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Computer Algebra Systems (computer + algebra_system)

Distribution by Scientific Domains
Mathematics and Statistics40%

Selected Abstracts

Exact integration of the stiffness matrix of an 8-node plane elastic finite element by symbolic computation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2008
L. Videla
Abstract Computer algebra systems (CAS) are powerful tools for obtaining analytical expressions for many engineering applications in both academic and industrial environments. CAS have been used in this paper to generate exact expressions for the stiffness matrix of an 8-node plane elastic finite element. The Maple software system was used to identify six basic formulas from which all the terms of the stiffness matrix could be obtained. The formulas are functions of the Cartesian coordinates of the corner nodes of the element, and elastic parameters Young's modulus and Poisson's ratio. Many algebraic manipulations were performed on the formulas to optimize their efficiency. The redaction in CPU time using the exact expressions as opposed to the classical Gauss,Legendre numerical integration approach was over 50%. In an additional study of accuracy, it was shown that the numerical approach could lead to quite significant errors as compared with the exact approach, especially as element distortion was increased.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source]

Gaussian approximation of exponential type orbitals based on B functions

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2009
Didier Pinchon
Abstract This work gives new, highly accurate optimized gaussian series expansions for the B functions used in molecular quantum mechanics. These functions are generally chosen because of their compact Fourier transform, following Shavitt. The inverse Laplace transform in the square root of the variable is used for Gauss quadrature in this work. Two procedures for obtaining accurate gaussian expansions have been compared for the required extended precision arithmetic. The first is based on Gaussian quadratures and the second on direct optimization. Both use the Maple computer algebra system. Numerical results are tabulated and compared with previous work. Special cases are found to agree before pushing the optimization technique further. The optimal gaussian expansions of B functions obtained in this work are available for reference. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source]

Numerical method to solve chemical differential-algebraic equations

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2002
Ercan Çelik
Abstract In this article, the solution of a chemical differential-algebraic equation model of general type F(y, y,, x) = 0 has been done using MAPLE computer algebra systems. The MAPLE program is given in the Appendix. First we calculate the Power series of the given equations system, then we transform it into Padé series form, which gives an arbitrary order for solving chemical differential-algebraic equation numerically. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source]

Infinitesimal deformations of double covers of smooth algebraic varieties

MATHEMATISCHE NACHRICHTEN, Issue 7 2006
awomir Cynk
Abstract The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. The space of all infinitesimal deformations has a representation as a direct sum of two subspaces. One is isomorphic to the space of simultaneous deformations of the branch locus and the base of the double covering. The second summand is the subspace of deformations of the double covering which induce trivial deformations of the branch divisor. The main result of the paper is a description of the effect of imposing singularities in the branch locus. As a special case we study deformations of Calabi,Yau threefolds which are non-singular models of double cover of the projective 3-space branched along an octic surface. We show that in that case the number of deformations can be computed explicitly using computer algebra systems. This gives a method to compute the Hodge numbers of these Calabi,Yau manifolds. In this case the transverse deformations are resolutions of deformations of double covers of projective space but not double covers of a blow-up of projective space. In the paper we gave many explicit examples. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Computer Algebra Algorithms for Control Related Tests of Implicit Dynamic Systems

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Kurt Schlacher
This contribution is focused on control related tests for implicit dynamic systems, like accessibility, observability or input to output, input to state linearizability. Since the performance of these tests needs tedious symbolic calculations, computer algebra systems are the ideal tool to cope with this problem. Accessibility and observability are exemplarily used to present a new approach based on Lie groups. It is shown that non accessible or non observable systems admit Lie-groups acting on their solutions such that distinguished parts remain unchanged. This fact allows us to apply this technique, as well as its realization by computer algebra algorithm, to several fundamental problems in control. [source]