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1.
Gauss—Seidel type relaxation techniques are applied in the context of strictly convex pure networks with separable cost functions.
The algorithm is an extension of the Bertsekas—Tseng approach for solving the linear network problem and its dual as a pair
of monotropic programming problems. The method is extended to cover the class of generalized network problems. Alternative
internal tactics for the dual problem are examined. Computational experiments —aimed at the improved efficiency of the algorithm
— are presented.
This research was supported in part by National Science Foundation Grant No. DCR-8401098-A0l. 相似文献
2.
This paper presents a new reduction algorithm for the efficient computation of the homology of cubical sets and polotypes.
The algorithm—particularly strong for low-dimensional sets embedded in high dimensions—runs in linear time. The paper presents
the theoretical background of the algorithm, the algorithm itself, experimental results based on an implementation for cubical
sets as well as some theoretical complexity estimates.
Both authors are partially supported by Polish MNSzW, Grant N201 037 31/3151. 相似文献
3.
For compact Riemann surfaces, the collar theorem and Bers’ partition theorem are major tools for working with simple closed
geodesics. The main goal of this article is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic two-dimensional
orbifolds are a particular case of such surfaces. We consider all cone angles to be strictly less than π to be able to consider
partitions.
Emily B. Dryden—partially supported by the US National Science Foundation grant DMS-0306752.
Hugo Parlier—supported by the Swiss National Science Foundation grants 21-57251.99 and 20-68181.02. 相似文献
4.
Gilles Godefroy 《Israel Journal of Mathematics》1988,61(3):301-331
We study the class of the Riesz subsets of abelian discrete groups, that is, the sets for which the F. and M. Riesz theorem
extends. We show that the “classical” tools of the theory — Riesz projections, localization in the Bohr sense, products —
are leading to Riesz sets which are satisfying nice additional properties, e.g., the Mooney-Havin result extends to this class.
We give an alternative proof of a result of A. B. Alexandrov, and we improve a construction of H. P. Rosenthal. The connection
is made between this class and theM-structure theory. We show a result of convergence at the boundary for holomorphic functions on the polydisc. The Bourgain-Davis
result on convergence of analytic martingales is improved. 相似文献
5.
Generators of some Ramanujan formulas 总被引:2,自引:0,他引:2
Jesús Guillera 《The Ramanujan Journal》2006,11(1):41-48
In this paper we prove some Ramanujan type formulas for 1/π but without using the theory of modular forms. Instead we use
the WZ—method created by H. Wilf and D. Zeilberger and find some hypergeometric functions in two variables which are second
components of WZ—pairs than can be certified using Zeilberger's EKHAD package. These certificates have an additional property
which allows us to get generalized Ramanujan's type series which are routinely proven by computer. We call these second hypergeometric
components of the WZ—pairs generators. Finding generators seems a hard task but using a kind of experimental research (explained
below), we have succeeded in finding some of them. Unfortunately we have not found yet generators for the most impressive
Ramanujan's formulas. We also prove some interesting binomial sums for the constant 1/π2. Finally we rewrite many of the obtained series using pochhammer symbols and study the rate of convergence.
2000 Mathematics Subject Classification Primary—33C20 相似文献
6.
T. B. Boffey 《TOP》1998,6(2):205-221
In recent years, interest has been shown in the optimal location of ‘extensive’ facilities in a network. Two such problems—the
Maximal Direct and Indirect Covering Tree problems—were introduced by Hutson and ReVelle. Previous solution techniques are
extended to provide an efficient algorithm for the Indirect Covering Tree problem and the generalization in which demand covered
is attenuated by distance. It is also shown that the corresponding problem is NP-hard when the underlying network is not a
tree. 相似文献
7.
8.
V. Y. Pan 《Journal of Mathematical Sciences》2006,134(5):2411-2424
We reexamine the Wiedemann—Coppersmith—Kaltofen—Villard algorithm for randomized computation of the determinant of an integer
matrix and substantially simplify and accelerate its bottleneck stage of computing the minimum generating matrix polynomial,
to make the algorithm practically promising while keeping it asymptotically fast. Bibliography: 58 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 316, 2004, pp. 163–187. 相似文献
9.
The aim of the paper is to relate computational and arithmetic questions about Euler’s constant γ with properties of the values
of the q-logarithm function, with natural choice of~q. By these means, we generalize a classical formula for γ due to Ramanujan, together with Vacca’s and Gosper’s series for
γ, as well as deduce irrationality criteria and tests and new asymptotic formulas for computing Euler’s constant. The main
tools are Euler-type integrals and hypergeometric series.
2000 Mathematics Subject Classification Primary—11Y60; Secondary—11J72, 33C20, 33D15
The work of the second author is supported by an Alexander von Humboldt research fellowship
Dedication: To Leonhard Euler on his 300th birthday. 相似文献
10.
Abstract. The Li—Li algorithm produced in [11] for the mixed volume computation of fully mixed polynomial systems is reconstructed
in this article for general semi-mixed polynomial systems. Taking the special structure of the semi-mixed supports of the
systems into account, the resulting algorithm, illustrated by numerical results, can dramatically speed up the mixed volume
computation, especially when the systems are unmixed. Even when applied to fully mixed systems, the new algorithm improves
the speed of the Li—Li algorithm by a considerable amount. 相似文献
11.
Loeb space methods are used to prove the existence of an optimal control for the two-dimensional stochastic Navier--Stokes
equations in a variety of settings—including that of control based on digital observations of the evolution of the solution. 相似文献
12.
Abstract. The Li—Li algorithm produced in [11] for the mixed volume computation of fully mixed polynomial systems is reconstructed
in this article for general semi-mixed polynomial systems. Taking the special structure of the semi-mixed supports of the
systems into account, the resulting algorithm, illustrated by numerical results, can dramatically speed up the mixed volume
computation, especially when the systems are unmixed. Even when applied to fully mixed systems, the new algorithm improves
the speed of the Li—Li algorithm by a considerable amount. 相似文献
13.
Shiwei He Sohail S. Chaudhry Zhonglin Lei Wang Baohua 《Annals of Operations Research》2009,168(1):169-179
We study a vendor selection problem in which the buyer allocates an order quantity for an item among a set of suppliers such
that the required aggregate quality, service, and lead time requirements are achieved at minimum cost. Some or all of these
characteristics can be stochastic and hence, we treat the aggregate quality and service as uncertain. We develop a class of
special chance-constrained programming models and a genetic algorithm is designed for the vendor selection problem. The solution
procedure is tested on randomly generated problems and our computational experience is reported. The results demonstrate that
the suggested approach could provide managers a promising way for studying the stochastic vendor selection problem.
The authors would like to thank the referees for providing constructive comments that led to an improved version of the paper.
Also, this research was partially supported by grants from National Natural Science Foundation (60776825)—China, 863 Programs
(2007AA11Z208)—China, Doctorate Foundation (20040004012)—China, Villanova University Research Sabbatical Fall 2006, and the
National Science Foundation (0332490)—USA. 相似文献
14.
We improve a result of Thangavelu on Riesz means associated with the twisted Laplacian. Askey—Wainger estimates for Laguerre
functions are the main tools used.
Research supported in part by KBN grants and by ECC under program “Fourier Analysis” contract no: CIPDCT 940001. 相似文献
15.
Higher order numerical differentiation on the Infinity Computer 总被引:1,自引:0,他引:1
Yaroslav D. Sergeyev 《Optimization Letters》2011,5(4):575-585
There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by
a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of information.
In this paper, a new way to do this is presented for a new kind of a computer—the Infinity Computer—able to work numerically
with finite, infinite, and infinitesimal numbers. It is proved that the Infinity Computer is able to calculate values of derivatives
of a higher order for a wide class of functions represented by computer procedures. It is shown that the ability to compute
derivatives of arbitrary order automatically and accurate to working precision is an intrinsic property of the Infinity Computer
related to its way of functioning. Numerical examples illustrating the new concepts and numerical tools are given. 相似文献
16.
Paweł Dłotko Tomasz Kaczynski Marian Mrozek Thomas Wanner 《Discrete and Computational Geometry》2011,46(2):361-388
In this paper we present a new algorithm for computing the homology of regular CW-complexes. This algorithm is based on the
coreduction algorithm due to Mrozek and Batko and consists essentially of a geometric preprocessing algorithm for the standard
chain complex generated by a CW-complex. By employing the concept of S-complexes the original chain complex can—in all known
practical cases—be reduced to a significantly smaller S-complex with isomorphic homology, which can then be computed using
standard methods. Furthermore, we demonstrate that in the context of non-uniform cubical grids this method significantly improves
currently available algorithms based on uniform cubical grids. 相似文献
17.
Benchmarking optimization software with performance profiles 总被引:9,自引:6,他引:3
We propose performance profiles — distribution functions for a performance metric — as a tool for benchmarking and comparing
optimization software. We show that performance profiles combine the best features of other tools for performance evaluation.
Received: February 2001 / Accepted: May 2001?Published online October 2, 2001 相似文献
18.
The number of spanning trees of a graph, also known as the complexity, is computed for graphs constructed by a replacement
procedure yielding a self-similar structure. It is shown that under certain symmetry conditions exact formulas for the complexity
can be given. These formulas indicate interesting connections to the theory of electrical networks. Examples include the well-known
Sierpiński graphs and their higher-dimensional analogues. Several auxiliary results are provided on the way—for instance,
a property of the number of rooted spanning forests is proven for graphs with a high degree of symmetry. 相似文献
19.
This paper presents two integer linear programming (ILP) models for cyclic scheduling of tasks with unit/general processing
time. Our work is motivated by digital signal processing (DSP) applications on FPGAs (Field-Programmable Gate Arrays)—hardware
architectures hosting several sets of identical arithmetic units. These hardware units can be formalized as dedicated sets
of parallel identical processors. We propose a method to find an optimal periodic schedule of DSP algorithms on such architectures
where the number of available arithmetic units must be determined by the scheduling algorithm with respect to the capacity
of the FPGA circuit. The emphasis is put on the efficiency of the ILP models. We show the advantages of our models in comparison
with common ILP models on benchmarks and randomly generated instances. 相似文献
20.
Jonathan M. Borwein 《Optimization Letters》2010,4(4):473-490