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Algebra
Kinds of Algebra Terms modified by Algebra Selected AbstractsTHE PUSH,PULL OF MARKETING AND ADVERTISING AND THE ALGEBRA OF THE CONSUMER'S MIND,JOURNAL OF SENSORY STUDIES, Issue 2 2007JEFF EWALD ABSTRACT This article suggests that the relationship between a brand and a product is a virtuous circle,the brand frames expectations for a product execution; and the product experience either strengthens the brand perceptions or weakens them. Empirical evidence, based on a comprehensive database of scores collected across multiple conjoint studies, then confirms the hypothesis that different product attributes synergize, or interact, with different brand names. [source] A 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] Vectors and Beyond: Geometric Algebra and its Philosophical SignificanceDIALECTICA, Issue 4 2009Peter Simons First page of article [source] An SL(2,,)-covariant, first order, ,-supersymmetric action for the D5-brane,FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 3 2005P. Fré Abstract The new first order, rheonomic, ,,supersymmetric formalism recently introduced by us for the world-volume action of the D3 brane is extended to the case of D5 branes. This extension requires the dual formulation of the Free Differential Algebra of type IIB supergravity in terms of 6,form gauge potentials which was so far missing and is given here. Furthermore relying on our new approach we are able to write the D5 world volume action in a manifestly SL(2,,) covariant form. This is important in order to solve the outstanding problem of finding the appropriate boundary actions of D3,branes on smooth ALE manifolds with twisted fields. The application of our results to this problem is however postponed to a subsequent publication. [source] Lie Algebra and the Mobility of Kinematic ChainsJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 8 2003J. M. Rico This paper deals with the application of Lie Algebra to the mobility analysis of kinematic chains. It develops an algebraic formulation of a group-theoretic mobility criterion developed recently by two of the authors of this publication. The instantaneous form of the mobility criterion presented here is based on the theory of subspaces and subalgebras of the Lie Algebra of the Euclidean group and their possible intersections. It is shown using this theory that certain results on mobility of over-constraint linkages derived previously using screw theory are not complete and accurate. The theory presented provides for a computational approach that would allow efficient automation of the new group-theoretic mobility criterion. The theory is illustrated using several examples. © 2003 Wiley Periodicals, Inc. [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] Matrix pencil equivalents of symmetric polynomial matrices,ASIAN JOURNAL OF CONTROL, Issue 2 2010Nicholas P. Karampetakis Abstract A new family of companion forms for polynomials and polynomial matrices has recently been developed in (Lin. Algebra Appl. 2003; 372: 325,331; Electron. J. Lin. Algebra 2004; 11:78,87) respectively. The application of these new companion forms to polynomial matrices with symmetries has been examined in (Electron. J. Lin. Algebra 2006; 15:107,114). In this work we extend the results presented in (Electron. J. Lin. Algebra 2006; 15:107,114) to the case of 2-D polynomial matrices. Thus, we provide a new matrix pencil that preserves both the symmetric structure and the structural invariants, of the original 2-D polynomial matrix. The results are also extended to the polynomial system matrix case. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Algebra and Geometry in the Old Babylonian Period: Matters Concerning ReedsCENTAURUS, Issue 4 2005Piedad Yuste One of the mathematical topics examined in the Old Babylonian period consisted of calculating the size of a reed which was used to measure either a longitude or the perimeter of a rectangle or trapezium. These subjects were solved, probably, applying the geometric construction called completing the square. In this paper, we analyse the problem texts on the tablets AO 6770 (5), Str 368, VAT 7532, and VAT 7535. [source] Structured Condition Numbers of Multiple EigenvaluesPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006María José Peláez We analyze the influence of matrix structure on the condition number of multiple, possibly defective eigenvalues. We show that the structured and unstructured Hölder condition numbers coincide for multiple eigenvalues of matrices belonging to certain classes of structured matrices, which can be characterized as either Jordan or Lie Algebras. We do this by explicitly finding a specific perturbation matrix, analogous to the classical Wilkinson perturbation, which attains the maximal variation within the class of structured matrices. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Granularity in Relational Formalisms,With Application to Time and Space RepresentationCOMPUTATIONAL INTELLIGENCE, Issue 4 2001Jérôme Euzenat Temporal and spatial phenomena can be seen at a more or less precise granularity, depending on the kind of perceivable details. As a consequence, the relationship between two objects may differ depending on the granularity considered. When merging representations of different granularity, this may raise problems. This paper presents general rules of granularity conversion in relation algebras. Granularity is considered independently of the specific relation algebra, by investigating operators for converting a representation from one granularity to another and presenting six constraints that they must satisfy. The constraints are shown to be independent and consistent and general results about the existence of such operators are provided. The constraints are used to generate the unique pairs of operators for converting qualitative temporal relationships (upward and downward) from one granularity to another. Then two fundamental constructors (product and weakening) are presented: they permit the generation of new qualitative systems (e.g. space algebra) from existing ones. They are shown to preserve most of the properties of granularity conversion operators. [source] A Primer on Topological PersistenceCOMPUTER GRAPHICS FORUM, Issue 3 2006Herbert Edelsbrunner The idea of topological persistence is to look at homological features that persist along a nested sequence of topo-logical spaces. As a typical example, we may take the sequence of sublevel sets of a function. The combinatorial characterization of persistence in terms of pairs of critical values and fast algorithms computing these pairs make this idea practical and useful in dealing with the pervasive phenomenon of noise in geometric and visual data. This talk will 1. recall the relatively short history of persistence and some of its older roots; 2. introduce the concept intuitively while pointing out where algebra is needed to solidify the more difficult steps; 3. discuss a few applications to give a feeling of the potential of the method in dealing with noise and scale. Besides the initial concept, the talk will touch upon recent extensions and their motivation. [source] Consistency of a Shared Versioned Model for Distributed CooperationCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 6 2005B. Firmenich As a rule the ultimate solution needs many iteration steps. Available CAD-systems support synchronous and distributed work on a document base. Therefore, cooperation between the engineers can be obtained only by the exchange of documents. It is generally known that an overall consistency of the planning material is not adequately addressed by this approach. In this article a solution approach focused upon consistency of the shared planning material in a distributed CAD environment is presented. Because of the nature of the planning process, version management is applied on an object basis. Project data are stored as object versions and relationships. The operations for the distributed cooperation are identified and their impact on the project data is described formally, using logical expressions and set theory. A formulation based upon an algebra of sets is presented. [source] Geometric algebra and transition-selective implementations of the controlled-NOT gateCONCEPTS IN MAGNETIC RESONANCE, Issue 1 2004Timothy F. Havel Geometric algebra provides a complete set of simple rules for the manipulation of product operator expressions at a symbolic level, without any explicit use of matrices. This approach can be used not only to describe the state and evolution of a spin system, but also to derive the effective Hamiltonian and associated propagator in full generality. In this article, we illustrate the use of geometric algebra via a detailed analysis of transition-selective implementations of the controlled-NOT gate, which plays a key role in NMR-based quantum information processing. In the appendices, we show how one can also use geometric algebra to derive tight bounds on the magnitudes of the errors associated with these implementations of the controlled-NOT. © 2004 Wiley Periodicals, Inc. Concepts Magn Reson Part A 23A: 49,62, 2004 [source] Measuring and modelling the performance of a parallel ODMG compliant object database serverCONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 1 2006Sandra de F. Mendes Sampaio Abstract Object database management systems (ODBMSs) are now established as the database management technology of choice for a range of challenging data intensive applications. Furthermore, the applications associated with object databases typically have stringent performance requirements, and some are associated with very large data sets. An important feature for the performance of object databases is the speed at which relationships can be explored. In queries, this depends on the effectiveness of different join algorithms into which queries that follow relationships can be compiled. This paper presents a performance evaluation of the Polar parallel object database system, focusing in particular on the performance of parallel join algorithms. Polar is a parallel, shared-nothing implementation of the Object Database Management Group (ODMG) standard for object databases. The paper presents an empirical evaluation of queries expressed in the ODMG Query Language (OQL), as well as a cost model for the parallel algebra that is used to evaluate OQL queries. The cost model is validated against the empirical results for a collection of queries using four different join algorithms, one that is value based and three that are pointer based. Copyright © 2005 John Wiley & Sons, Ltd. [source] Field theory on nonanticommutative superspaceFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 4-5 2008M. Dimitrijevi Abstract We discuss a deformation of the Hopf algebra of supersymmetry (SUSY) transformations based on a special choice of a twist. As usual, algebra itself remains unchanged, but the comultiplication changes. This leads to a deformed Leibniz rule for SUSY transformations. Superfields are multiplied by using a ,-product which is noncommutative, hermitian and finite when expanded in power series of the deformation parameter. One possible deformation of the Wess-Zumino action is proposed and analysed in detail. Differently from most of the literature concerning this subject, we work in Minkowski space-time. [source] Single particle representation of parabose extension of conformal supersymmetryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 4-5 2008I. Salom Abstract We consider generalized conformal supersymmetry constructed as parabose N = 4 algebra. It is shown that Green's ansatz representations have, in this context, natural interpretation as multi particle spaces. The simplest nontrivial representation is shown to correspond to a massless particle of arbitrary helicity, and some peculiar properties of this space are pointed out. [source] String theory: exact solutions, marginal deformations and hyperbolic spacesFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2 2007D. Orlando Abstract This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the CFT description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In he final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze direct products of constant-curvature spaces and find solutions with hyperbolic spaces. [source] Dependence of s -waves on continuous dimension: The quantum oscillator and free systemsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 12 2006K.B. Wolf Abstract Wavefunctions with rotational symmetry (i.e., zero angular momentum) in D dimensions, are called s -waves. In quantum quadratic systems (free particle, harmonic and repulsive oscillators), their radial parts obey Schrödinger equations with a fictitious centrifugal (for integer D , 4) or centripetal (for D = 2) potential. These Hamiltonians close into the three-dimensional Lorentz algebra so(2,1), whose exceptional interval corresponds to the critical range of continuous dimensions 0 < D < 4, where they exhibit a one-parameter family of self-adjoint extensions in ,2(,+). We study the characterization of these extensions in the harmonic oscillator through their spectra which , except for the Friedrichs extension , are not equally spaced, and we build their time evolution Green function. The oscillator is then contracted to the free particle in continuous- D dimensions, where the extension structure is mantained in the limit of continuous spectra. Finally, we compute the free time evolution of the expectation values of the Hamiltonian, dilatation generator, and square radius between three distinct sets of ,heat'-diffused localized eigenstates. This provides a simple group-theoretic description of the purported contraction/expansion of Gaussian-ring s -waves in D > 0 dimensions. [source] Ricci flows and infinite dimensional algebrasFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6-7 2004I. Bakas The renormalization group equations of two-dimensional sigma models describe geometric deformations of their target space when the world-sheet length changes scale from the ultra-violet to the infra-red. These equations, which are also known in the mathematics literature as Ricci flows, are analyzed for the particular case of two-dimensional target spaces, where they are found to admit a systematic description as Toda system. Their zero curvature formulation is made possible with the aid of a novel infinite dimensional Lie algebra, which has anti-symmetric Cartan kernel and exhibits exponential growth. The general solution is obtained in closed form using Bäcklund transformations, and special examples include the sausage model and the decay process of conical singularities to the plane. Thus, Ricci flows provide a non-linear generalization of the heat equation in two dimensions with the same dissipative properties. Various applications to dynamical problems of string theory are also briefly discussed. Finally, we outline generalizations to higher dimensional target spaces that exhibit sufficient number of Killing symmetries. [source] Boundaries, defects and Frobenius algebrasFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2003J. Fuchs The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new computational tools. The construction of CFT correlators based on combining tools from topological field theory and non-commutative algebra in tensor categories, which we summarize in this contribution, allows e.g. to discuss, apart from boundary conditions, also defect lines and disorder fields. [source] The Assessment of Land Resources: Achievements and New ChallengesGEOGRAPHICAL RESEARCH, Issue 2 2002Donald A. Davidson It is surprising that despite all the pleas and policies regarding the development of sustainable land use systems, there is still considerable ignorance regarding the nature and significance of land resources. This paper traces the development and achievements of land evaluation during the 20th century, with particular reference to soils. The most active period was between 1950 and around 1980 with the development of soil and land capability surveys, methodological advances initiated with the FAO Framework for Land Evaluation, and regional land resource assessments. Thus there were considerable achievements in land evaluation by the early 1980s, and subsequently there have been important advances in the subject through the application of GIS, spatial analysis, modelling and fuzzy set algebra. Since the late 1990s there has been a phenomenal rise in interest in soil quality assessment. Considerable debate has focussed on definition, and methods of assessment and monitoring. The latter part of this paper discusses the major challenges to the development and application of land evaluation. The inadequacy of much soil survey data in terms of variables, quality, spatial coverage and scale is emphasised. Also, there is a continuing need to highlight the centrality of land resource issues in any attempt to develop sustainable land use systems. [source] On shear-wave triplications in a multilayered transeversely isotropic medium with vertical symmetry axisGEOPHYSICAL PROSPECTING, Issue 4 2010Yuriy Roganov ABSTRACT The presence of triplications (caustics) can be a serious problem in seismic data processing and analysis. The traveltime curve becomes multi-valued and the geometrical spreading correction factor tends to zero due to energy focusing. We analyse the conditions for the qSV-wave triplications in a homogeneous transversely isotropic medium with vertical symmetry axis. The proposed technique can easily be extended to the case of horizontally layered vertical symmetry axis medium. We show that the triplications of the qSV-wave in a multilayered medium imply certain algebra. We illustrate this algebra on a two-layer vertical symmetry axis model. [source] Monte Carlo probabilistic sensitivity analysis for patient level simulation models: efficient estimation of mean and variance using ANOVAHEALTH ECONOMICS, Issue 10 2007Anthony O'Hagan Abstract Probabilistic sensitivity analysis (PSA) is required to account for uncertainty in cost-effectiveness calculations arising from health economic models. The simplest way to perform PSA in practice is by Monte Carlo methods, which involves running the model many times using randomly sampled values of the model inputs. However, this can be impractical when the economic model takes appreciable amounts of time to run. This situation arises, in particular, for patient-level simulation models (also known as micro-simulation or individual-level simulation models), where a single run of the model simulates the health care of many thousands of individual patients. The large number of patients required in each run to achieve accurate estimation of cost-effectiveness means that only a relatively small number of runs is possible. For this reason, it is often said that PSA is not practical for patient-level models. We develop a way to reduce the computational burden of Monte Carlo PSA for patient-level models, based on the algebra of analysis of variance. Methods are presented to estimate the mean and variance of the model output, with formulae for determining optimal sample sizes. The methods are simple to apply and will typically reduce the computational demand very substantially. Copyright © 2006 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] Lie-Poisson integrators: A Hamiltonian, variational approachINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Zhanhua Ma Abstract In this paper we present a systematic and general method for developing variational integrators for Lie-Poisson Hamiltonian systems living in a finite-dimensional space ,,*, the dual of Lie algebra associated with a Lie group G. These integrators are essentially different discretized versions of the Lie-Poisson variational principle, or a modified Lie-Poisson variational principle proposed in this paper. We present three different integrators, including symplectic, variational Lie-Poisson integrators on G×,,* and on ,,×,,*, as well as an integrator on ,,* that is symplectic under certain conditions on the Hamiltonian. Examples of applications include simulations of free rigid body rotation and the dynamics of N point vortices on a sphere. Simulation results verify that some of these variational Lie-Poisson integrators are good candidates for geometric simulation of those two Lie-Poisson Hamiltonian systems. Copyright © 2009 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] A return map algorithm for general isotropic elasto/visco-plastic materials in principal spaceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Luciano Rosati Abstract We describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto/visco-plastic models whose yield function incorporates the third stress invariant . The developments presented are based upon original results, proved in the paper, concerning the derivatives of eigenvalues and eigenprojectors of symmetric second-order tensors with respect to the tensor itself and upon an original algebra of fourth-order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument . The analysis, initially referred to the small-strain case, is then extended to a formulation for the large deformation regime; for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the Lagrangian description of large-strain elastoplasticity. Copyright © 2004 John Wiley & Sons, Ltd. [source] A general high-order finite element formulation for shells at large strains and finite rotationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Y. Ba Abstract For hyperelastic shells with finite rotations and large strains a p -finite element formulation is presented accommodating general kinematic assumptions, interpolation polynomials and particularly general three-dimensional hyperelastic constitutive laws. This goal is achieved by hierarchical, high-order shell models. The tangent stiffness matrices for the hierarchical shell models are derived by computer algebra. Both non-hierarchical, nodal as well as hierarchical element shape functions are admissible. Numerical experiments show the high-order formulation to be less prone to locking effects. Copyright © 2003 John Wiley & Sons, Ltd. [source] Databases for interval probabilitiesINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 9 2004Wenzhong Zhao We present a database framework for the efficient storage and manipulation of interval probability distributions and their associated information. Although work on interval probabilities and on probabilistic databases has appeared before, ours is the first to combine these into a coherent and mathematically sound framework including both standard relational queries and queries based on probability theory. In particular, our query algebra allows users not only to query existing interval probability distributions, but also to construct new ones by means of conditionalization and marginalization, as well as other more common database operations. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 789,815, 2004. [source] | ||||||||||||||||||||||||||||||||||