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71.
Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois. 相似文献
72.
Hiroshi Sugita 《Probability Theory and Related Fields》1994,100(1):117-130
Summary We show that each holomorphic Wiener function has a skeleton which is intrinsic from several viewpoints. In particular, we study the topological aspects of the skeletons by using the local Taylor expansion for holomorphic Wiener functions.Supported in part by the Grant-in-Aid for Science Research 03740120 Min. Education 相似文献
73.
Summary. In this paper we are interested in two phase flow problems in porous media. We use a Dual Mesh Method to discretize this
problem with finite volume schemes. In a simplified case (elliptic - hyperbolic system) we prove the convergence of approximate
solutions to the exact solutions. We use the Dual Mesh Method in physically complex problems (heterogeneous cases with non
constant total mobility). We validate numerically the Dual Mesh Method on practical examples by computing error estimates
for different test-cases.
Received March 21, 1997 / Revised version received October 13, 1997 相似文献
74.
We consider the Abelian gauge theory related to the interaction between the solitary waves of the nonlinear Klein-Gordon equation
and the electromagnetic field. We analyze the existence of electromagnetostatic solutions and, in particular, of vortices.
Dedicated to the memory of Professor Aldo Cossu 相似文献
75.
Ronald Ortner 《Operations Research Letters》2007,35(5):619-626
In ergodic MDPs we consider stationary distributions of policies that coincide in all but n states, in which one of two possible actions is chosen. We give conditions and formulas for linear dependence of the stationary distributions of n+2 such policies, and show some results about combinations and mixtures of policies. 相似文献
76.
In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of these orders in terms of a class of generalized riffle shuffles. 相似文献
77.
This paper examines the steady state behaviour of a batch arrival queue with two phases of heterogeneous service along and Bernoulli schedule vacation under multiple vacation policy, where after two successive phases service or first vacation the server may go for further vacations until it finds a new batch of customer in the system. We carry out an extensive stationary analysis of the system, including existence of stationary regime, queue size distribution of idle period process, embedded Markov chain steady state distribution of stationary queue size, busy period distribution along with some system characteristics. 相似文献
78.
Michael J. Puls 《Archiv der Mathematik》2007,88(6):500-506
Let p be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first L
p
-cohomology space of some groups that have one end. We also make a connection between the first L
p
-cohomolgy space and the Floyd boundary of the Cayley graph of a group. We apply the result about Floyd boundaries to show
that there exists a real number p such that the first L
p
-cohomology space of a nonelementary hyperbolic group does not vanish.
Received: 4 August 2006 Revised: 2 November 2006 相似文献
79.
We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups.
Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued
processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the
problem. Comparison and global properties of solutions are also studied.
Accepted 29 August 2001. Online publication 17 December 2001. 相似文献
80.
Bruno Zimmermann 《Monatshefte für Mathematik》2002,135(3):253-258
We give a list including all finite groups G which admit smooth orientation preserving actions on homology 3-spheres (arbitrary actions, i.e. possibly with fixed points;
if the action is free then the group G has periodic cohomology and the classification of such groups is well known). The main work in this direction is due to M.
Reni. In the present paper, we complete and extend his results for the case of nonsolvable groups G.
Received 19 March 2001; in revised form 15 September 2001 相似文献