共查询到20条相似文献,搜索用时 31 毫秒
1.
Tom Braden Anthony Licata Nicholas Proudfoot Ben Webster 《Advances in Mathematics》2010,225(4):2002-2049
Given a hyperplane arrangement in an affine space equipped with a linear functional, we define two finite-dimensional, noncommutative algebras, both of which are motivated by the geometry of hypertoric varieties. We show that these algebras are Koszul dual to each other, and that the roles of the two algebras are reversed by Gale duality. We also study the centers and representation categories of our algebras, which are in many ways analogous to integral blocks of category O. 相似文献
2.
Radu Ioan Bo? 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(2):374-384
Considering a general optimization problem, we attach to it by means of perturbation theory two dual problems having in the constraints a subdifferential inclusion relation. When the primal problem and the perturbation function are particularized different new dual problems are obtained. In the special case of a constrained optimization problem, the classical Wolfe and Mond-Weir duals, respectively, follow as particularizations of the general duals by using the Lagrange perturbation. Examples to show the differences between the new duals are given and a gate towards other generalized convexities is opened. 相似文献
3.
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate
spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical
duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification
structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module
homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular
random duality pair together with some important random compatible invariants. 相似文献
4.
《Annals of Pure and Applied Logic》2023,174(5):103245
This paper introduces the category of b-frames as a new tool in the study of complete lattices. B-frames can be seen as a generalization of posets, which play an important role in the representation theory of Heyting algebras, but also in the study of complete Boolean algebras in forcing. This paper combines ideas from the two traditions in order to generalize some techniques and results to the wider context of complete lattices. In particular, we lift a representation theorem of Allwein and MacCaull to a duality between complete lattices and b-frames, and we derive alternative characterizations of several classes of complete lattices from this duality. This framework is then used to obtain new results in the theory of complete Heyting algebras and the semantics of intuitionistic propositional logic. 相似文献
5.
Jean-Paul Penot 《Journal of Global Optimization》2008,40(1-3):319-338
We look for a general framework in which the Ekeland duality can be formulated. We propose a scheme in which the parameter
sets are provided with a coupling function which induces a conjugacy. The decision spaces are not supposed to have any special
structure. We examine several examples. In particular, we consider some special classes of generalized convex functions. 相似文献
6.
E. L. Peterson 《Journal of Optimization Theory and Applications》1978,26(1):43-50
A specialization of unconstrained duality (involving problems without explicit constraints) to constrained duality (involving problems with explicit constraints) provides an efficient mechanism for extending to the latter many important theorems that were previously established for the former.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-73-2516. 相似文献
7.
Guram Bezhanishvili 《Topology and its Applications》2010,157(6):1064-1080
We introduce zero-dimensional de Vries algebras and show that the category of zero-dimensional de Vries algebras is dually equivalent to the category of Stone spaces. This shows that Stone duality can be obtained as a particular case of de Vries duality. We also introduce extremally disconnected de Vries algebras and show that the category of extremally disconnected de Vries algebras is dually equivalent to the category of extremally disconnected compact Hausdorff spaces. As a result, we give a simple construction of the Gleason cover of a compact Hausdorff space by means of de Vries duality. We also discuss the insight that Stone duality provides in better understanding of de Vries duality. 相似文献
8.
Richard G. Belshoff Edgar E. Enochs Juan Ramon Garcí a Rozas 《Proceedings of the American Mathematical Society》2000,128(5):1307-1312
Let be a commutative noetherian ring and let be the minimal injective cogenerator of the category of -modules. A module is said to be reflexive with respect to if the natural evaluation map from to is an isomorphism. We give a classification of modules which are reflexive with respect to . A module is reflexive with respect to if and only if has a finitely generated submodule such that is artinian and is a complete semi-local ring.
9.
Dale Husemoller 《Journal d'Analyse Mathématique》1967,18(1):161-171
10.
There are several examples in linear algebra and number theory of theorems which are formally similar to the well-known duality theorem of linear programming. The object of this paper is to present a general setting in which we can state and prove a simple criterion for such duality theorems to hold. 相似文献
11.
Ralph Strebel 《Journal of Pure and Applied Algebra》1976,8(1):75-96
Duality relations given in terms of natural isomorphisms are shown to be related with a straightforward generalization of the operation of taking the dual HomR(P, R) of a finitely generated projective module P. The obtained results allow to characterize duality groups (in the sense of Bieri-Eckmann) and inverse duality groups in a perspicuous way, and to generalize two main result of Matlis [13]. 相似文献
12.
Simon Gindikin 《中国科学A辑(英文版)》2008,51(4):562-567
We discuss the horospherical duality as a geometrical background of harmonic analysis on semisimple symmetric spaces. 相似文献
13.
This paper investigates endoprimal algebras using techniques from universal
algebra but not from duality theory, and thereby exposes quite directly how endoprimality
occurs. 相似文献
14.
The roof dual bound for quadratic unconstrained binary optimization is the basis for several methods for efficiently computing the solution to many hard combinatorial problems. It works by constructing the tightest possible lower-bounding submodular function, and instead of minimizing the original objective function, the relaxation is minimized. However, for higher-order problems the technique has been less successful. A standard technique is to first reduce the problem into a quadratic one by introducing auxiliary variables and then apply the quadratic roof dual bound, but this may lead to loose bounds.We generalize the roof duality technique to higher-order optimization problems. Similarly to the quadratic case, optimal relaxations are defined to be the ones that give the maximum lower bound. We show how submodular relaxations can efficiently be constructed in order to compute the generalized roof dual bound for general cubic and quartic pseudo-boolean functions. Further, we prove that important properties such as persistency still hold, which allows us to determine optimal values for some of the variables. From a practical point of view, we experimentally demonstrate that the technique outperforms the state of the art for a wide range of applications, both in terms of lower bounds and in the number of assigned variables. 相似文献
15.
We extend the theory of chiral and factorization algebras, developed for curves by Beilinson and Drinfeld (American Mathematical
Society Colloquium Publications, 51. American Mathematical Society, Providence, RI, 2004), to higher-dimensional varieties. This extension entails the development of the homotopy theory of chiral and factorization
structures, in a sense analogous to Quillen’s homotopy theory of differential graded Lie algebras. We prove the equivalence
of higher-dimensional chiral and factorization algebras by embedding factorization algebras into a larger category of chiral
commutative coalgebras, then realizing this interrelation as a chiral form of Koszul duality. We apply these techniques to
rederive some fundamental results of Beilinson and Drinfeld (American Mathematical Society Colloquium Publications, 51. American
Mathematical Society, Providence, RI, 2004) on chiral enveloping algebras of *{\star} -Lie algebras. 相似文献
16.
It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a generalization of this fact and prove a converse of the generalization. To be precise, we exhibit a one-to-one correspondence (up to isomorphism) between soft sheaf representations of universal algebras over stably compact spaces and frame homomorphisms from the dual frames of such spaces into subframes of pairwise commuting congruences of the congruence lattices of the universal algebras. For distributive-lattice-ordered algebras this allows us to dualize such sheaf representations. 相似文献
17.
Alexander Kuznetsov 《Publications Mathématiques de L'IHéS》2007,105(1):157-220
We introduce a notion of homological projective duality for smooth algebraic varieties in dual projective spaces, a homological
extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are homologically
projectively dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an
equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections
are equivalent. We also investigate homological projective duality for projectivizations of vector bundles. 相似文献
18.
《Discrete Applied Mathematics》1987,16(1):87-90
Min algebra has been used (Cuninghame-Greem [2], Hoffman [3]) to obtain results in operations research and graph theory. It has previously been seen primarily as an efficient way to describe a system of minimum relations. In this note we develop an elimination scheme for inductively solving systems of min algebraic equations and then prove a theorem of the alternative which is closely related to one of the duality models described in [3]. This work was developed in relation to tag systems [1]. These results provide a first step toward broadening min algebra from a modeling scheme to a solution technique. 相似文献
19.
A demonstration is given that the resolving multipliersused by Kantorovich in the solution of a production planningmodel are directly related to dual variables. The interpretationis based on the linear programme formulated by Vajda to representthe Kantorovich model. A numerical example is given. 相似文献
20.
J. W. Nieuwenhuis 《Journal of Optimization Theory and Applications》1983,41(3):481-490
In this note, we consider the following multiple-objective linear program: maxCx, such thatAx=b,x≧0, and its associated Isermann dual program: minUb, such thatUAW≤Cw, for now≧0. We give a simple proof of the known fact that, for every dual efficient pointU°, there is a primal efficient pointx°, such thatU°b=Cx°. Parts of the ingredients in this proof are useful in exploring the structure of the dual feasible set of function values {Ub¦UAw≤Cw, for now≧0}. 相似文献