The symbolic-numeric computing described here consists of an extensive symbolic pre-processing of systems of differential-algebraic equations (DAE), followed by the numerical integration of the system obtained. The application area is multibody dynamics. We deal symbolically with a DAE system using differentiation and elimination methods to find all the hidden constraints, and produce a system ...

We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schrödinger equation for diatomic molecules. Our approach employs Neumann’s expansion of the Coulomb repulsion 1/jx yj, solves the resulting integrals symbolically in closed form and subsequently performs a numeric Taylor...

The symbolic-numeric computing described here consists of an extensive symbolic pre-processing of systems of differential-algebraic equations (DAE), followed by the numerical integration of the system obtained. The application area is multibody dynamics. We deal symbolically with a DAE system using differentiation and elimination methods to find all the hidden constraints, and produce a system ...

Many extensions to existing qualitative simulation packages allow combined use of available numeric and qualitative information . Some provide numeric integration across two qualitative states but none of them highlights numerically or semi-quantitatively the qualitatively predicted time points . Moreover, high accuracy at time points is only achieved by a fine level of granularity across the e...

In this paper we study formation of platoons and their velocity–size distribution in freeway traffic using the stochastic Master equation approach. The solution to the Master equation and the moments of the distribution are obtained by numeric integration. We also discuss a possible generalization of this approach to the case of a multi–lane traffic flow and propose a microscopic, particle–hopp...

In this study integral form and new recursive formulas for Favard constants and some connected with them numeric and Fourier series are obtained. The method is based on preliminary integration of Fourier series which allows for establishing finite recursive representations for the summation. It is shown that the derived recursive representations are numerically more effective than known represe...

The integration of constraint solvers into proof planning has pushed the problem solving horizon. Proof planning benefits from the general functionalities of a constraint solver such as consistency check, constraint inference, as well as the search for instantiations. However, off-the-shelf constraint solvers need to be extended in order to be be integrated appropriately: In particular, for cor...

This paper proposes a qualitative representation for kinematic robots. First, qualitative geometric primitives are introduced by combining a qualitative orientation component and qualitative translation component using normalisation. A position in Cartesian space can be mathematically described by the scalable primitives. Secondly, the qualitative positions of the components of a robot are deri...

High field wigglers for synchrotron radiation production have usually rather complex distribution of magnetic field, and particle motion through it can hardly be treated analytically. This paper concerns a simple and reliable receipt for a symplectic algorithm to track a particle through such fields. Input data for numeric integration are taken directly from results of magnetic mapping or simul...

Determination and early detection of emerging trends can be retrieved from numeric data as well as from texts. Using texts for trend mining brings advances for the recognition process. The systematic integration of informaion descriptions and metadata schemes enable the additional semantic analysis of the available information. In this paper, we introduce the issue of trend recognition in infor...