  
Relation Algebras ◽  
Matrix Relation

The Zone Method: A New Explicit Matrix Relation to Calculate the Total Exchange Areas in Anisotropically Scattering Medium Bounded by Anisotropically Reflecting Walls

2002 ◽  
Vol 124 (4) ◽  
pp. 696-703 ◽  
Author(s):  
J. M. Goyhe´ne`che ◽  
J. F. Sacadura
Keyword(s):  
Complex Geometry ◽  
Anisotropic Scattering ◽  
Radiative Properties ◽  
Scattering Medium ◽  
Zone Method ◽  
Indirect Exchange ◽  
Matrix Relation ◽  
Definition Of ◽  
New Formulation ◽  
Total Exchange

A new explicit matrix relation for the calculation of the total exchange areas (TEA) in emitting, absorbing and anisotropically scattering semi-transparent medium bounded by emitting, absorbing and anisotropically reflecting walls has been established. It has been used to directly determine the TEA as a function of radiative properties and geometry of the medium and its boundaries. Computation calls for direct exchange areas (DEA) and indirect exchange areas (IEA). A new definition of these exchange areas reduces their integration order and provides practical energy balance relations for their computation in the case of complex geometry elements. The new formulation is applied in the case of an emitting, absorbing and linearly anisotropic scattering semi-transparent slab bounded by black surfaces. This method is also applicable to nongray medium using the weighted sum of gray gases model.

Elastic bending wave on the edge of a semi-infinite plate reinforced by a strip plate

2019 ◽  
Vol 24 (10) ◽  
pp. 3319-3330 ◽  
Author(s):  
Ahmed SM Alzaidi ◽  
Julius Kaplunov ◽  
Ludmila Prikazchikova
Keyword(s):  
Dispersion Relation ◽  
Elastic Waves ◽  
Rectangular Cross Section ◽  
Infinite Plate ◽  
Numerical Data ◽  
Free Edge ◽  
Matrix Relation ◽  
Strip Plate ◽  
Effective Conditions ◽  
Bending Wave

Elastic waves localised near the edge of a semi-infinite plate reinforced by a strip plate are considered within the framework of the 2D classical theory for plate bending. The boundary value problem for the strip plate is subject to asymptotic analysis, assuming that a typical wavelength is much greater than the strip thickness. As a result, effective conditions along the interface corresponding to a plate reinforced by a beam with a narrow rectangular cross-section are established. They support an approximate dispersion relation perturbing that for a homogeneous plate with a free edge. The accuracy of the approximate dispersion relation is tested by comparison with the numerical data obtained from the ‘exact’ matrix relation for a composite plate. The effect of the problem parameters on the localisation rate is studied.

Matrix relation algebras

1987 ◽  
Vol 41 (2) ◽  
pp. 75-80
Author(s):  
L. A. Skornyakov
Keyword(s):  
Relation Algebras ◽  
Matrix Relation

ROD MODELING OF STRUCTURES LEVERING MECHANISMS WITH DISTRIBUTED INERTIA

2020 ◽  
Vol 69 (1) ◽  
pp. 269-284
Author(s):  
Е. Тemirbekov ◽  
◽  
G. Тukeshova ◽  
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Center Of Mass ◽  
Element Model ◽  
Finite Element Models ◽  
The Finite Element Method ◽  
Contact Points ◽  
Spatial Movement ◽  
Reaction Forces ◽  
Matrix Relation

To reduce inertia of moving links into resultant force and moment vectors and to represent center of mass as node in finite element models are widely-used in mechanical calculations of linkage mechanisms. Considering distributed inertia of motion makes possible to create more precise finite element models in spatial linkage structures. By algebraically summing all the distributed inertial loads acting in both directions, perpendicular and along the axis of a constant cross section link, we can show that their intensity varies linearly along the length of link. Using this approach together with Chasles theorem for a point of free rigid body in projections onto the moving axes in the finite element method for rectilinear homogeneous rod, we reach to a more precise finite element model considering analytically distributed inertia of motion. Besides, we obtained subvectors in matrix relation which binds the generalized reaction forces acting at the contact points of the rod element with nodal generalized elastic movements. These subvectors includes the weight and inertia of a distributed spatial movement of link.

scholarly journals On induced permutation matrices and the symmetric group

1936 ◽  
Vol 5 (1) ◽  
pp. 1-13 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Symmetric Group ◽  
Matrix Representation ◽  
Zero Element ◽  
Natural Order ◽  
Third Order ◽  
The Third ◽  
Permutation Matrices ◽  
The Matrix ◽  
Matrix Relation ◽  
Image Position

The n! operations Ai of permutations upon n different ordered symbols correspond to n! matrices Ai of the nth order, which have in each row and in each column only one non-zero element, namely a unit. Such matrices Ai are called permutation matrices, since their effect in premultiplying an arbitrary column vector x = {x1x2….xn} is to impress the permutation Ai upon the elements xi. For example the six matrices of the third orderare permutation matrices. It is convenient to denote them bywhere the bracketed indices refer to the permutations of natural order. Clearly the relation Ai Aj = Ak entails the matrix relation AiAj = Ak; in other words, the n! matrices Ai, give a matrix representation of the symmetric group of order n!.

Degree of matrix relation algebras

2002 ◽  
Vol 48 (3) ◽  
pp. 301-308 ◽  
Author(s):  
M. El Bachraoui ◽  
M. Van de Vel
Keyword(s):  
Relation Algebras ◽  
Matrix Relation

Collision of a chondrule with matrix: Relation between static strength of matrix and impact pressure

Icarus ◽  
2013 ◽  
Vol 226 (1) ◽  
pp. 111-118 ◽  
Author(s):  
Nagisa Machii ◽  
Akiko M. Nakamura ◽  
Carsten Güttler ◽  
Dirk Beger ◽  
Jürgen Blum
Keyword(s):  
Static Strength ◽  
Impact Pressure ◽  
Matrix Relation
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