Weak Morita Duality

Abstract

The notion of a weak Morita duality between subcategories of Mod-R and S-Mod is introduced and investigated. This concept includes dualities induced by cotilting modules over finite dimensional algebras, the R-dual for both noetherian rings of injective dimension ≤ 1 and the Matlis duality domains, as well as the first author's generalized Morita duality. Moreover it yields a “cotilting theorem” dual to the classical tilting theorem, and a characterization of generalized Morita duality.     

Duality for multimodules

Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and involutions; tensor products and contractions; inner products; first-order differential operators. A construction of an (involutive) colored properad of multimodules is suggested.     

Duality for Variational Problems with Pseudo-Invexity

In this paper the duality results of Mond, Chandra and Husain for variational problems are extended to generalized invex (pseudo-invex) functions     

Duality for variational problems with b-vex functions

Concept of B-vexity has been extended for continuous functions and applied to establish sufficiency and duality for variational problems. Both fixed end points and free boundary value problems are considered     

长度有限的模的对偶

本文推广了局部对偶理论并讨论了长度为有限的模的同调维数．     

Conjugate Functions for Convex and Nonconvex Duality

We study conjugate duality with arbitrary coupling functions. Our only tool is a certain support property, which is automatically fulfilled in the two most widely used special cases, namely the case where the underlying space is a topological vector space and the coupling functions are the continuous linear ones, and the case where the underlying space is a metric space and the coupling functions are the continuous ones. We obtain thereby a simultaneous axiomatic extension of these two classical models. Also included is a condition for global optimality, which requires only the mentioned support property.     

Duality theorem for a generalized Fermat-Weber problem

The classical Fermat-Weber problem is to minimize the sum of the distances from a point in a plane tok given points in the plane. This problem was generalized by Witzgall ton-dimensional space and to allow for a general norm, not necessarily symmetric; he found a dual for this problem. The authors generalize this result further by proving a duality theorem which includes as special cases a great variety of choices of norms in the terms of the Fermat-Weber sum. The theorem is proved by applying a general duality theorem of Rockafellar. As applications, a dual is found for the multi-facility location problem and a nonlinear dual is obtained for a linear programming problem with a priori bounds for the variables. When the norms concerned are continuously differentiable, formulas are obtained for retrieving the solution for each primal problem from the solution of its dual.     

集合函数多目标规划的拉格朗日型对偶定理

本文在［１］的基础上．给出了集合函数多目标规划的拉格朗日型弱对偶定理，严格对偶定理和逆对偶定理．     

Symmetric Duality and Self-duality for Nonsmooth Mathematical Programming

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Duality respecting representations and compatible complexity measures for gammoids

We show that every gammoid has special digraph representations, such that a representation of the dual of the gammoid may be easily obtained by reversing all arcs. In an informal sense, the duality notion of a poset applied to the digraph of a special representation of a gammoid commutes with the operation of forming the dual of that gammoid. We use these special representations in order to define a complexity measure for gammoids, such that the classes of gammoids with bounded complexity are closed under duality, minors, and direct sums.     

Duality and statistical tests of optimality for two stage stochastic programs

We present alternative methods for verifying the quality of a proposed solution to a two stage stochastic program with recourse. Our methods revolve around implications of a dual problem in which dual multipliers on the nonanticipativity constraints play a critical role. Using randomly sampled observations of the stochastic elements, we introduce notions of statistical dual feasibility and sampled error bounds. Additionally, we use the nonanticipativity multipliers to develop connections to reduced gradient methods. Finally, we propose a statistical test based on directional derivatives. We illustrate the applicability of these tests via some examples. This work was supported in part by Grant No. NSF-DMI-9414680 from the National Science Foundation     

Duality for minmax programming involving V-invex functions

Sufficient optimality conditions and duality results for a class of minmax programming problems are obtained under V-invexity type assumptions on objective and constraint functions. Applications of these results to certain fractional and generalized fractional programming problems are also presented     

非凸异分母分式多目标规划解的充分条件及对偶定理

指出了文[6]中的一个错误，基于不变凸性，对异分母分式多目标规划进行了讨论．在简单的正交假设下，给出了一系列解的充分条件，并建立了Mond－Weir型对偶定理．     

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.     

Duality techniques for certain integral transforms to be starlike

For β<1, let denote the class of all normalized analytic functions f such that

     

Duality for Weakly Co-Hopfian and Generalized Hopfian Modules

Abstract

Duality like connections are established for generalized Hopfian modules and weakly co-Hopfian modules. A generalization of ring Hopficity is also introduced and this concept is studied for matrix rings.     

Local Duality for Modules over Noetherian Commutative Rings

Some applications of the general theorem on the existence of local duality for modules over Noetherian commutative rings are given. Let be a Noetherian commutative ring, let be a set of maximal ideals in , and let . Then the category of Artinian modules is dual to the category of Noetherian modules. Several structural results are proved, including the theorem on the structure of Artinian modules over principal ideal domains. For rings of special kinds, double centralizer theorems are proved. Bibliography: 5 titles.