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991.
992.
H. Frankowska 《Journal of Optimization Theory and Applications》1989,60(2):277-296
We prove sufficient conditions for the instantaneous local controllability of nonlinear (nonsmooth) control systems with feedback. We introduce for that purpose the high-order variations of the reachable map, which is related strongly to its shape. It is a direction in which the reachable map evolves. The cone of variations is convex. This allows one to prove the following theorem: if there exist variationsv
1, ...,v
p
such that int co{v
1, ...,v
p
}, then the system is small-time locally controllable at the point of equilibrium. We provide a short proof of the main result of Sussmann (Ref. 12) and extend it to differential inclusions.This work was supported in part by FCAR of Canada. 相似文献
993.
A plane curveC can be approximated by a parametric cubic spline as follows. Points (x
i
,y
i
) are chosen in order alongC and a monotonically increasing variable is assigned values
i
at the points (x
i
,y
i
):
i
= the cumulative chordal distance from (x
1
,y
1
). The points (
i
,x
i
) and (
i
,y
i
) are then fitted separately by cubic splinesx() andy(), to obtain : (x(),y()). This paper establishes estimates for the errors involved in approximatingC by . It is found that the error in position betweenC and decreases likeh
3, whereh is the maximum length of arc between consecutive knots onC. For first derivatives, the error behaves likeh
2; for second derivatives, likeh. 相似文献
994.
A moving-grid approach for optimization and dynamics of protein-protein complexes is introduced, which utilizes cubic B-spline interpolation for rapid energy and force evaluation. The method allows for the efficient use of full electrostatic potentials joined smoothly to multipoles at long distance so that multiprotein simulation is possible. Using a recently published benchmark of 58 protein complexes, we examine the performance and quality of the grid approximation, refining cocrystallized complexes to within 0.68 A RMSD of interface atoms, close to the optimum 0.63 A produced by the underlying MMFF94 force field. We quantify the theoretical statistical advantage of using minimization in a stochastic search in the case of two rigid bodies, and contrast it with the underlying cost of conjugate gradient minimization using B-splines. The volumes of conjugate gradient minimization basins of attraction in cocrystallized systems are generally orders of magnitude larger than well volumes based on energy thresholds needed to discriminate native from nonnative states; nonetheless, computational cost is significant. Molecular dynamics using B-splines is doubly efficient due to the combined advantages of rapid force evaluation and large simulation step sizes. Large basins localized around the native state and other possible binding sites are identifiable during simulations of protein-protein motion. In addition to providing increased modeling detail, B-splines offer new algorithmic possibilities that should be valuable in refining docking candidates and studying global complex behavior. 相似文献
995.
996.
In this article, we obtain some stability results for parametric weak vector equilibrium problem with set-valued mappings. By using a scalarization method, we establish sufficient conditions for the semicontinuity of the approximate solution mappings to parametric set-valued weak vector equilibrium problem under weak assumptions. These results extend and improve some known results in the literature. 相似文献
997.
998.
Yu. V. Kupriyanova 《Computational Mathematics and Mathematical Physics》2008,48(2):195-200
A Hermite spline of third degree is constructed on a three-dimensional simplex. The deviation of its directional derivatives up to the third order is estimated in angle-free terms. The resulting estimates hold for any tetrahedron irrespective of its geometry. 相似文献
999.
B. I. Kvasov 《Computational Mathematics and Mathematical Physics》2008,48(4):539-548
The problem of constructing a hyperbolic interpolation spline can be formulated as a differential multipoint boundary value problem. Its discretization yields a linear system with a five-diagonal matrix, which may be ill-conditioned for unequally spaced data. It is shown that this system can be split into diagonally dominant tridiagonal systems, which are solved without computing hyperbolic functions and admit effective parallelization. 相似文献
1000.
本文讨论生成锥内部凸-锥-类凸集值向量优化问题的超有效解.在生成锥内部凸-锥类凸假设下,建立了集值向量优化问题在超有效意义下的标量化、Lagrangian乘子和鞍点定理 相似文献