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Basis Vectors (basis + vector)
Selected AbstractsComputation on symmetry-invariant basesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2003Jian Wu Abstract There is standard methodology available to facilitate electronic structure computations on a space that is invariant under a symmetry group. Here, we focus on additional consequences that arise if the basis itself is invariant under the symmetry group (i.e., in the case that application of symmetry operations to each basis vector yields, up to proportionality, a single basis vector). In illustration of the formal development, examples are considered where the symmetries are point-group symmetries and the basis vectors are Slater determinants over singly occupied atomic orbitals, as for an open-shell valence bond (VB) model. Several other types of examples are mentioned, e.g., a basis of chemically motivated resonance structures, as for a VB model, or an orbital basis of atomic orbitals for a one-electron Hückel-type model. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 7,22, 2003 [source] The application of modified lapped transform domain median filter to narrow,band interference excision in DSSS systemsEUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS, Issue 4 2001Chongni Li Guangruihu A novel communication receiver which uses lapped transform (LT) incorporating modified median filter (MMF) algorithm is designed for narrow,band interference (NB1) excision. Comparing to traditional Fourier Transform, LT has longer basis vectors, less spectral leakage, thus better frequency resolution. The LT domain MMF algorithm takes full advantages of the direct sequence spread spectrum signal, as well as the characteristics of LT, performs the transform domain filtering twice. The first filtering locates the position of interference and mitigates most of them. The second filtering was performed in a small neighborhood of the located interference. So LT domain MMF algorithm can completely mitigate the interference without distorting the desired signal. Simulation results demonstrated the improved BER performance and increased robustness of our approach. [source] A study of thickness optimization of golf club heads to maximize release velocity of ballsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2004Kenji Nakai Abstract In the present study, the shape optimization of a golf club head is investigated. The problem of maximizing the release velocity of the ball after impact is treated under the constraint of a specified weight of club head. The thickness distribution of the clubface is chosen as the design variable for optimization. The basis vector method, which is an approximating method for optimization problems in which the sensitivity cannot be derived analytically, is employed. The basis vector represents a fundamental change of shape, and it is preferable to obtaining effective results that the basis vectors be mutually independent. A simple approach to create the basis vectors using eigenmodes is also presented. The theory of impedance matching is confirmed numerically by a two-dimensional example. A three-dimensional example is given to show that this approach is effective for optimal design of the golf club head. Copyright © 2004 John Wiley & Sons, Ltd. [source] Efficient modal analysis of systems with local stiffness uncertaintiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6-7 2009S. F. Wojtkiewicz Abstract The characterization of the uncertainty in modal quantities of an uncertain linear structural system is essential to the rapid determination of its response to arbitrary loadings. Although the size of many computational structural models used is extremely large, i.e. thousands of equations, the uncertainty to be analyzed is oftentimes localized to very small regions of the model. This paper addresses the development of an efficient, computational methodology for the modal analysis of linear structural systems with local stiffness uncertainties. The newly developed methodology utilizes an enriched basis that consists of the sub-spectrum of a nominal structural system augmented with additional basis vectors generated from a knowledge of the structure of the stiffness uncertainty. In addition, methods for determining bounds on the approximate modal frequencies and mode shapes are discussed. Numerical results demonstrate that the algorithm produces highly accurate results with greatly reduced computational effort. Copyright © 2009 John Wiley & Sons, Ltd. [source] Lower-bound limit analysis by using the EFG method and non-linear programmingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2008Shenshen Chen Abstract Intended to avoid the complicated computations of elasto-plastic incremental analysis, limit analysis is an appealing direct method for determining the load-carrying capacity of structures. On the basis of the static limit analysis theorem, a solution procedure for lower-bound limit analysis is presented firstly, making use of the element-free Galerkin (EFG) method rather than traditional numerical methods such as the finite element method and boundary element method. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration. The reduced-basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. The self-equilibrium stress field is expressed by a linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve these non-linear programming sub-problems and determine the maximal load amplifier. Numerical examples show that it is feasible and effective to solve the problems of limit analysis by using the EFG method and non-linear programming. Copyright © 2007 John Wiley & Sons, Ltd. [source] Computation on symmetry-invariant basesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2003Jian Wu Abstract There is standard methodology available to facilitate electronic structure computations on a space that is invariant under a symmetry group. Here, we focus on additional consequences that arise if the basis itself is invariant under the symmetry group (i.e., in the case that application of symmetry operations to each basis vector yields, up to proportionality, a single basis vector). In illustration of the formal development, examples are considered where the symmetries are point-group symmetries and the basis vectors are Slater determinants over singly occupied atomic orbitals, as for an open-shell valence bond (VB) model. Several other types of examples are mentioned, e.g., a basis of chemically motivated resonance structures, as for a VB model, or an orbital basis of atomic orbitals for a one-electron Hückel-type model. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 7,22, 2003 [source] FBR: a robust method to determine the basis matrix of the Bravais lattice from oscillation imagesJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3-2 2000Klaus Döhring The FBR (Fourier basis reconstruction) method described in this paper has been designed to determine the basis matrix of the Bravais lattice with respect to the laboratory frame of reference and without prior knowledge of cell constants, particularly for protein crystals of comparatively low quality. It is based on Fourier analysis of a three-dimensional intensity distribution in reciprocal space, which is directly obtained from observed intensity distributions, provided that they are recorded by the rotation method using a fixed X-ray wavelength, resulting in a direct-space determination of the basis vectors. After a description of the motivation and theory behind the method, it is tested by application to numerically generated images of a virtual sample crystal and to experimental data of a lysozyme crystal with well known cell constants. Finally, FBR is applied to a set of images of bacteriorhodopsin crystals suffering from strong anisotropic spot broadening; this case provided the original motivation for the present work. [source] Investigation into the protein composition of human tear fluid using centrifugal filters and drop coating deposition Raman spectroscopyJOURNAL OF RAMAN SPECTROSCOPY, Issue 2 2009Jacob Filik Abstract Drop coating deposition Raman spectroscopy (DCDRS) is a simple method of analysing weak protein solutions. This study is another step in evaluating the analysis of tear fluid by DCDRS as a future medical diagnostic technique. The main aims of this study are to determine whether the DCDR spectra from tear samples contain signals from more than one protein (so relative levels can be measured) and, if so, are the proteins homogeneously distributed in the dried ring of the deposited material. Tear samples were collected from four healthy volunteers and pooled prior to analysis. Proteins were separated by mass into three groups using centrifugal filters. These groups contained proteins with (1) masses greater than 100 kDa, (2) masses between 100 and 50 kDa and (3) masses between 50 and 3 kDa. DCDR spectra from each of these protein group solutions displayed significant differences, confirming that the mass separation had been successful. When used as basis vectors for least-squares fitting, these spectra (and that of urea) produced excellent fits to the normal tear spectra. Least-squares fitting of spectra from the same point on a single sample and from several drops of the same sample showed that the tear DCDR spectra were highly reproducible. Raman point mapping of the tear ring showed significant radial ring variation, especially towards the outer edge of the ring. The specific peak changes in the protein signal across the ring suggested that the difference in the outer edge was due to protein desiccation as opposed to inhomogeneous protein deposition. Copyright © 2008 John Wiley & Sons, Ltd. [source] | |||||||||||||