Home About us Contact
|
Home About us Contact | ||
|
|
||
Linear Algebra (linear + algebra)
Selected AbstractsA digital simulation of the vibration of a two-mass two-spring systemCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 3 2010Wei-Pin Lee Abstract In this study, we developed a computer program to simulate the vibration of a two-mass two-spring system by using Visual BASIC. Users can enter data for the two-mass two-spring system. The software will derive the eigenvalue problem from the input data. Then the software solves the eigenvalue problem and illustrates the results numerically and graphically on the screen. In addition, the program uses animation to demonstrate the motions of the two masses. The displacements, velocities, and accelerations of the two bodies can be shown if the corresponding checkboxes are selected. This program can be used in teaching courses, such as Linear Algebra, Advanced Engineering Mathematics, Vibrations, and Dynamics. Use of the software may help students to understand the applications of eigenvalue problems and related topics such as modes of vibration, natural frequencies, and systems of differential equations. © 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 18: 563,573, 2010; View this article online at wileyonlinelibrary.com; DOI 10.1002/cae.20241 [source] Digital simulation of the transformation of plane stressCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 1 2009Wei-Pin Lee Abstract In this study, we developed a computer program to simulate the transformation of plane stress by using Visual Basic.NET. We applied the equations of stress transformation to plane stress problems to calculate the stresses with respect to the 1,2 axes, which are rotated counterclockwise through an angle , about the x,y origin, and showed the visual results on the screen. In addition, we used animation to observe the change of plane stress. This program was then used in teaching courses, such as Mechanics of Materials and Linear Algebra. Use of the software may help students to understand principal stresses, principal axes, Mohr's circle, eigenvalues, eigenvectors, similar matrices, and invariants. © 2008 Wiley Periodicals, Inc. Comput Appl Eng Educ 17: 25,33, 2009; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae20180 [source] ,Numerical Linear Algebra with Applications' impact factor for 2008 has been published to be 0.822NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 9 2009Article first published online: 20 AUG 200 Abstract The Journal ,Numerical Linear Algebra with Applications' has received its 2008 impact factor. The impact factor for 2008 has been published to be 0.822, an increase from 0.696 in 2007. Copyright © 2009 John Wiley & Sons, Ltd. [source] Decomposition of symmetric mass,spring vibrating systems using groups, graphs and linear algebraINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2007A. Kaveh Abstract The main objective of this article is to develop a methodology for an efficient calculation of the eigenvalues for symmetric mass,spring systems in order to reduce the size of the eigenproblem involved. This is achieved using group-theoretical method, whereby the model of a symmetric mass,spring system is decomposed into appropriate submodels. The eigenvalues of the entire system is then obtained by calculating the eigenvalues of its submodels. The results are compared to those of the existing methods based on graph theory and linear algebra. Examples are provided to illustrate the simplicity and efficiency of the present method. Copyright © 2006 John Wiley & Sons, Ltd. [source] Block diagonalization of Laplacian matrices of symmetric graphs via group theoryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007A. Kaveh Abstract In this article, group theory is employed for block diagonalization of Laplacian matrices of symmetric graphs. The inter-relation between group diagonalization methods and algebraic-graph methods developed in recent years are established. Efficient methods are presented for calculating the eigenvalues and eigenvectors of matrices having canonical patterns. This is achieved by using concepts from group theory, linear algebra, and graph theory. These methods, which can be viewed as extensions to the previously developed approaches, are illustrated by applying to the eigensolution of the Laplacian matrices of symmetric graphs. The methods of this paper can be applied to combinatorial optimization problems such as nodal and element ordering and graph partitioning by calculating the second eigenvalue for the Laplacian matrices of the models and the formation of their Fiedler vectors. Considering the graphs as the topological models of skeletal structures, the present methods become applicable to the calculation of the buckling loads and the natural frequencies and natural modes of skeletal structures. Copyright © 2006 John Wiley & Sons, Ltd. [source] Partial pole assignment for the vibrating system with aerodynamic effectNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2004Wen-Wei Lin Abstract The partial pole assignment (PPA) problem is the one of reassigning a few unwanted eigenvalues of a control system by feedback to suitably chosen ones, while keeping the remaining large number of eigenvalues unchanged. The problem naturally arises in modifying dynamical behaviour of the system. The PPA has been considered by several authors in the past for standard state,space systems and for quadratic matrix polynomials associated with second-order systems. In this paper, we consider the PPA for a cubic matrix polynomial arising from modelling of a vibrating system with aerodynamics effects and derive explicit formulas for feedback matrices in terms of the coefficient matrices of the polynomial. Our results generalize those of a quadratic matrix polynomial by Datta et al. (Linear Algebra Appl. 1997;257: 29) and is based on some new orthogonality relations for eigenvectors of the cubic matrix polynomial, which also generalize the similar ones reported in Datta et al. (Linear Algebra Appl. 1997;257: 29) for the symmetric definite quadratic pencil. Besides playing an important role in our solution for the PPA, these orthogonality relations are of independent interests, and believed to be an important contribution to linear algebra in its own right. Copyright © 2003 John Wiley & Sons, Ltd. [source] Prediction of Tyrosinase Inhibition Activity Using Atom-Based Bilinear IndicesCHEMMEDCHEM, Issue 4 2007Yovani Marrero-Ponce Prof. Abstract A set of novel atom-based molecular fingerprints is proposed based on a bilinear map similar to that defined in linear algebra. These molecular descriptors (MDs) are proposed as a new means of molecular parametrization easily calculated from 2D molecular information. The nonstochastic and stochastic molecular indices match molecular structure provided by molecular topology by using the kth nonstochastic and stochastic graph-theoretical electronic-density matrices, Mk and Sk, respectively. Thus, the kth nonstochastic and stochastic bilinear indices are calculated using Mk and Sk as matrix operators of bilinear transformations. Chemical information is coded by using different pair combinations of atomic weightings (mass, polarizability, vdW volume, and electronegativity). The results of QSAR studies of tyrosinase inhibitors using the new MDs and linear discriminant analysis (LDA) demonstrate the ability of the bilinear indices in testing biological properties. A database of 246 structurally diverse tyrosinase inhibitors was assembled. An inactive set of 412 drugs with other clinical uses was used; both active and inactive sets were processed by hierarchical and partitional cluster analyses to design training and predicting sets. Twelve LDA-based QSAR models were obtained, the first six using the nonstochastic total and local bilinear indices and the last six with the stochastic MDs. The discriminant models were applied; globally good classifications of 99.58 and 89.96,% were observed for the best nonstochastic and stochastic bilinear indices models in the training set along with high Matthews correlation coefficients (C) of 0.99 and 0.79, respectively, in the learning set. External prediction sets used to validate the models obtained were correctly classified, with accuracies of 100 and 87.78,%, respectively, yielding C values of 1.00 and 0.73. This subset contains 180 active and inactive compounds not considered to fit the models. A simulated virtual screen demonstrated this approach in searching tyrosinase inhibitors from compounds never considered in either training or predicting series. These fitted models permitted the selection of new cycloartane compounds isolated from herbal plants as new tyrosinase inhibitors. A good correspondence between theoretical and experimental inhibitory effects on tyrosinase was observed; compound CA6 (IC50=1.32,,M) showed higher activity than the reference compounds kojic acid (IC50=16.67,,M) and L -mimosine (IC50=3.68,,M). [source] Averages of characteristic polynomials in random matrix theoryCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2006A. Borodin We compute averages of products and ratios of characteristic polynomials associated with orthogonal, unitary, and symplectic ensembles of random matrix theory. The Pfaffian/determinantal formulae for these averages are obtained, and the bulk scaling asymptotic limits are found for ensembles with Gaussian weights. Classical results for the correlation functions of the random matrix ensembles and their bulk scaling limits are deduced from these formulae by a simple computation. We employ a discrete approximation method: the problem is solved for discrete analogues of random matrix ensembles originating from representation theory, and then a limit transition is performed. Exact Pfaffian/determinantal formulae for the discrete averages are proven using standard tools of linear algebra; no application of orthogonal or skew-orthogonal polynomials is needed. © 2005 Wiley Periodicals, Inc. [source] | |||||||||||||