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1.
Iterative Algorithms for Nonlinear Operators   总被引:33,自引:0,他引:33  
Iterative algorithms for nonexpansive mappings and maximal monotoneoperators are investigated. Strong convergence theorems areproved for nonexpansive mappings, including an improvement ofa result of Lions. A modification of Rockafellar’s proximalpoint algorithm is obtained and proved to be always stronglyconvergent. The ideas of these algorithms are applied to solvea quadratic minimization problem.  相似文献
2.
Convolutions, Transforms, and Convex Bodies   总被引:17,自引:0,他引:17  
The paper studies convex bodies and star bodies in Rn by usingRadon transforms on Grassmann manifolds, p-cosine transformson the unit sphere, and convolutions on the rotation group ofRn. It presents dual mixed volume characterizations of i-intersectionbodies and Lp-balls which are related to certain volume inequalitiesfor cross sections of convex bodies. It considers approximationsof special convex bodies by analytic bodies and various finitesums of ellipsoids which preserve special geometric properties.Convolution techniques are used to derive formulas for mixedvolumes, mixed surface measures, and p-cosine transforms. Theyare also used to prove characterizations of geometric functionals,such as surface area and dual quermassintegrals. 1991 MathematicsSubject Classification: 52A20, 52A40.  相似文献
3.
All Modules Have Flat Covers   总被引:15,自引:0,他引:15  
In this paper we give two different proofs that the flat coverconjecture is true: that is, every module has a flat cover.The two proofs are of completely different nature, and, we hope,will have different applications. The first of the two proofs(due to the third author) is essentially an application of thework of P. Eklof and J. Trlifaj (work which is more set-theoretic).The second proof (due to the first two authors) is more direct,and has a model-theoretic flavour.  相似文献
4.
The Tracial Topological Rank of C*-Algebras   总被引:11,自引:0,他引:11  
We introduce the notion of tracial topological rank for C*-algebras.In the commutative case, this notion coincides with the coveringdimension. Inductive limits of C*-algebrasof the form PMn(C(X))P,where X is a compact metric space with dim X k, and P is aprojection in Mn(C(X)), have tracial topological rank no morethan k. Non-nuclear C*-algebras can have small tracial topologicalrank. It is shown that if A is a simple unital C*-algebra withtracial topological rank k (< ), then
(i) A is quasidiagonal,
(ii) A has stable rank 1,
(iii) A has weakly unperforatedK0(A),
(iv) A has the following Fundamental Comparabilityof Blackadar:if p, q A are two projections with (p) < (q)for all tracialstates on A, then p q
. 2000 MathematicsSubject Classification: 46L05, 46L35.  相似文献
5.
How To Make Ext Vanish   总被引:9,自引:0,他引:9  
We describe a general construction of a module A from a givenmodule B such that Ext(B, A) = 0, and we apply it to answerseveral questions on splitters, cotorsion theories and saturatedrings.  相似文献
6.
Crystal Bases for Quantum Affine Algebras and Combinatorics of Young Walls   总被引:8,自引:0,他引:8  
In this paper we give a realization of crystal bases for quantumaffine algebras using some new combinatorial objects which wecall the Young walls. The Young walls consist of colored blockswith various shapes that are built on a given ground-state walland can be viewed as generalizations of Young diagrams. Therules for building Young walls and the action of Kashiwara operatorsare given explicitly in terms of combinatorics of Young walls.The crystal graph of a basic representation is characterizedas the set of all reduced proper Young walls. The characterof a basic representation can be computed easily by countingthe number of colored blocks that have been added to the ground-statewall. 2000 Mathematical Subject Classification: 17B37, 17B65,81R50, 82B23.  相似文献
7.
Discretization methods for ordinary differential equations basedon the use of matrix exponentials have been known for decades.This set of ideas has come off age and acquired greater interestrecently, within the context of geometric integration and discretizationmethods on manifolds based on the use of Lie-group actions. In the present paper we study the approximation of the matrixexponential in a particular context: given a Lie group G andits Lie algebra g, we seek approximants F(t B) of exp(t B) suchthat F(t B) G if B g. Having fixed a basis V1, ..., Vd ofg, we write F(t B) as a composition of exponentials of the typeexp(i (t) Vi), where i for i = 1, 2, ..., d are scalar functions.In this manner it becomes possible to increase the order ofthe approximation without increasing the number of exponentialsto evaluate and multiply together. We study order conditionsand implementation details and conclude the paper with somenumerical experiments. Received 24 March 1999. Accepted 22 November 1999.  相似文献
8.
This paper deals with non-constant positive steady-state solutionsof a predator-prey system with non-monotonic functional response,also called Holling type-IV interaction terms, and diffusionunder the homogeneous Neumann boundary condition. We first establishpositive upper and lower bounds for such solutions, and thenstudy their non-existence, global existence and bifurcation.2000 Mathematics Subject Classification 35J55, 92D25.  相似文献
9.
Topological properties of fuzzy numbers   总被引:8,自引:0,他引:8  
10.
Let be a smooth bounded domain in RN. We prove general uniquenessresults for equations of the form – u = aub(x)f(u) in , subject to u = on . Our uniqueness theorem is establishedin a setting involving Karamata's theory on regularly varyingfunctions, which is used to relate the blow-up behavior of u(x)with f(u) and b(x), where b 0 on and a certain ratio involvingb is bounded near . A key step in our proof of uniqueness usesa modification of an iteration technique due to Safonov. 2000Mathematics Subject Classification 35J25 (primary), 35B40, 35J60(secondary).  相似文献
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