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Real Line (real + line)

Distribution by Scientific Domains
Mathematics and Statistics85%

Selected Abstracts

On a model for electromagnetic processes inside and outside a ferromagnetic body

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2008
Martin Brokate
Abstract One-dimensional Maxwell's equations are considered in a ferromagnetic body surrounded by vacuum. Existence and uniqueness of solution for the resulting system of partial differential equations with hysteresis on the whole real line is proved under suitable constitutive hypotheses. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On the solutions of the Moisil,Théodoresco system

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2008
Juan Bory Reyes
Abstract A structure theorem is proved for the solutions to the Moisil,Théodoresco system in open subsets of ,3. Furthermore, it is shown that the Cauchy transform maps L2(,2, ,0, 2+) isomorphically onto H2(,+3, ,0, 3+), thus proving an elegant generalization to ,2 of the classical notion of an analytic signal on the real line. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Existence of solution in elastic wave scattering by unbounded rough surfaces

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2002
T. Arens
We consider the two-dimensional problem of the scattering of a time-harmonic wave, propagating in an homogeneous, isotropic elastic medium, by a rough surface on which the displacement is assumed to vanish. This surface is assumed to be given as the graph of a function ,,C1,1(,). Following up on earlier work establishing uniqueness of solution to this problem, existence of solution is studied via the boundary integral equation method. This requires a novel approach to the study of solvability of integral equations on the real line. The paper establishes the existence of a unique solution to the boundary integral equation formulation in the space of bounded and continuous functions as well as in all Lp spaces, p,[1, ,] and hence existence of solution to the elastic wave scattering problem. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Plotting Robust Root Locus For Polynomial Families Of Multilinear Parameter Dependence Based On Zero Inclusion/Exclusion Tests

ASIAN JOURNAL OF CONTROL, Issue 2 2003
Chyi Hwang
ABSTRACT The Mapping Theorem by Zadeh and Desoer [17] is a sufficient condition for the zero exclusion of the image or value set of an m -dimensional box B under a multilinear mapping f: Rm , C, where R and C denote the real line and the complex plane, respectively. In this paper, we present a sufficient condition for the zero inclusion of the value set f(B). On the basis of these two conditions and the iterative subdivision of the box B, we propose a numerical procedure for testing whether or not the value set f(B) includes the origin. The procedure is easy to implement and is more efficient than that based on constructing the value set f(B) explicitly. As an application, the proposed zero inclusion test procedure is used along with a homotopy continuation algorithm to trace out the boundary curves of the robust root loci of polynomial families with multilinear parametric uncertainties. [source]

Bayesian Optimal Designs for Phase I Clinical Trials

BIOMETRICS, Issue 3 2003
Linda M. Haines
Summary. A broad approach to the design of Phase I clinical trials for the efficient estimation of the maximum tolerated dose is presented. The method is rooted in formal optimal design theory and involves the construction of constrained Bayesian c - and D -optimal designs. The imposed constraint incorporates the optimal design points and their weights and ensures that the probability that an administered dose exceeds the maximum acceptable dose is low. Results relating to these constrained designs for log doses on the real line are described and the associated equivalence theorem is given. The ideas are extended to more practical situations, specifically to those involving discrete doses. In particular, a Bayesian sequential optimal design scheme comprising a pilot study on a small number of patients followed by the allocation of patients to doses one at a time is developed and its properties explored by simulation. [source]

Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior,

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 4 2008
Yoram Last
We prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions (Jacobi parameters approach the free ones and are of bounded variation). We prove that for ergodic discrete Schrödinger operators, Poisson behavior implies a positive Lyapunov exponent. Both results depend on a priori bounds on eigenvalue spacings for which we provide several proofs. © 2007 Wiley Periodicals, Inc. [source]

Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2006
Barry Simon
We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to the density of zeros. Zeros away from the a.c. spectrum have limit points mod p and only finitely many of them. © 2005 Wiley Periodicals, Inc. [source]