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951.
We introduce and discuss the dual of a chain geometry. Each chain geometry is canonically isomorphic to its dual. This allows
us to show that there are isomorphisms of chain geometries that arise from antiisomorphisms of the underlying rings.
Received 13 December 2000. 相似文献
952.
A Mond–Weir type multiobjective variational mixed integer symmetric dual program over arbitrary cones is formulated. Applying the separability and generalized F-convexity on the functions involved, weak, strong and converse duality theorems are established. Self duality theorem is proved. A close relationship between these variational problems and static symmetric dual minimax mixed integer multiobjective programming problems is also presented. 相似文献
953.
C. Y. Wang X. Q. Yang X. M. Yang 《Journal of Optimization Theory and Applications》2007,135(1):85-100
In the context of an inequality constrained optimization problem, we present a unified nonlinear Lagrangian dual scheme and
establish necessary and sufficient conditions for the zero duality gap property. From these results, we derive necessary and
sufficient conditions for four classes of zero duality gap properties and establish the equivalence among them. Finally, we
obtain the convergence of an optimal path for the unified scheme and present a sufficient condition for the finite termination
of the optimal path.
This research was partially supported by the Research Grants Council of Hong Kong Grant PolyU 5250/03E, the National Natural
Science Foundation of China Grants 10471159 and 10571106, NCET, and the Natural Science Foundation of Chongqing 相似文献
954.
Wayne Lawton 《Journal of Fourier Analysis and Applications》2008,14(4):588-605
We prove that a real analytic subset of a torus group that is contained in its image under an expanding endomorphism is a
finite union of translates of closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and Wang for real
analytic varieties. Our proof uses real analytic geometry, topological dynamics, and Fourier analysis.
相似文献
955.
We investigate the connections between four-dimensional, N = 2 M-theory vacua constructed as orbifolds of type II, heterotic, and type I strings. All these models have the same massless spectrum, which contains an equal number of vector multiplets and hypermultiplets, with a gauge group of the maximal rank allowed in a perturbative heterotic string construction. We find evidence for duality between two type I compactifications recently proposed and a new heterotic construction that we present here. This duality allows us to gain insight into the non-perturbative properties of these models. In particular we consider gravitational corrections to the effective action. 相似文献
956.
We investigate how to modify a simple graph G combinatorially to obtain a sequentially Cohen-Macaulay graph. We focus on adding configurations of whiskers to G, where to add a whisker one adds a new vertex and an edge connecting this vertex to an existing vertex of G. We give various sufficient conditions and necessary conditions on a subset S of the vertices of G so that the graph G∪W(S), obtained from G by adding a whisker to each vertex in S, is a sequentially Cohen-Macaulay graph. For instance, we show that if S is a vertex cover of G, then G∪W(S) is a sequentially Cohen-Macaulay graph. On the other hand, we show that if G?S is not sequentially Cohen-Macaulay, then G∪W(S) is not a sequentially Cohen-Macaulay graph. Our work is inspired by and generalizes a result of Villarreal on the use of whiskers to get Cohen-Macaulay graphs. 相似文献
957.
A pro-C*-algebra is a (projective) limit of C*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C*-algebras can be seen as non-commutative k-spaces. An element of a pro-C*-algebra is bounded if there is a uniform bound for the norm of its images under any continuous *-homomorphism into a C*-algebra. The *-subalgebra consisting of the bounded elements turns out to be a C*-algebra. In this paper, we investigate pro-C*-algebras from a categorical point of view. We study the functor (−)
b
that assigns to a pro-C*-algebra the C*-algebra of its bounded elements, which is the dual of the Stone-Čech-compactification. We show that (−)
b
is a coreflector, and it preserves exact sequences. A generalization of the Gelfand duality for commutative unital pro-C*-algebras is also presented. 相似文献
958.
We use variational methods to provide a concise development of a number of basic results in convex and functional analysis.
This illuminates the parallels between convex analysis and smooth subdifferential theory.
Research was supported by NSERC and by the Canada Research Chair Program and National Science Foundation under grant DMS 0102496. 相似文献
959.
Results concerning extensions of monotone operators have a long history dating back to a classical paper by Debrunner and
Flor from 1964. In 1999, Voisei obtained refinements of Debrunner and Flor’s work for n-cyclically monotone operators. His proofs rely on von Neumann’s minimax theorem as well as Kakutani’s fixed point theorem.
In this note, we provide a new proof of the central case of Voisei’s work. This proof is more elementary and rooted in convex
analysis. It utilizes only Fitzpatrick functions and Fenchel–Rockafellar duality.
相似文献
960.
R. I. Boţ E. R. Csetnek A. Moldovan 《Journal of Optimization Theory and Applications》2008,139(1):67-84
In this paper, we deal with regularity conditions formulated by making use of the quasirelative interior and/or of the quasi-interior
of the sets involved, guaranteeing strong duality for a convex optimization problem with cone (and equality) constraints and
its Lagrange dual. We discuss also some recent results on this topic, which are proved to have either superfluous or contradictory
assumptions. Several examples illustrate the theoretical considerations.
Research made during the third author’s two months visit in Chemnitz as part of bilateral project CNR-DFG. The second author
was supported by a Graduate Fellowship of the Free State Saxony, Germany. 相似文献