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1.
This is a continuation of the paper [14]. It is shown that any finite subdirect product of exchange rings satisfying the n-stable range condition is still an exchange ring satisfying the n-stable range condition. Furthermore, we give necessary and sufficient conditions on matrices over an exchange ring R, under which R satisfies the n-stable range condition. This generalizes the corresponding results for unit-regular rings and the stable range one condition.2000 Mathematics Subject Classification: 19B10, 16E50This work was supported by the National Natural Science Foundation of China (Grant No. 19801012) and the Ministry of Education of China. 相似文献
2.
This paper gives a necessary condition for the Hartley proper efficiency in a vector optimization problem whose objectives and constraints are described by multifunctions F and G. This condition is established under a quasiconvexity requirement of the support functions of F and G or the generalized cone-convexity of a multifunction constructed from F and G. 相似文献
3.
Y. X. Zhao S. Y. Wang L. Coladas Uria 《Journal of Optimization Theory and Applications》2010,145(1):186-195
This paper discusses some properties of r-convexity and its relations with some other types of convexity. A characterization of convex functions in terms of r-convexity is given without assuming differentiability. The concept of strict r-convexity is introduced. For a twice continuously differentiable function f, it is shown that the strict r-convexity of f is equivalent to a certain condition on ∇
2
f. Further, it is shown that this condition is satisfied by quasiconvex functions satisfying a less stringent condition. 相似文献
4.
Faiz A. Al-Khayyal 《Mathematical Programming》1991,51(1-3):247-255
We simplify a result by Mangasarian on the existence of solutions to the linear complementarity problem. The simplified condition gives a new geometric interpretation of the result. When used to characterize the matrix classesQ andQ
0, our condition suggests a finitely checkable sufficient condition forP andP
0.This work was supported in part by the Office of Naval Research under Contract No. N00014-86-K-0173, and by general research development funds provided by the Georgia Institute of Technology. 相似文献
5.
In this note, we show that LipschitzianQ-matrices areP-matrices by obtaining a necessary condition on LipschitzianQ
0-matrices. The sufficiency of this condition has also been established by the first two authors along with another coauthor
(Murthy, Parthasarathy and Sriparna, 1995).
This work was done while I visited ISI, Delhi Center during March–April, 1994. I want to express my sincere thanks for their
kind hospitality. 相似文献
6.
Ursula Schirmeier 《Potential Analysis》1992,1(2):133-140
A classical result of G. Bouligand states that bounded harmonic functions can be extended across closed polar sets. F.-Y. Maeda replaced the boundedness assumption by the condition of energy finiteness for harmonic spaces with Green function.This paper proves this result for generalP-harmonic spaces and shows that the extension property for a harmonic functionu and the condition of energy finiteness are equivalent to a majorization property foru
2
. 相似文献
7.
Any ring with Krull dimension satisfies the ascending chain condition on semiprime ideals. This result does not hold more generally for modules. In particular if Ris the first Weyl algebra over a field of characteristic 0 then there are Artinian R-modules which do not satisfy the ascending chain condition on prime submodules. However, if Ris a ring which satisfies a polynomial identity then any R-module with Krull dimension satisfies the ascending chain condition on prime submodules, and, if Ris left Noethe-rian, also the ascending chain condition on semiprime submodules. 相似文献
8.
This paper gives sensitivity analyses by two approaches forL andU in the factorizationA=LU for general perturbations inA which are sufficiently small in norm. By the matrix-vector equation approach, we derive the condition numbers for theL andU factors. By the matrix equation approach we derive corresponding condition estimates. We show how partial pivoting and complete
pivoting affect the sensitivity of the LU factorization.
The material presented here is a part of the first author's PhD thesis under the supervision of the second author. This research
was supported by NSERC of Canada Grant OGP0009236. 相似文献
9.
Sun-Sig Byun 《Journal of Evolution Equations》2007,7(3):415-428
This work treats Lp regularity theory for weak solutions of parabolic equations in divergence form with discontinuous coefficients on nonsmooth
domains. We essentially obtain an optimal condition on the coefficients under which the global W1,p regularity theory holds.
This work was supported by SNU foundation in 2005. 相似文献
10.
This paper is motivated by the question of whether the invariants β, Δ,cΔ completely characterize isomorphism of Markov chains by finitary isomorphisms that have finite expected coding times (fect).
We construct a finitary isomorphism with fect under an additional condition. Whether coincidence of β, Δ,cΔ implies the required condition remains open. 相似文献
11.
We construct an example of a 2-dimensional Stein normal space X with one singular point x
0 such that X\{x
0} is simply connected and it satisfies the disk condition. This answers a question raised by Forn?ss and Narasimhan. We also
prove that any increasing union of Stein open sets contained in a Stein space of dimension 2 satisfies the disk condition.
Starting from the above example we exhibit, without using deformation theory, a new type of 2-dimensional holes which cannot
be filled. 相似文献
12.
Ali Abkar 《Czechoslovak Mathematical Journal》2007,57(3):877-883
We consider a nonnegative superbiharmonic function w satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation
formula for w in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already
found by the author for superbihamonic functions w satisfying the condition 0 ⩽ w(z) ⩽ C(1-|z|) in the unit disk. As an application we shall see that the polynomials are dense in weighted Bergman spaces whose weights
are superbiharmonic and satisfy the stated growth condition near the boundary.
Research supported in part by IPM under the grant number 83310011. 相似文献
13.
Let be a hypergraph. A panchromatic t-colouring of is a t-colouring of its vertices such that each edge has at least one vertex of each colour; and is panchromatically t-choosable if, whenever each vertex is given a list of t colours, the vertices can be coloured from their lists in such a way that each edge receives at least t different colours. The Hall ratio of is . Among other results, it is proved here that if every edge has at least t vertices and whenever , then is panchromatically t-choosable, and this condition is sharp; the minimum such that every t-uniform hypergraph with is panchromatically t-choosable satisfies ; and except possibly when t = 3 or 5, a t-uniform hypergraph is panchromatically t-colourable if whenever , and this condition is sharp. This last result dualizes to a sharp sufficient condition for the chromatic index of a hypergraph
to equal its maximum degree.
Received November 10, 1998
RID="*"
ID="*" This work was carried out while the first author was visiting Nottingham, funded by Visiting Fellowship Research Grant
GR/L54585 from the Engineering and Physical Sciences Research Council. The work of this author was also partly supported by
grants 96-01-01614 and 97-01-01075 of the Russian Foundation for Fundamental Research. 相似文献
14.
Séverine Rigot 《Calculus of Variations and Partial Differential Equations》2000,10(4):389-406
Quasi minimizers for the perimeter are measurable subsets G of such that
for all variations of G with and for a given increasing function such that . We prove here that, given , G a reduced quasi minimizer, and , there are , with , and , homeomorphic to a closed ball with radius t in , such that for some absolute constant . The constant above depends only on n, and . If moreover for some , we prove that we can find such a ball such that is a dimensional graph of class . This will be obtained proving that a quasi minimizer is equivalent to some set which satisfies the condition B. This condition
gives some kind of uniform control on the flatness of the boundary and then criterions proven by Ambrosio-Paolini and Tamanini
can be applied to get the required regularity properties.
Received: July 12, 1999 / Accepted: October 1, 1999 相似文献
15.
This article addresses a wave equation on a exterior domain in ? d (d odd) with nonlinear time-dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving a nonlinear non-autonomous differential equation 相似文献
16.
In this paper the accuracy of LU factorization of tridiagonal matrices without pivoting is considered. Two types of componentwise condition numbers for the L and U factors of tridiadonal matrices are presented and compared. One type is a condition number with respect to small relative perturbations of each entry of the matrix. The other type is a condition number with respect to small componentwise perturbations of the kind appearing in the backward error analysis of the usual algorithm for the LU factorization. We show that both condition numbers are of similar magnitude. This means that the algorithm is componentwise forward stable, i.e., the forward errors are of similar magnitude to those produced by a componentwise backward stable method. Moreover the presented condition numbers can be computed in O(n) flops, which allows to estimate with low cost the forward errors.
AMS subject classification (2000) 65F35, 65F50, 15A12, 15A23, 65G50.Received October 2003. Accepted August 2004. Communicated by Per Christian Hansen.Froilán M. Dopico: This research has been partially supported by the Ministerio de Ciencia y Tecnología of Spain through grants BFM2003-06335-C03-02 (M. I. Bueno) and BFM2000-0008 (F. M. Dopico). 相似文献
17.
Ladislav Bican 《Annali dell'Universita di Ferrara》2005,51(1):61-67
Sunto LetG andH be abstract classes of modules. The classH is said to have theG-property if to each infinite cardinal λ there exists a cardinal κ>λ such that for everyF∈H with |F|≥κ and every its submoduleK with |F/K|≤λ there exists a submoduleL ofK such thatF/L/teG and |F/L|<κ. This condition is stronger than the condition (P) requiringL≠0 instead of |F/L|<κ, which was introduced and investigated in [8]. In this note we are going to study the relations of this more general condition
to the existence of precovers with respect to some classes of modules. As an application we obtain some sufficient conditions
for the existence of σ-torsionfree precovers related to a given hereditary torsion theory σ for the categoryR-mod. This result is closely related to and in some sense extends that of [5].
The research has been partially supported by the Grant Agency of the Czech Republic, grant #GAČR 201/03/0937 and also by the
institutional grant MSM 113 200 007. 相似文献
18.
Wei-Liem Loh 《Annals of the Institute of Statistical Mathematics》1994,46(1):147-164
This paper contains two results. The first establishes, under mild assumptions, the validity of an Edgeworth expansion with remaindero(N
–1/2) for aU-statistic with a kernel of degree two using observations from anm-dependent shift. The second result gives a necessary and sufficient condition for the distribution of a sum ofm-dependent random variables to possess an Edgeworth expansion. This generalizes a result of Bickel and Robinson from the i.i.d. case to them-dependent case.This research was supported in part by National Science Foundation, Grant DMS 89-23071. 相似文献
19.
C. I. Goldstein 《Numerische Mathematik》1982,38(1):61-82
Summary The finite element method with non-uniform mesh sizes is employed to approximately solve Helmholtz type equations in unbounded domains. The given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary. This approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases. This results in a great reduction in the number of equations to be solved. It is proved that optimal error estimates hold inL
2,H
1 andL
, provided that certain relationships hold between the frequency, mesh size and outer radius. 相似文献
20.
LetF be a multivalued field on the manifoldM and letN be a submanifold ofM, possibly with boundary. We give a sufficient condition for the self-accessibility property of the pair (N, F), that is:N is contained in the interior of the attainable set fromN at a time smaller or equal toT, for everyT>0 (at the timeT, ifN is compact). To obtain such a condition, a modification of Petrov's implicit function theorem is proved (Ref. 1). Finally, a necessary condition for the self-accessibility property is given.This work was performed under the auspices of the Consiglio Nazionale delle Ricerche, Rome, Italy. 相似文献