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The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large. 相似文献
4.
Enrique J. Baran 《Monatshefte für Chemie / Chemical Monthly》1991,122(6-7):479-481
Summary Mean amplitudes of vibration for OTeF
5
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have been calculated from known spectroscopic and structural data in a wide temperature range. The results are briefly discussed in comparison with those of related species. 相似文献
5.
Julie Clutterbuck Oliver C. Schnürer Felix Schulze 《Calculus of Variations and Partial Differential Equations》2007,29(3):281-293
We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge
spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay
rates.
The authors are members of SFB 647/B3 “Raum – Zeit – Materie: Singularity Structure, Long-time Behaviour and Dynamics of Solutions
of Non-linear Evolution Equations”. 相似文献
6.
Roberta Filippucci 《Journal of Mathematical Analysis and Applications》2007,334(1):604-620
In this paper we study first nonexistence of radial entire solutions of elliptic systems of the mean curvature type with a singular or degenerate diffusion depending on the solution u. In particular we extend a previous result given in [R. Filippucci, Nonexistence of radial entire solutions of elliptic systems, J. Differential Equations 188 (2003) 353-389]. Moreover, in the scalar case we obtain nonexistence of all entire solutions, radial or not, of differential inequalities involving again operators of the mean curvature type and a diffusion term. We prove that in the scalar case, nonexistence of entire solutions is due to the explosion of the derivative of every nonglobal radial solution in the right extremum of the maximal interval of existence, while in that point the solution is bounded. This behavior is qualitatively different with respect to what happens for the m-Laplacian operator, studied in [R. Filippucci, Nonexistence of radial entire solutions of elliptic systems, J. Differential Equations 188 (2003) 353-389], where nonexistence of entire solutions is due, even in the vectorial case, to the explosion in norm of the solution at a finite point. Our nonexistence theorems for inequalities extend previous results given by Naito and Usami in [Y. Naito, H. Usami, Entire solutions of the inequality div(A(|Du|)Du)?f(u), Math. Z. 225 (1997) 167-175] and Ghergu and Radulescu in [M. Ghergu, V. Radulescu, Existence and nonexistence of entire solutions to the logistic differential equation, Abstr. Appl. Anal. 17 (2003) 995-1003]. 相似文献
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Dorota G?azowska Janusz Matkowski 《Journal of Mathematical Analysis and Applications》2007,331(2):1187-1199
The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g. 相似文献
8.
Mark A. S. Aarons 《Calculus of Variations and Partial Differential Equations》2006,25(2):205-246
We study the forced mean curvature flow of graphs in Minkowski space and prove longtime existence of solutions. When the forcing
term is a constant, we prove convergence to either a constant mean curvature hypersurface or a translating soliton – depending
on the boundary conditions at infinity.
It is a pleasure to thank my PhD advisors Klaus Ecker and Gerhard Huisken for their assistance and encouragement. I also thank
Maria Athanassenas, Oliver Schnürrer and Marty Ross for their interest and useful comments, and the Max Planck Gesellschaft
for financial support. 相似文献
9.
Kenneth Sörensen 《Central European Journal of Operations Research》2006,14(2):193-207
In this paper, we argue that vehicle routing solutions are often tactical decisions, that should not be changed too often
or too much. For marketing or other reasons, vehicle routing solutions should be stable, i.e. a new solution (when e.g. new customers require service) should be as similar as possible to a solution already in
use. Simultaneously however, this new solution should still have a good quality in the traditional sense (e.g. small total
travel cost). In this paper, we develop a way to measure the difference between two vehicle routing solutions. We use this
distance measure to create a metaheuristic approach that will find solutions that are “close” (in the solution space) to a
given baseline solution and at the same time have a high quality in the sense that their total distance traveled is small.
By using this approach, the dispatcher is offered a choice of Pareto-optimal solutions, allowing him to make a trade-off between
changing his existing solution and allowing a longer travel distance. Some experiments are performed to show the effectiveness
of the approach. 相似文献
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