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1.
In this work we analyze the paper “Brimberg, J. (1995): The Fermat-Weber location problem revisited. Mathematical Programming 71, 71–76” which claims to close the question on the conjecture posed by Chandrasekaran and Tamir in 1989 on the convergence
of the Weiszfeld algorithm. Some counterexamples are shown to the proofs showed in Brimberg’s paper.
Received: January 1999 / Accepted: December 2001?Published online April 12, 2002
RID="*"
ID="*"Partially supported by PB/11/FS/97 of Fundación Séneca of the Comunidad Autónoma de la Región de Murcia
RID="**"
ID="**"Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica (I+I+D), project TIC2000-1750-C06-06
RID="*"
RID="**" 相似文献
2.
Dedicated to the memory of Paul Erdős
We extend a result of J. Alexander and D. Zagier on the Garsia entropy of the Erdős measure. Our investigation heavily relies
on methods from combinatorics on words. Furthermore, we introduce a new singular measure related to the Farey tree.
Received October 7, 1999
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ID="†" This author is supported by the START-project Y96-MAT of the Austrian Science Fund
RID="‡"
ID="‡" This author is supported by the Austrian Science Fund (FWF) grant P14200-MAT
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ID="*" This author is supported by the Austrian Science Fund (FWF) grant S8307-MAT 相似文献
3.
Dedicated to the memory of Paul Erdős
A graph is called -free if it contains no cycle of length four as an induced subgraph. We prove that if a -free graph has n vertices and at least edges then it has a complete subgraph of vertices, where depends only on . We also give estimates on and show that a similar result does not hold for H-free graphs––unless H is an induced subgraph of . The best value of is determined for chordal graphs.
Received October 25, 1999
RID="*"
ID="*" Supported by OTKA grant T029074.
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ID="**" Supported by TKI grant stochastics@TUB and by OTKA grant T026203. 相似文献
4.
5.
6.
We study homotopy equivalences of p-completions of classifying spaces of finite groups. To each finite group G and each prime p, we associate a finite category ℒ
p
c
(G) with the following properties. Two p-completed classifying spaces BG
p
∧ and BG’
p
∧ have the same homotopy type if and only if the associated categories ℒ
p
c
(G) and ℒ
p
c
(G’) are equivalent. Furthermore, the topological monoid Aut(BG
p
∧) of self equivalences is determined by the self equivalences of the associated category ℒ
p
c
(G).
Oblatum 5-VII-2001 & 28-VIII-2002?Published online: 8 November 2002
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ID="*"C. Broto is partially supported by DGICYT grant PB97–0203.
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ID="**"R. Levi is partially supported by EPSRC grant GR/M7831.
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ID="***"B. Oliver is partially supported by UMR 7539 of the CNRS. 相似文献
7.
Summary. We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms.
Received March 28, 2000 / Revised version received June 23, 2000 / Published online March 8, 2002
RID="*"
ID="*" Supported by the National Science Foundation under grant DMS-9870187
RID="**"
ID="**" Supported by the National Science Foundation under grant DMS-9803340 and by the Army Research Office under grant DAAD-19-99-1-0160 相似文献
8.
Dedicated to the memory of Paul Erdős
We provide an elementary proof of the fact that the ramsey number of every bipartite graph H with maximum degree at most is less than . This improves an old upper bound on the ramsey number of the n-cube due to Beck, and brings us closer toward the bound conjectured by Burr and Erdős. Applying the probabilistic method
we also show that for all and there exists a bipartite graph with n vertices and maximum degree at most whose ramsey number is greater than for some absolute constant c>1.
Received December 1, 1999
RID="*"
ID="*" Supported by NSF grant DMS-9704114
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ID="**" Supported by KBN grant 2 P03A 032 16 相似文献
9.
10.
We prove versions of the Dual Ramsey Theorem and the Dual Ellentuck Theorem for families of partitions which are defined
in terms of games.
Received: 8 July 1999 Published online: 19 December 2002
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ID="*" The author wishes to thank the Swiss National Science Foundation for supporting him.
The authors thank the referee for helpful comments.
Mathematics Subject Classification (2000): 03E02, 05D10, 03E35
Key words or phrases: Dual Ramsey Theorem – Dual Ellentuck Theorem – Partitions – Games 相似文献
11.
Imre Patyi 《Mathematische Annalen》2003,326(3):417-441
Let X be a complex Banach space with a countable unconditional basis, Ω⊂X pseudoconvex open, G a complex Banach Lie group. We show that a Runge–type approximation hypothesis on X, G (which we also prove for G a solvable Lie group) implies that any holomorphic cocycle on Ω with values in G can be resolved holomorphically if it can be resolved continuously.
Received: 1 March 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 32L05, 32E30, 46G20
RID="*"
ID="*" Kedves Szímuskának.
RID="*"
ID="*" To my dear Wife. 相似文献
12.
In this paper we develop a method for classifying an unknown data vector as belonging to one of several classes. This method
is based on the statistical methods of maximum likehood and borrowed strength estimation. We develop an MPEC procedure (for
Mathematical Program with Equilibrium Constraints) for the classification of a multi-dimensional observation, using a finite
set of observed training data as the inputs to a bilevel optimization problem. We present a penalty interior point method
for solving the resulting MPEC and report numerical results for a multispectral minefield classification application. Related
approaches based on conventional maximum likehood estimation and a bivariate normal mixture model, as well as alternative
surrogate classification objective functions, are described.
Received: October 26, 1998 / Accepted: June 11, 2001?Published online March 24, 2003
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ID="***"The authors of this work were all partially supported by the Wright Patterson Air Force Base via Veda Contract F33615-94-D-1400.
The first and third author were also supported by the National Science Foundation under grant DMS-9705220.
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ID="*"The work of this author was based on research supported by the U.S. National Science Foundation under grant CCR-9624018.
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ID="**"The work of this author was supported by the Office of Naval Research under grant N00014-95-1-0777. 相似文献
13.
In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without
changing the core of the game. These games will be called buyer-seller exact games and satisfy the condition that each mixed-pair
coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyer-seller
exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization
of those assignment games which are buyer-seller exact in terms of the assignment matrix, attainable upper and lower core
bounds for the mixed-pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical
representation of a “45o-lattice” by means of the core of an assignment game can now be answered.
Received: March 2002/Revised version: January 2003
RID="*"
ID="*" Institutional support from research grants BEC 2002-00642 and SGR2001-0029 is gratefully acknowledged
RID="**"
ID="**" The authors thank the referees for their comments 相似文献
14.
Dedicated to the memory of Paul Erdős
In [9] Thomassen proved that a -connected graph either contains k vertex disjoint odd cycles or an odd cycle cover containing at most 2k-2 vertices, i.e. he showed that the Erdős–Pósa property holds for odd cycles in highly connected graphs. In this paper, we
will show that the above statement is still valid for 576k-connected graphs which is essentially best possible.
Received November 17, 1999
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ID="*" This work was supported by a post-doctoral DONET grant.
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ID="†" This work was supported by an NSF-CNRS collaborative research grant.
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ID="‡" This work was performed while both authors were visiting the LIRMM, Université de Montpellier II, France. 相似文献
15.
This paper introduces an exact primal augmentation algorithm for solving general linear integer programs. The algorithm iteratively
substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine
inequalities. We prove that various versions of our algorithm are finite. It is a major concern in this paper to show how
the subproblem of replacing a column can be accomplished effectively. An implementation of the presented algorithms is given.
Computational results for a number of hard 0/1 integer programs from the MIPLIB demonstrate the practical power of the method.
Received: April 23, 2001 / Accepted: May 2002
Published online: March 21, 2003
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="*"
ID="*" Supported by grants FKZ 0037KD0099 and FKZ 2495A/0028G of the Kultusministerium of Sachsen-Anhalt.
RID="#"
ID="#"Supported by a Gerhard-Hess-Preis and grant WE 1462 of the Deutsche Forschungsgemeinschaft, and by the European DONET
program TMR ERB FMRX-CT98-0202.
Mathematics Subject Classification (1991): 90C10 相似文献
16.
Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems 总被引:1,自引:0,他引:1
Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with
Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains
and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem
can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists
in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz
and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation
is possible and can be done in different ways.
Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002
RID="*"
ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and
NSF DMS-9802367
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ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated 相似文献
17.
Summary. In this paper, we consider some nonlinear inexact Uzawa methods for iteratively solving linear saddle-point problems. By
means of a new technique, we first give an essential improvement on the convergence results of Bramble-Paschiak-Vassilev for
a known nonlinear inexact Uzawa algorithm. Then we propose two new algorithms, which can be viewed as a combination of the
known nonlinear inexact Uzawa method with the classical steepest descent method and conjugate gradient method respectively.
The two new algorithms converge under very practical conditions and do not require any apriori estimates on the minimal and
maximal eigenvalues of the preconditioned systems involved, including the preconditioned Schur complement. Numerical results
of the algorithms applied for the Stokes problem and a purely linear system of algebraic equations are presented to show the
efficiency of the algorithms.
Received December 8, 1999 / Revised version received September 8, 2001 / Published online March 8, 2002
RID="*"
ID="*" The work of this author was partially supported by a grant from The Institute of Mathematical Sciences, CUHK
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ID="**" The work of this author was partially supported by Hong Kong RGC Grants CUHK 4292/00P and CUHK 4244/01P 相似文献
18.
S.Yu. Orevkov 《Mathematische Annalen》2002,324(4):657-673
Let be a rational curve of degree d which has only one analytic branch at each point. Denote by m the maximal multiplicity of singularities of C. It is proven in [MS] that . We show that where is the square of the “golden section”. We also construct examples which show that this estimate is asymptotically sharp.
When , we show that and this estimate is sharp. The main tool used here, is the logarithmic version of the Bogomolov-Miyaoka-Yau inequality.
For curves as above we give an interpretation of this inequality in terms of the number of parameters describing curves of
a given degree and the number of conditions imposed by singularity types.
Received: 11 February 2000 / Published online: 8 November 2002
RID="*"
ID="*" Partially supported by Grants RFFI-96-01-01218 and DGICYT SAB95-0502 相似文献
19.
In this paper we study a solution for discrete cost allocation problems, namely, the serial cost sharing method. We show
that this solution can be computed by applying the Shapley value to an appropriate TU game and we present a probabilistic
formula. We also define for cost allocation problems a multilinear function in order to obtain the serial cost sharing method
as Owen (1972) did for the Shapley value in the cooperative TU context. Moreover we show that the pseudo average cost method
is equivalent to an extended Shapley value.
Received April 2000/Revised January 2003
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ID="*" Authors are indebted to two anonymous referees for especially careful and useful comments. This research has been
partially supported by the University of the Basque Country (projects UPV 036.321-HA197/98, UPV 036.321-HA042/99) and DGES
Ministerio de Educación y Ciencia (project PB96-0247). 相似文献
20.
We rigorously prove that the solution surface of the intermediate surface diffusion flow converges to that of the averaged
mean curvature flow locally in time as the diffusion coefficient tends to infinity. As an application of this convergence
result, we show that the intermediate surface diffusion flow can drive embedded hypersurfaces into self-intersections.
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ID="*"Partially supported by the Japan Society for the Promotion of Science, Grant No. 10304010, 12814024. 相似文献