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41.
R. J. Vanderbei 《Mathematical Programming》1989,43(1-3):31-44
The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual. 相似文献
42.
A new geometrical method to determine the surface damage threshold for ultrashort pulses is presented. It consists in the formation of a surface damage profile by a movement of the sample across the laser beam focus. A single measurement of the maximum transversal dimension of this damage profile, which depends solely on the laser beam power, is used to calculate the local damage threshold intensity. It is also theoretically shown that the damage in the transverse dimension can be controlled under the diffraction-limited spot. 相似文献
43.
A piecewise linearization method based on the linearization of nonlinear ordinary differential equations in small intervals, that provides piecewise analytical solutions in each interval and smooth solutions everywhere, is developed for the study of the limit cycles of smooth and non-smooth, conservative and non-conservative, nonlinear oscillators. It is shown that this method provides nonlinear maps for the displacement and velocity which depend on the previous values through the nonlinearity and its partial derivatives with respect to time, displacement and velocity, and yields non-standard finite difference formulae. It is also shown by means of five examples that the piecewise linearization method presented here is more robust and yields more accurate (in terms of displacement, energy and frequency) solutions than the harmonic balance procedure, the method of slowly varying amplitude and phase, and other non-standard finite difference equations. 相似文献
44.
I. J. Tchoupaeva 《Journal of Mathematical Sciences》2006,135(5):3409-3419
Some geometric theorems can be stated in coordinate-free form as polynomials in Grassman algebra and can be proven by the anticommutative Gröbner basis method. In this article, we analyze some properties of both sets of hypotheses and conclusions of the theorem. 相似文献
45.
R. J. Hinde 《Few-Body Systems》2006,38(2-4):187-191
We compute the vibrational coupling between two H2 molecules from ab initio quantum chemical calculations of the H2-H2 potential carried out at the full configuration interaction level of theory using the atom-centered aug-cc-pVTZ basis set
for hydrogen. We compare the full configuration interaction results with those obtained using two variants of coupled cluster
theory and find that a fully iterative treatment of connected triples may be required to estimate the H2-H2 vibrational coupling accurately using coupled cluster theory. 相似文献
46.
J. M. Rubi 《Journal of statistical physics》2006,123(2):497-498
47.
In this paper we study root system generalizations of the quantum Bose-gas on the circle with pair-wise delta-function interactions.
The underlying symmetry structures are shown to be governed by the associated graded algebra of Cherednik's (suitably filtered)
degenerate double affine Hecke algebra, acting by Dunkl-type differential-reflection operators. We use Gutkin's generalization
of the equivalence between the impenetrable Bose-gas and the free Fermi-gas to derive the Bethe ansatz equations and the Bethe
ansatz eigenfunctions. 相似文献
48.
J. Matkowski 《Aequationes Mathematicae》2002,64(3):297-303
Summary. Iteration semigroups of weighted quasi-arithmetic mean-type mappings are considered. Existence and uniqueness of a mean which is invariant with respect to a continuous semigroup of mean-type mapping is proved. 相似文献
49.
In this paper, we explore the interplay of four different conjectures on certain zero-sum problems in Zp Zp. This study of the inter-relations between these conjectures leads to the conclusion that determining the structure of minimal zero sequences (see below for the precise definition) is crucial. Also, we study the analogous situation in Zn. 相似文献
50.
A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with zb‐ for the left and zb+ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献