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Mathematics and Statistics Faculty Publications

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Articles 391 - 418 of 418

Full-Text Articles in Mathematics

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni Jan 1992

On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In R N Ii. Radial Symmetry, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

The main purpose of this paper is to prove Theorems 1 and 2 of the preceding paper, Part I, together with their extensions and related symmetry results. To make this part essentially self-contained, we shall apply the method developed in Section 2 to equations with radial symmetry. Combining the asymptotic behavior and the "moving plane" technique, we are then able to obtain the desired results.


Introduction To The Variational Bicomplex, Ian M. Anderson Jan 1992

Introduction To The Variational Bicomplex, Ian M. Anderson

Mathematics and Statistics Faculty Publications

The variational bicomplex was first introduced in the mid 1970's as a means of studying the inverse problem of the calculus of variations. This is the problem of characterizing those differential equations which are the Euler-Lagrange equations for a classical, unconstrained variational problem. Since then, the variational bicomplex has emerged as an effective means for studying other formal, differential-geometric aspects of the calculus of variations. Moreover, it has been shown that the basic variational bicomplex constructed to solve the inverse problem can be modified in various ways and that the cohomology groups associated with these modified bicomplexes are relevant to …


A Mathematical Model For Outgassing And Contamination, Weifu Fang, Meir Shillor, E. Stahel, E. Epstein, C. Ly, J. Mcniel, E. Zaron Oct 1991

A Mathematical Model For Outgassing And Contamination, Weifu Fang, Meir Shillor, E. Stahel, E. Epstein, C. Ly, J. Mcniel, E. Zaron

Mathematics and Statistics Faculty Publications

A model for the mathematical description of the processes of outgassing and contamination in a vacuum system is proposed. The underlying assumptions are diffusion in the source, convection and diffusion in the cavity, mass transfer across the source-cavity interface, and a generalization of the Langmuir isotherm for the sorption kinetics on the target. Three approximations are considered where the asymptotic behavior of the model for large time is shown as well as the dependence and sensitivity of the model on some of the parameters. Some numerical examples of the full model are then presented together with a proof of the …


Boundary C1, Α Regularity For Variational Inequalities, Fang-Hua Lin, Yi Li Aug 1991

Boundary C1, Α Regularity For Variational Inequalities, Fang-Hua Lin, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.


Analysis And Finite-Element Approximation Of Optimal-Control Problems For The Stationary Navier-Stokes Equations With Distributed And Neumann Controls, Max D. Gunzburger, L. Hou, Tom Svobodny Jul 1991

Analysis And Finite-Element Approximation Of Optimal-Control Problems For The Stationary Navier-Stokes Equations With Distributed And Neumann Controls, Max D. Gunzburger, L. Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

We examine certain analytic and numerical aspects of optimal control problems for the stationary Navier-Stokes equations. The controls considered may be of either the distributed or Neumann type; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show the existence of optimal solutions and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. Then, we consider the approximation, by finite element methods, of solutions of the …


Refined Approximations Of The Solutions Of A Coupled System With Turning Points, W. A. Harris, S. Shao Jan 1991

Refined Approximations Of The Solutions Of A Coupled System With Turning Points, W. A. Harris, S. Shao

Mathematics and Statistics Faculty Publications

We present in this paper the asymptotic behavior of solutions of a boundary value problem for a coupled system of differential equations u″ = ν, εν″ + f(u, u′)ν′ - g(x, u, u′)ν = 0 on a compact interval I, where f(u, u′) has turning points in I. We provide upper and lower solutions, β(x, ε) and α(x, ε), respectively, which bound solutions, exhibiting boundary layer and interior layer behavior, for which limε → 0+ {β(x, ε) - α(x, ε)} = 0 uniformly on I.


Analysis And Finite Element Approximation Of Optimal Control Problems For The Stationary Navier-Stokes Equations With Dirichlet Controls, M. D. Gunzburger, L. S. Hou, Tom Svobodny Jan 1991

Analysis And Finite Element Approximation Of Optimal Control Problems For The Stationary Navier-Stokes Equations With Dirichlet Controls, M. D. Gunzburger, L. S. Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

Optimal control problems for the stationary Navier-Stokes equations are examined from analytical and numerical points of view. The controls considered are of Dirichlet type, that is, control is effected through the velocity field on (or the mass flux through) the boundary; the functionals minimized are either the viscous dissipation or the L4-distance of candidate flows to some desired flow. We show that optimal solutions exist and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. The n, finite …


Berry-Esseen-Type Bounds For Signed Linear Rank Statistics With A Broad Range Of Scores, Munsup Seoh Sep 1990

Berry-Esseen-Type Bounds For Signed Linear Rank Statistics With A Broad Range Of Scores, Munsup Seoh

Mathematics and Statistics Faculty Publications

The Berry-Esseen-type bounds of order N−1/2 for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry. The results are obtained with a broad range of regression constants and scores (allowed to be generated by discontinuous score generating functions, but not necessarily) restricted by only mild conditions, while almost all previous results are obtained with continuously differentiable score generating functions. Furthermore, the proof is very short and elementary, based on the conditioning argument.


Bimodules Over Cartan Subalgebras, Richard Mercer Apr 1990

Bimodules Over Cartan Subalgebras, Richard Mercer

Mathematics and Statistics Faculty Publications

Given a Cartan subalgebra A of a non Neumann algebra M, the techniques of Feldman and Moore are used to analyze the partial isometries v in M such that v* Av is contained in A. Orthonormal bases for M consisting of such partial isometries are discussed, and convergence of the resulting generalized fourier series is shown to take place in the Bures A-topology. The Bures A-topology is shown to be equivalent to the strong topology on the unit ball of M. These ideas are applied to A-bimodules and to give a simplified and intuitive proof of the Spectral Theorem …


On The Equivalence Of The Operator Equations Xa + Bx = C And X - P(-B)Xp(A)(-1) = W In A Hilbert-Space, P A Polynomial, Tapas Mazumdar, David Miller Apr 1990

On The Equivalence Of The Operator Equations Xa + Bx = C And X - P(-B)Xp(A)(-1) = W In A Hilbert-Space, P A Polynomial, Tapas Mazumdar, David Miller

Mathematics and Statistics Faculty Publications

We consider the solution of (*) XA+BX = C for bounded operators A,B,C and X on a Hilbert space, A normal. We establish the existence of a polynomial p and a bounded operator W with the property that the unique solution X of (*) also solves X − p(−B)Xp(A)−1 = W uniquely. A known iterative algorithm can be applied to the latter equation to solve (*).


Spatial Critical Points Of Solutions Of A One-Dimensional Nonlinear Parabolic Problem, Larry Turyn Aug 1989

Spatial Critical Points Of Solutions Of A One-Dimensional Nonlinear Parabolic Problem, Larry Turyn

Mathematics and Statistics Faculty Publications

The number of spatial critical points is nonincreasing in time, for positive, analytic solutions of a scalar, nonlinear, parabolic partial differential equation in one space dimension. While proving this, we answer the question: What happens to a critical point which loses simplicity?


Asymptotic Analysis Of Model Problems For A Coupled System, F. A. Howes, S. Shao Jan 1989

Asymptotic Analysis Of Model Problems For A Coupled System, F. A. Howes, S. Shao

Mathematics and Statistics Faculty Publications

No abstract provided.


On The Existence And Symmetry Properties Of Finite Total Mass Solutions Of The Matukuma Equation, The Eddington Equation And Their Generalizations, Yi Li, Wei-Ming Ni Jan 1989

On The Existence And Symmetry Properties Of Finite Total Mass Solutions Of The Matukuma Equation, The Eddington Equation And Their Generalizations, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.


Remarks On A Semilinear Elliptic Equation On Rn, Yi Li Jul 1988

Remarks On A Semilinear Elliptic Equation On Rn, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.


Spectral Measures, Orthogonal Polynomials, And Absolute Continuity, Joanne Dombrowski Jul 1988

Spectral Measures, Orthogonal Polynomials, And Absolute Continuity, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

This paper studies the spectral measure of an unbounded tridiagonal matrix operator for which the matrix entries satisfy a certain growth condition, and presents a sufficient condition for the existence of an absolutely continuous part. The results are related to a class of orthogonal polynomials with exponential weights.


On Conformal Scalar Curvature Equations In Rn, Yi Li, Wei-Ming Ni Jan 1988

On Conformal Scalar Curvature Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.


Cyclic Operators, Commutators, And Absolutely Continuous Measures, Joanne Dombrowski Jul 1987

Cyclic Operators, Commutators, And Absolutely Continuous Measures, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

Commutator equations are used to study the relationship between the tridiagonal matrix structure of an unbounded cyclic selfadjoint operator and its spectrum. Sufficient conditions are given for absolute continuity. Results are related to the study of systems of orthogonal polyomials for which the measure of orthogonality is supported on an unbounded subset of the real line.


Orthogonal Polynomials, Measures And Recurrence Relations, Joanne Dombrowski, Paul Nevai May 1986

Orthogonal Polynomials, Measures And Recurrence Relations, Joanne Dombrowski, Paul Nevai

Mathematics and Statistics Faculty Publications

Properties of measures associated with orthogonal polynomials are investigated in terms of the coefficients of the three term recurrence formula satisfied by the orthogonal polynomials.


L(P) Estimates For Maximal Functions And Hilbert-Transforms Along Flat Convex Curves In R(2), Hasse Carlsson, Michael Christ, Antonio Cordoba, Javier Duoandikoetxea, Jose L. Rudio De Francia, Jim Vance, Stephen Wainger, David Weinberg Apr 1986

L(P) Estimates For Maximal Functions And Hilbert-Transforms Along Flat Convex Curves In R(2), Hasse Carlsson, Michael Christ, Antonio Cordoba, Javier Duoandikoetxea, Jose L. Rudio De Francia, Jim Vance, Stephen Wainger, David Weinberg

Mathematics and Statistics Faculty Publications

No abstract provided.


Cramer Type Large Deviations For Generalized Rank Statistics, Munsup Seoh, Stegan S. Ralescu, Madan L. Puri Jan 1985

Cramer Type Large Deviations For Generalized Rank Statistics, Munsup Seoh, Stegan S. Ralescu, Madan L. Puri

Mathematics and Statistics Faculty Publications

A Cramer type large deviation theorem is proved under alternatives as well as under hypothesis for the generalized linear rank statistic which includes as special cases (unsigned) linear rank statistics, signed linear rank statistics, linear combination of functions of order statistics, and a rank combinatorial statistic.


Perturbation Of Periodic Boundary-Conditions, Larry Turyn Jan 1984

Perturbation Of Periodic Boundary-Conditions, Larry Turyn

Mathematics and Statistics Faculty Publications

We consider perturbations of the problem (*) - x'' + bx = lambda ax, x(0) - x(1) = 0 = x'(0) - x'(1) both by changes of the boundary conditions and by addition of nonlinear terms. We assume that at lambda = lambda 0 there are two linearly independent solutions of the unperturbed problem (*) and that a(dot) is bounded away from zero. When only the boundary conditions are perturbed either the Hill’s discriminant or the method of Lyapunov–Schmidt reduces the problem to 0 = det ((lambda - lambda 0)A - epsilon …


Evidence Of Intrinsic Double Acceptor In Gaas, Phil Won Yu, W. C. Mithel, M. G. Mier, S. S. Li, Weizhen Wang Jan 1982

Evidence Of Intrinsic Double Acceptor In Gaas, Phil Won Yu, W. C. Mithel, M. G. Mier, S. S. Li, Weizhen Wang

Mathematics and Statistics Faculty Publications

Acceptors present in undoped p‐type conducting GaAs have been studied with photoluminescence, temperature‐dependent Hall measurements, deep level transient spectroscopy, and spark source mass spectrometry. It is shown that p‐type conduction is due to presence of the shallow acceptor CAs and the cation antisite double acceptor GaAs. The first and second ionization energies determined for GaAs are 77 and 230 meV from the valence‐band edge.


On The Existence Of Global Variational Principles, Ian M. Anderson, T. Duchamp Oct 1980

On The Existence Of Global Variational Principles, Ian M. Anderson, T. Duchamp

Mathematics and Statistics Faculty Publications

In studying physical phenomena one frequently encounters differential equations which arise from a variational principle, i.e. the equations are the Euler-Lagrangequations obtained from the fundamental (or action) integral of a problem in the calculus of variations. Because solutions to the Euler-Lagrange equations determine the possible extrema of the fundamental integral, the first step in the solution of a given problem in the calculus of variations is to obtain the appropriate Euler-Lagrange equations. This state of affairs suggests the so-called inverse problem, viz. does a given differential equation arise from a variational principle and, if so, what is the Lagrangian for …


Quasi-Triangular Matrices, Joanne Dombrowski Jan 1978

Quasi-Triangular Matrices, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

It is shown that there exist quasitriangular operators which cannot be represented as quasitriangular matrices.


On The Structure Of Divergence-Free Tensors, Ian M. Anderson Jan 1978

On The Structure Of Divergence-Free Tensors, Ian M. Anderson

Mathematics and Statistics Faculty Publications

Contravariant rank two tensors which are divergence‐free on one index and which are constructed from the metric tensor, an auxiliary collection of arbitrary tensor fields, and the first and second partial derivatives of these quantities are classified. The results generalize existing mathematical arguments in support of the Einstein field equations


Positive Perturbations Of Unbounded Operators, Joanne Dombrowski Jan 1977

Positive Perturbations Of Unbounded Operators, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.


A Characterization Of The Einstein Tensor In Terms Of Spinors, Ian M. Anderson, D. Lovelock Jan 1976

A Characterization Of The Einstein Tensor In Terms Of Spinors, Ian M. Anderson, D. Lovelock

Mathematics and Statistics Faculty Publications

All tensors of contravariant rank two which are divergence‐free on one index, concomitants of a spinor field σiAX together with its first two partial derivatives, and scalars under spin transformations are constructed. The Einstein and metric tensors are the only candidates.


The Absolute Continuity Of Phase Operators, Joanne Dombrowski, G. H. Fricke Jan 1975

The Absolute Continuity Of Phase Operators, Joanne Dombrowski, G. H. Fricke

Mathematics and Statistics Faculty Publications

This paper studies the spectral properties of a class of operators known as phase operators which originated in the study of harmonic oscillator phase. Ifantis conjectured that such operators had no point spectrum. It was later shown that certain phase operators were, in fact, absolutely continuous and that all phase operators at least had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous.