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In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem. 相似文献
146.
A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows 总被引:6,自引:0,他引:6
Michael Polacek Richard F. Hartl Karl Doerner Marc Reimann 《Journal of Heuristics》2004,10(6):613-627
The aim of this paper is to propose an algorithm based on the philosophy of the Variable Neighborhood Search (VNS) to solve Multi Depot Vehicle Routing Problems with Time Windows. The paper has two main contributions. First, from a technical point of view, it presents the first application of a VNS for this problem and several design issues of VNS algorithms are discussed. Second, from a problem oriented point of view the computational results show that the approach is competitive with an existing Tabu Search algorithm with respect to both solution quality and computation times. 相似文献
147.
Manuel Ritoré Cé sar Rosales 《Transactions of the American Mathematical Society》2004,356(11):4601-4622
We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.
We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.
148.
N. S. Kazak E. G. Katranji I. A. Utkin A. A. Ryzhevich A. N. Khilo 《Journal of Applied Spectroscopy》2004,71(5):697-701
The phenomenon of self-diffraction of Bessel light beams (BLB) in a nonlinear liquid medium has been studied experimentally and theoretically for the first time. Diffraction maxima which do not correspond to integer orders for an induced periodic structure have been registered. It has been shown that the appearance of these maxima is due to the initial BLB modulation, which can be caused by the departure of the axicon refracting surface from the ideal conical surface, as well as by the imperfection of the form of the Gaussian beam incident on the axicon. 相似文献
149.
林诒勋 《高校应用数学学报(英文版)》2003,18(3):361-369
§ 1 IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th… 相似文献
150.
Based on the generalized Huygens-Fresnel diffraction integral, a recurrence propagation equation of Hermite-Gaussian (H-G) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for H-G beams of any order. The advantages of our analytical results are analyzed, and the application is illustrated with numerical examples. 相似文献