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81.
We prove the dispersionless Hirota equations for the dispersionless Toda, dispersionless coupled modified KP and dispersionless KP hierarchies using an idea from classical complex analysis. We also prove that the Hirota equations characterize the tau functions for each of these hierarchies. As a result, we establish the links between the hierarchies. 相似文献
82.
Some Remarks on the Minty Vector Variational Inequality 总被引:4,自引:0,他引:4
Yang X. M. Yang X. Q. Teo K. L. 《Journal of Optimization Theory and Applications》2004,121(1):193-201
In this paper, we establish some relations between a Minty vector variational inequality and a vector optimization problem under pseudoconvexity or pseudomonotonicity, respectively. Our results generalize those of Ref. 1. 相似文献
83.
An important question in discrete optimization under uncertainty is to understand the persistency of a decision variable, i.e., the probability that it is part of an optimal solution. For instance, in project management,
when the task activity times are random, the challenge is to determine a set of critical activities that will potentially
lie on the longest path. In the spanning tree and shortest path network problems, when the arc lengths are random, the challenge
is to pre-process the network and determine a smaller set of arcs that will most probably be a part of the optimal solution
under different realizations of the arc lengths. Building on a characterization of moment cones for single variate problems,
and its associated semidefinite constraint representation, we develop a limited marginal moment model to compute the persistency
of a decision variable. Under this model, we show that finding the persistency is tractable for zero-one optimization problems
with a polynomial sized representation of the convex hull of the feasible region. Through extensive experiments, we show that
the persistency computed under the limited marginal moment model is often close to the simulated persistency value under various
distributions that satisfy the prescribed marginal moments and are generated independently. 相似文献
84.
This paper deals with the problem of characterizing the pairs of vertices x,y in a connected graph G such that G3 - {x,y} is hamiltonian, where G3 is the cube of G. It is known that the cube G3 is 2-hamiltonian if G is 2-connected. In this paper, we first prove the stronger result that G3 - {x,y} is hamiltonian if either x or y is not a cut-vertex of G, and then proceed to characterize those cut-vertices x and y of G such that G3 -{x,y} is hamiltonian. As a simple consequence of these, we obtain Schaar's characterization of a connected graph G such that G3 is 2-hamiltonian. 相似文献
85.
Let D = (V 1, V 2; A) be a directed bipartite graph with |V 1| = |V 2| = n ≥ 2. Suppose that d D (x) + d D (y) ≥ 3n for all x ∈ V 1 and y ∈ V 2. Then, with one exception, D contains two vertex-disjoint directed cycles of lengths 2n 1 and 2n 2, respectively, for any positive integer partition n = n 1 + n 2. This proves a conjecture proposed in [9]. 相似文献
86.
X.X. HUANG K. L. TEO X. Q. YANG 《数学学报(英文版)》2006,22(5):1283-1296
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program. 相似文献
87.
88.
The sought-after member of the [(PDBP)
n
AgX]
m
(n, m=1,4; 2,2; 3,1; PDBP=5-Phenyldibenzophosphole, X=halides) series, the tetrameric [(PDBP)AgCl]4 cluster has been prepared and structurally characterized. The [P4Ag4Cl4] cluster core of [(PDBP)AgCl]4 bears striking similarity to that of [(Ph3P)AgCl]4. 相似文献
89.
A general methodology for the determination of all possible stereoisomers of heteronuclear clusters is reported. The paper is divided into three parts: (1) nomenclature—wherein a systematic numbering system for multi-component clusters under which each and every stereoisomer of a given cluster can be uniquely identified is presented; (2) methodology—wherein the general principles for the determination of symmetry analogs are discussed; and (3) computer algorithm—wherein the implementation of the symmetry principles is described. These principles and algorithms are applied to binary (two-component) systems using octahedral and icosahedral clusters as examples. 相似文献
90.