Matrix analysis of an anisotropic optical thin film

Based on Maxwell's equations, standard boundary conditions are imposed on resultant electric- and magnetic-field vectors at interfaces, and the propagating characteristics of extraordinary waves, such as the forward- and backward-propagating directions of wave vectors, rays and their corresponding refractive indices are determined in a uniaxially birefringent thin film. Furthermore, 2 x 2 characteristic matrices of a birefringent thin film are derived including multiple reflections for the extraordinary wave.

THE MATRIX ANALYSIS FOR AN OPTICAL FREE-SPACE SWITCHING NETWORK AND AN OPTICAL CROSSOVER NETWORK WITH 4-FUNCTION INTERCHANGE NODES

A matrix analysis for free-space switching networks, such as perfect shuffle-exchange omega, crossover and Banyan is presented. On the basis of matrix analysis, the equivalence of these three switching networks and the route selection between input and output ports are simply explained. Furthermore, an optical crossover switching network, where MQW SEED arrays are used as electrically addressed four-function interchange nodes, is described and the optical crossover interconnection of 64 x 64, and high-speed four-function, interchange nodes is demonstrated in the experiment.

A study of matrix analysis methods for inelastic structures. Project no. 1467, Task no. 146701, prepared under Contract no. AF 33 (657)-8717 by Massachusetts Institute of Technology, Aeroelastic and Structures Research Laboratory.

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Rank regression analysis of correlated water quality data from South East Queensland

With growing population and fast urbanization in Australia, it is a challenging task to maintain our water quality. It is essential to develop an appropriate statistical methodology in analyzing water quality data in order to draw valid conclusions and hence provide useful advices in water management. This paper is to develop robust rank-based procedures for analyzing nonnormally distributed data collected over time at different sites. To take account of temporal correlations of the observations within sites, we consider the optimally combined estimating functions proposed by Wang and Zhu (Biometrika, 93:459-464, 2006) which leads to more efficient parameter estimation. Furthermore, we apply the induced smoothing method to reduce the computational burden. Smoothing leads to easy calculation of the parameter estimates and their variance-covariance matrix. Analysis of water quality data from Total Iron and Total Cyanophytes shows the differences between the traditional generalized linear mixed models and rank regression models. Our analysis also demonstrates the advantages of the rank regression models for analyzing nonnormal data.

Higher order derivatives and norms of certain matrix functions

Tese de doutoramento, Matemática (Álgebra Lógica e Fundamentos), Universidade de Lisboa, Faculdade de Ciências, 2014

Conformational analysis of antibody binding site using EDMA methods /

Euclidean distance matrix analysis (EDMA) methods are used to distinguish whether or not significant difference exists between conformational samples of antibody complementarity determining region (CDR) loops, isolated LI loop and LI in three-loop assembly (LI, L3 and H3) obtained from Monte Carlo simulation. After the significant difference is detected, the specific inter-Ca distance which contributes to the difference is identified using EDMA.The estimated and improved mean forms of the conformational samples of isolated LI loop and LI loop in three-loop assembly, CDR loops of antibody binding site, are described using EDMA and distance geometry (DGEOM). To the best of our knowledge, it is the first time the EDMA methods are used to analyze conformational samples of molecules obtained from Monte Carlo simulations. Therefore, validations of the EDMA methods using both positive control and negative control tests for the conformational samples of isolated LI loop and LI in three-loop assembly must be done. The EDMA-I bootstrap null hypothesis tests showed false positive results for the comparison of six samples of the isolated LI loop and true positive results for comparison of conformational samples of isolated LI loop and LI in three-loop assembly. The bootstrap confidence interval tests revealed true negative results for comparisons of six samples of the isolated LI loop, and false negative results for the conformational comparisons between isolated LI loop and LI in three-loop assembly. Different conformational sample sizes are further explored by combining the samples of isolated LI loop to increase the sample size, or by clustering the sample using self-organizing map (SOM) to narrow the conformational distribution of the samples being comparedmolecular conformations. However, there is no improvement made for both bootstrap null hypothesis and confidence interval tests. These results show that more work is required before EDMA methods can be used reliably as a method for comparison of samples obtained by Monte Carlo simulations.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Menu Analysis: Review and Evaluation

In the article - Menu Analysis: Review and Evaluation - by Lendal H. Kotschevar, Distinguished Professor School of Hospitality Management, Florida International University, Kotschevar’s initial statement reads: “Various methods are used to evaluate menus. Some have quite different approaches and give different information. Even those using quite similar methods vary in the information they give. The author attempts to describe the most frequently used methods and to indicate their value. A correlation calculation is made to see how well certain of these methods agree in the information they give.” There is more than one way to look at the word menu. The culinary selections decided upon by the head chef or owner of a restaurant, which ultimately define the type of restaurant is one way. The physical outline of the food, which a patron actually holds in his or her hand, is another. These descriptions are most common to the word, menu. The author primarily concentrates on the latter description, and uses the act of counting the number of items sold on a menu to measure the popularity of any particular item. This, along with a formula, allows Kotschevar to arrive at a specific value per item. Menu analysis would appear a difficult subject to broach. How does a person approach a menu analysis, how do you qualify and quantify a menu; it seems such a subjective exercise. The author offers methods and outlines on approaching menu analysis from empirical perspectives. “Menus are often examined visually through the evaluation of various factors. It is a subjective method but has the advantage of allowing scrutiny of a wide range of factors which other methods do not,” says Distinguished Professor, Kotschevar. “The method is also highly flexible. Factors can be given a score value and scores summed to give a total for a menu. This allows comparison between menus. If the one making the evaluations knows menu values, it is a good method of judgment,” he further offers. The author wants you to know that assigning values is fundamental to a pragmatic menu analysis; it is how the reviewer keeps score, so to speak. Value merit provides reliable criteria from which to gauge a particular menu item. In the final analysis, menu evaluation provides the mechanism for either keeping or rejecting selected items on a menu. Kotschevar provides at least three different matrix evaluation methods; they are defined as the Miller method, the Smith and Kasavana method, and the Pavesic method. He offers illustrated examples of each via a table format. These are helpful tools since trying to explain the theories behind the tables would be difficult at best. Kotschevar also references examples of analysis methods which aren’t matrix based. The Hayes and Huffman - Goal Value Analysis - is one such method. The author sees no one method better than another, and suggests that combining two or more of the methods to be a benefit.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.