scholarly journals Matrix Dimensional Analysis for Electromagnetic Quantities

2021 ◽  
Vol 6 (2) ◽  
pp. 636-644
Author(s):  
Mostafa Ali Rushdi ◽  
Ali Muhammad Rushdi
Keyword(s):  
Dimensional Analysis ◽  
Matrix Solution ◽  
Distributed Representations ◽  
The Matrix ◽  
Technical Details ◽  
Electromagnetic Quantities

We utilize the electromagnetically-oriented LTI∅ dimensional basis in the matrix solution of dimensional-analysis (DA) problems involving mainly electromagnetic quantities, whether these quantities are lumped or distributed. Representations in the LTI∅ basis (compared with the standard MLTI basis) are more informative and much simpler. Moreover, matrix DA computations employing the LTI∅ basis are more efficient and much less error prone. Extensive discussions of two demonstrative examples expose technical details of a novel DA scheme, and clarify many important facets of modern dimensional analysis.

Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

2004 ◽  
Vol 59 (9) ◽  
pp. 621-622 ◽  
Author(s):  
Fatih Ucun ◽  
Vesile Gūçlü
Keyword(s):  
Gas Phase ◽  
Condensed Phase ◽  
Matrix Method ◽  
Solid Phase ◽  
Force Constants ◽  
Matrix Solution ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

ASYMPTOTIC EXPANSIONS FOR RIEMANN–HILBERT PROBLEMS

2008 ◽  
Vol 06 (03) ◽  
pp. 269-298 ◽  
Author(s):  
W.-Y. QIU ◽  
R. WONG
Keyword(s):  
Asymptotic Expansion ◽  
Complex Analysis ◽  
Elementary Proof ◽  
Hilbert Problem ◽  
Jump Condition ◽  
Similar Type ◽  
Matrix Solution ◽  
Jump Matrix ◽  
The Matrix ◽  
Riemann Hilbert Problem

Let Γ be a piecewise smooth contour in ℂ, which could be unbounded and may have points of self-intersection. Let V(z, N) be a 2 × 2 matrix-valued function defined on Γ, which depends on a parameter N. Consider a Riemann–Hilbert problem for a matrix-valued analytic function R(z, N) that satisfies a jump condition on the contour Γ with the jump matrix V(z, N). Assume that V(z, N) has an asymptotic expansion, as N → ∞, on Γ. An elementary proof is given for the existence of a similar type of asymptotic expansion for the matrix solution R(z, N), as n → ∞, for z ∈ ℂ\Γ. Our method makes use of only complex analysis.

MALDI imaging mass spectrometry of lipids by adding lithium salts to the matrix solution

2011 ◽  
Vol 401 (1) ◽  
pp. 75-87 ◽  
Author(s):  
Christopher D. Cerruti ◽  
David Touboul ◽  
Vincent Guérineau ◽  
Vanessa W. Petit ◽  
Olivier Laprévote ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Imaging Mass Spectrometry ◽  
Lithium Salts ◽  
Maldi Imaging ◽  
Matrix Solution ◽  
The Matrix ◽  
Maldi Imaging Mass Spectrometry

The Hermes 8 Element for the Matrix Displacement Method

1968 ◽  
Vol 72 (691) ◽  
pp. 613-617 ◽  
Author(s):  
J. H. Argyris ◽  
I. Fried ◽  
D. W. Scharpf
Keyword(s):  
Dimensional Analysis ◽  
Three Dimensional ◽  
Displacement Method ◽  
The Matrix ◽  
Interpolation Techniques ◽  
Hermitian Interpolation

The description of the LUMINA element in T.N. 11 is followed by another three-dimensional interpolation element, called HERMES 8, available in the ASKA language and briefly mentioned in ref. 1. Just as the LUMINA set, the HERMES element represents a general hexahedronal element with curved faces and has proved a most useful component block for three-dimensional analysis of complex bodies. The cardinal idea underlying the HERMES development aims at combining the advantages of the Lagrangian and Hermitian interpolation techniques.

Asymptotic studies of closely spaced, highly conducting cylinders

1988 ◽  
Vol 415 (1848) ◽  
pp. 185-196 ◽  
Keyword(s):  
Potential Distribution ◽  
Transport Problem ◽  
Asymptotic Region ◽  
Multipole Moments ◽  
Matrix Solution ◽  
Truncation Errors ◽  
The Matrix ◽  
Square Array ◽  
Conducting Cylinders ◽  
Small Cylinder

We consider the solution of the scalar transport problem for a pair of nearly touching cylinders of high conductivity. We obtain an expression for the set of multipole moments of the potential distribution for this problem in terms of the hypergeometric function. We apply this expression in the estimation of truncation errors occurring in the matrix solution of the corresponding transport problem for the square array of cylinders. Consequently, we are able to calculate the array transport coefficient for arbitrarily high cylinder conductivities, and arbitrarily small cylinder separations. We derive and verify an expression for this coefficient which is uniformly valid throughout the whole asymptotic region when highly conducting cylinders approach touching.

Performance Analysis of State-Dependent M/Hk/1/L Queue with Balking

2012 ◽  
Vol 198-199 ◽  
pp. 732-736
Author(s):  
Rui Ling Tian ◽  
De Quan Yue ◽  
Xi Jun Wu
Keyword(s):  
Performance Measures ◽  
Numerical Experiments ◽  
Cost Model ◽  
Critical Value ◽  
Block Matrix ◽  
Matrix Solution ◽  
Steady State Probability ◽  
State Dependent ◽  
The Matrix ◽  
Performance Analyses

In this paper, we present an analysis for an queue with balking and state-dependent service. By using the block matrix solution, we first deduce the matrix form iterative formula of the steady-state probability. We also derive some performance measures of the system. Based on these performance analyses, we develop a cost model to determine numerically the system’s optimal cost and critical value. Finally, we perform a sensitivity analysis through numerical experiments.

Books Rank with Modified PageRank Algorithm

2014 ◽  
Vol 915-916 ◽  
pp. 1266-1271
Author(s):  
Han Bai ◽  
Wei Lv ◽  
Xun Liao
Keyword(s):  
Initial Value Problems ◽  
Matrix Solution ◽  
Initial Value ◽  
Pagerank Algorithm ◽  
Operational Characteristics ◽  
The Matrix

This paper analyzes the operational characteristics of the library. Based on this, the author improve the traditional PageRank algorithm to rank for similar books. This innovation is that according to the characteristics of the PageRank algorithm, reduced times, books, readers, book by three to a unified relationship plane up, through the matrix solution to the PageRank relations in the initial value problems return, and achieve the algorithm.

Dramatic Improvements in the Matrix Solution Time for Method of Moment Problems Involving Stripline Interconnects

2007 ◽  
Vol 30 (3) ◽  
pp. 570-579 ◽  
Author(s):  
Xing Wang ◽  
Zhaohui Zhu ◽  
Yi Cao ◽  
Steven L. Dvorak ◽  
John L. Prince
Keyword(s):  
Solution Time ◽  
Moment Problems ◽  
Method Of Moment ◽  
Matrix Solution ◽  
The Matrix

The TRIAX 6 Element for Axisymmetric Analysis by the Matrix Displacement Method

1966 ◽  
Vol 70 (672) ◽  
pp. 1102-1105 ◽  
Author(s):  
J. H. Argyris
Keyword(s):  
Ab Initio ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Displacement Method ◽  
Specific Element ◽  
Axisymmetric State ◽  
The Matrix ◽  
Preceding Note ◽  
Limiting Condition

The investigation of axisymmetric states of stress by the matrix displacement method may, in principle, be carried out as an ordinary exercise of three-dimensional analysis, using TETRA 4, TETRA 10 or other suitable elements. However, this approach is clearly not the most efficient by not taking advantage ab initio of the inherent simplifications arising in an axisymmetric state; this leads to an unnecessary inflation of the number of unknowns and complexity of the mesh. A number of techniques to deal with this limiting condition of a three-dimensional state have been developed at the ISD. The theory for one specific element, TRIAX 6 which evolves most naturally from the tapered TRIM 6 element analysed in the preceding note 8 is presented.

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