On existence and uniqueness of a vector minimizing a convex function

In this paper, theorems on existence and uniqueness of a vector minimizing a closed proper convex functionf are given, extending previous results on this topic. Necessary and sufficient conditions are presented for convex functions with additional properties. Iff attains its infimum atx withoutx being unique, linear functionsd'x with unique or bounded values are identified. Applicability of results is demonstrated in regression analysis of failure times, including the Cox model.

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Zusammenfassung In dieser Arbeit werden, für eine geschlossene eigentlich konvexe Funktionf, Existenz und Eindeutigkeit eines minimierenden Vektors untersucht und frühere Resultate zu diesem Thema verallgemeinert. Für konvexe Funktionen mit zusätzlichen Eigenschaften werden notwendige und hinreichende Bedingungen für Existenz bzw. Eindeutigkeit angegeben. Fallsf sein Minimum inx annimmt, ohne daßx eindeutig ist, werden lineare Funktionend'x mit eindeutigen oder beschränkten Werten identifiziert. Die Anwendbarkeit der Resultate wird in der Regressionsanalyse von Lebensdauern, etwa mit dem Cox Modell, demonstriert.

     

Duality and saddle-point type optimality for generalized nonlinear fractional programming

In this paper, we establish two theorems of alternative with generalized subconvexlikeness. We introduce two dual models for a generalized fractional programming problem. Theorems of alternative are then applied to establish duality theorems and a saddle-point type optimality condition.     

Affine Poisson structures

We establish a one-to-one correspondence between the set of all equivalence classes of affine Poisson structures (defined on the dual of a finite dimensional Lie algebra) and the set of all equivalence classes of central extensions of the Lie algebra by ℝ. We characterize all the affine Poisson structures defined on the duals of some lower dimensional Lie algebras. It is shown that under a certain condition every Poisson structure locally looks like an affine Poisson structure. As an application, we show the role played by affine Poisson structures in mechanics. Finally, we prove some involution theorems.     

具浓度相关迁移率的对流扩散Cahn-Hilliard方程

In this paper, we study the global existence of classical solutions for the convective-diffusive Cahn-Hilliard equation with concentration dependent mobility. Based on the Schauder type estimates, we establish the global existence of classicalsolutions.     

描述地球物理流动的磁流体型发展方程定常解的Lr指数稳定性

本文证明了R^n(n=2,3)中有界区域上描述地球物理流动的磁流体型发展方程的定常解的存在唯一性，在外力满足适当的条件下，证明了任何非定常的L^r(r≥2）有界解当t→∞时按指数次幂趋于定常解。     

Controllability of Nonlinear Systems in Banach Spaces: A Survey

This paper presents a survey on research using fixed-point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces. Also discussed is the use of this technique in K-controllability and boundary controllability problems for nonlinear systems and integrodifferential systems in abstract spaces.     

A Global Stability Theorem for Transversely Holomorphic Foliations

We prove a global stability theorem for transversely holomorphic foliations of complex codimension one: if there exists a compact leaf with finite holonomy, then the foliation is a Seifert fibration (that is, every leaf is compact and has finite holonomy).     

Geometric stable distributions in Banach spaces

Geometric stable laws have become an object of attention in recent publications dealing with heavy tailed modeling. Many applications require understanding geometric stable laws on infinite dimensional spaces. This paper studies geometric stable laws on Banach spaces, and their place in the more general family of geometric infinitely divisible laws. Furthermore, we discuss rates of convergence in the domains of attraction of geometric stable laws in Banach spaces.Research was supported by NSF Grant DMS-9103452 and a NATO Scientific Affairs Division Grant CRG 900798. University of California, at Santa Barbara, Santa Barbara, California 93102.Research was supported by ONR Grant N00014-90-J-1287 and United States Israel Binational Science Foundation. School of Operations Research, and Industrial Engineering, Cornell University, Ithaca, New York 14853.     

Ergodicity of Jackson-type queueing networks

This paper gives a pathwise construction of Jackson-type queueing networks allowing the derivation of stability and convergence theorems under general probabilistic assumptions on the driving sequences; namely, it is only assumed that the input process, the service sequences and the routing mechanism are jointly stationary and ergodic in a sense that is made precise in the paper. The main tools for these results are the subadditive ergodic theorem, which is used to derive a strong law of large numbers, and basic theorems on monotone stochastic recursive sequences. The techniques which are proposed here apply to other and more general classes of discrete event systems, like Petri nets or GSMPs. The paper also provides new results on the Jackson-type networks with i.i.d. driving sequences which were studied in the past.The work of this author was supported in part by a grant from the European Commission DG XIII, under the BRA Qmips contract.The work of this author was supported by a sabbatical grant from INRIA Sophia Antipolis.