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Many Solutions (many + solution)

Distribution by Scientific Domains
Mathematics and Statistics66%

Selected Abstracts

Consistency of quasi-static boundary value problems in electromagnetic modelling

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2006
S. Suuriniemi
Abstract This paper analyses the possibility to computationally settle consistency of field problems, especially those arising from electromagnetic modelling: the electromagnetic theory is expressed in field-oriented concepts, which allow for formulation of boundary value problems with no solution at all or infinitely many solutions. This possibility of such inconsistent problems decreases the productivity of electromagnetic design software. This paper relates the consistency question to topological aspects of the model domain, and proposes a scheme for routine computation of the relevant topological aspects of electromagnetic models. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Infinitely many solutions for polyharmonic elliptic problems with broken symmetries

MATHEMATISCHE NACHRICHTEN, Issue 1 2003
Sergio Lancelotti
Abstract By means of a perturbation argument devised by P. Bolle, we prove the existence of infinitely many solutions for perturbed symmetric polyharmonic problems with non,homogeneous Dirichlet boundary conditions. An extension to the higher order case of the estimate from below for the critical values due to K. Tanaka is obtained. [source]

Block s-step Krylov iterative methods

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2010
Anthony T. Chronopoulos
Abstract Block (including s-step) iterative methods for (non)symmetric linear systems have been studied and implemented in the past. In this article we present a (combined) block s-step Krylov iterative method for nonsymmetric linear systems. We then consider the problem of applying any block iterative method to solve a linear system with one right-hand side using many linearly independent initial residual vectors. We present a new algorithm which combines the many solutions obtained (by any block iterative method) into a single solution to the linear system. This approach of using block methods in order to increase the parallelism of Krylov methods is very useful in parallel systems. We implemented the new method on a parallel computer and we ran tests to validate the accuracy and the performance of the proposed methods. It is expected that the block s-step methods performance will scale well on other parallel systems because of their efficient use of memory hierarchies and their reduction of the number of global communication operations over the standard methods. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Emerging uses of SIP in service provider networks

BELL LABS TECHNICAL JOURNAL, Issue 1 2003
Guy J. Zenner
The session initiation protocol (SIP) has emerged as a viable protocol for providing numerous services within today's networks. SIP was closely modeled after http to make it an easily extensible protocol that could provide connectivity in new converged Internet protocol (IP) networks. The inherent extensibility of SIP has allowed SIP to be used in many ways not envisioned by its creators. What started as a simple protocol for setting up a media stream between two endpoints has since found numerous seemingly unrelated uses. With many solutions using SIP being proposed and implemented, it is often hard to determine how best to use SIP for a particular solution. The purpose of this paper is to give the reader a framework for categorizing various SIP capabilities through the concept of usage models and to help the reader understand the various ways SIP can be used in both evolutionary and revolutionary ways in real-world networks. This paper assumes the reader has a basic understanding of SIP and its inner workings. © 2003 Lucent Technologies Inc. [source]

Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2008
Tobias H. Colding
We show that for a Schrödinger operator with bounded potential on a manifold with cylindrical ends, the space of solutions that grows at most exponentially at infinity is finite dimensional and, for a dense set of potentials (or, equivalently, for a surface for a fixed potential and a dense set of metrics), the constant function 0 is the only solution that vanishes at infinity. Clearly, for general potentials there can be many solutions that vanish at infinity. One of the key ingredients in these results is a three circles inequality (or log convexity inequality) for the Sobolev norm of a solution u to a Schrödinger equation on a product N × [0, T], where N is a closed manifold with a certain spectral gap. Examples of such N's are all (round) spheres ,,n for n , 1 and all Zoll surfaces. Finally, we discuss some examples arising in geometry of such manifolds and Schrödinger operators.© 2007 Wiley Periodicals, Inc. [source]