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Articles 841 - 870 of 985

Full-Text Articles in Applied Mathematics

Stability Properties And Integrability Of The Resolvent Of Linear Volterra Equations, Muhammad Islam, Paul W. Eloe Jan 1995

Stability Properties And Integrability Of The Resolvent Of Linear Volterra Equations, Muhammad Islam, Paul W. Eloe

Mathematics Faculty Publications

Integrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.

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A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn Jan 1995

A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn

Mathematics Faculty Publications

The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rn into R that was strictly increasing with respect to the new order imposed on Rn. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces …

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Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller Jan 1995

Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller

Mathematics and Statistics Faculty Publications

No abstract provided.

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Reconstruction Of Semiconductor Doping Profile From Lbic Image, Weifu Fang, Kazufumi Ito Aug 1994

Reconstruction Of Semiconductor Doping Profile From Lbic Image, Weifu Fang, Kazufumi Ito

Mathematics and Statistics Faculty Publications

In this paper, the authors study the reconstruction of a semiconductor doping profile or, equivalently, the equilibrium potential, from its LBIC (laser-beam-induced current) image. For the one-dimensional case, the authors first characterize the attainable class of current measurements, and from this they show the nonuniqueness of the inverse problem. Then the reconstruction of the equilibrium potential is reduced to finding two constants subject to some constraints. A reconstruction algorithm is established based on a least squares formulation of the problem. The case of noise-collapsed data is also discussed. For a special case of two-dimensional domain, the authors apply the one-dimensional …

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Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li Jul 1994

Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li

Mathematics and Statistics Faculty Publications

In this paper we prove the existence of self-similar solutions to the anisotropic curve shortening equation.

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Remarks On Automorphisms Of Subfactors, Phan Loi Jun 1994

Remarks On Automorphisms Of Subfactors, Phan Loi

Mathematics and Statistics Faculty Publications

We establish certain properties of automorphisms on an inclusion of AFD type II1 factors with finite index and finite depth and discuss their applications to the classification problem of AFD type III subfactors, including a different proof of a result on subfactors with principal graph Dn.

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Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho Nov 1993

Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho

Mathematics and Statistics Faculty Publications

Controllability and stabilizability of a system of coupled strings with control applied at the coupled points is studied. By investigating the properties of certain exponential series, it is shown that the system is approximate controllable if and only if related systems of uncoupled strings do not share a common eigenvalue. A sufficient condition for exact controllability is also obtained in terms of the Riesz basis properties of those exponential series.

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Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen Oct 1993

Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We describe a class of measurable subsets Ω in Rd such that L2(Ω) has an orthogonal basis of frequencies eλ(x) = ei2πλ.x(x ε Ω) indexed by λ ∈ Λ ⊂ Rd. We show that such spectral pairs (Ω, Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L2(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis of mu may be built instead from a natural representation of the Cuntz …

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Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk Sep 1993

Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk

Mathematical Sciences Technical Reports (MSTR)

Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …

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Tracking Plasma Lactate Concentration In Vivo With A Catheter-Tip L-Lactate Sensor, Brett T. Weinzapfel, Mark D. Ball, Lee R. Waite, Nacer E. Abrouk, Shun P. Lim Mar 1993

Tracking Plasma Lactate Concentration In Vivo With A Catheter-Tip L-Lactate Sensor, Brett T. Weinzapfel, Mark D. Ball, Lee R. Waite, Nacer E. Abrouk, Shun P. Lim

Mathematical Sciences Technical Reports (MSTR)

To circumvent the problems of repeated blood sampling for in vitro analysis, a catheter-tip L-lactate sensor has been developed. The sensor was tested in anesthetized pigs (n=6). The sensor in vivo tracked the lactate concentration non-linearly, seeming to obey Michaelis-Menten kinetics. Calibration time was short, typically 1.5 min per lactate standard. Furthermore, time drift was small, typically -1.3% to -3.3% per hour of in vivo use.

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Modeling And Analysis For Laser Beam Induced Current Images In Semiconductors, Weifu Fang, Stavros Busenberg, Kazufumi Ito Feb 1993

Modeling And Analysis For Laser Beam Induced Current Images In Semiconductors, Weifu Fang, Stavros Busenberg, Kazufumi Ito

Mathematics and Statistics Faculty Publications

A mathematical model is developed for the new nondestructive optical technique called laser-beam-induced currents (LBIC), which can be used to detect electrically active regions and defects in semiconductors. The wellposedness of the model equations is shown, and an approximate model that simplifies the numerical implementation of the identification problem is obtained. Some numerical results are presented to show that the approximate model preserves the significant features that the LBIC technique has been experimentally shown to possess.

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The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer Feb 1993

The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer

Mathematics and Statistics Faculty Publications

We study the group of all ''R-automorphisms'' of a countable equivalence relation R on a standard Borel space, special Borel automorphisms whose graphs lie in R. We show that such a group always contains periodic maps of each order sufficient to generate R. A construction based on these periodic maps leads to totally nonperiodic R-automorphisms all of whose powers have disjoint graphs. The presence of a large number of periodic maps allows us to present a version of the Rohlin Lemma for R-automorphisms. Finally we show that this group always contains copies of free …

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On Infinite Delay Integral Equations Having Nonlinear Perturbations, Muhammad Islam Jan 1993

On Infinite Delay Integral Equations Having Nonlinear Perturbations, Muhammad Islam

Mathematics Faculty Publications

The existence of bounded solutions and periodic solutions is studied for a system of infinite delay integral equations having nonlinear perturbations. An equivalent system of equations is obtained in terms of the resolvent kernel. Then the existence results are shown for the equivalent equations. Contraction principle, Schauder’s fixed point theorem, and monotone method are used in the study.

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Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi Jan 1993

Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi

Mathematics Faculty Research Publications

We consider control problems with trajectories which involve ordinary measureable control functions and controls which are measures. The payoff involves a running cost in time and a running cost against the control measures. In the optimal control problem we are trying to minimize this payoff with both controls. In the differential game problem we are trying to minimize the cost with the ordinary controls assuming that the measure controls are chosen to maximize the cost. We will characterize the value functions in both cases using viscosity solution theory by deriving the Bellman and Isaacs equations.

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Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni Jan 1993

Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

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On The Positive Solutions Of The Matukuma Equation, Yi Li Jan 1993

On The Positive Solutions Of The Matukuma Equation, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

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Identifiability Of Semiconductor Defects From Lbic Images, Weifu Fang, Kazufumi Ito Dec 1992

Identifiability Of Semiconductor Defects From Lbic Images, Weifu Fang, Kazufumi Ito

Mathematics and Statistics Faculty Publications

The identifiability of defects in a semiconductor from its laser-beam-induced current (LBIC) image is studied. It is shown that the LBIC technique is reliable for detecting any spatial defects in the semiconductor material. Continuous dependence of the current measurements on the spatial defects is proved, and sensitivity is also discussed in certain cases.

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Interactive Graphics System For The Study Of Variance/Covariance Structures Of Bivariate And Multivariate Normal Populations, Ronald G. Garlicki Sep 1992

Interactive Graphics System For The Study Of Variance/Covariance Structures Of Bivariate And Multivariate Normal Populations, Ronald G. Garlicki

Theses and Dissertations

This research created a graphics oriented computer program which was used as part of a Visualization, Verbalization, Algorithization and Mathematization (VVAM) learning protocol. The curriculum for this research was the study of variance/covariance structures of bivariate and multivariate normal populations. The program displays the geometric images corresponding to the various possible covariance structures. These images facilitate and encourage experiment-based self discovery learning. The program encourages the student to take an active role in their own education. The program created is self contained, calculating all the statistical values it requires to create the various geometric images. The students have complete control …

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Inverse Problems For Metal Oxide Semiconductor Field-Effect Transistor Contact Resistivity, Weifu Fang, Ellis Cumberbatch Jun 1992

Inverse Problems For Metal Oxide Semiconductor Field-Effect Transistor Contact Resistivity, Weifu Fang, Ellis Cumberbatch

Mathematics and Statistics Faculty Publications

Inverse problems arising from the identification of transistor contact resistivity and contact window location are studied. A one-point boundary measurement of the potential is shown to be sufficient to identify each from a one-parameter monotone family, and such identification is both stable and continuously dependent on the parameter. For a nonmonotone family of locations with resistivity given, similar results are obtained for measurement made on almost all boundary points.

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Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar Mar 1992

Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar

Mathematics Faculty Research Publications

A multidimensional Wiener process is controlled by an additive process of bounded variation. A convex nonnegative function measures the cost associated with the position of the state process, and the cost of controlling is proportional to the displacement induced. We minimize a limiting time-average expected (ergodic) criterion. Under reasonable assumptions, we prove that the optimal discounted cost converges to the optimal ergodic cost. Moreover, under some additional conditions there exists a convex Lipschitz continuous function solution to the corresponding Hamilton-Jacobi-Bellman equation which provides an optimal stationary feedback control.

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

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

Mathematics and Statistics Faculty Publications

No abstract provided.

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Boundary Velocity Control Of Incompressible-Flow With An Application To Viscous Drag Reduction, Max D. Gunzberger, Lisheng Hou, Tom Svobodny Jan 1992

Boundary Velocity Control Of Incompressible-Flow With An Application To Viscous Drag Reduction, Max D. Gunzberger, Lisheng Hou, Tom Svobodny

Mathematics and Statistics Faculty Publications

An optimal boundary control problem for the Navier-Stokes equations is presented. The control is the velocity on the boundary, which is constrained to lie in a closed, convex subset of H1/2 of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in all application to viscous drag reduction.

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Uniqueness Of Radial Solutions Of Semilinear Elliptic Equations, Man Kam Kwong, Yi Li Jan 1992

Uniqueness Of Radial Solutions Of Semilinear Elliptic Equations, Man Kam Kwong, Yi Li

Mathematics and Statistics Faculty Publications

E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one finite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coefficients.

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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.

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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 …

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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.

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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 …

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Shadow Casting Phenomena At Newgrange, Frank Prendergast Jan 1991

Shadow Casting Phenomena At Newgrange, Frank Prendergast

Articles

A digital model of the Newgrange passage tomb and surrounding ring of monoliths known as the Great Circle is used to investigate sunrise shadow casting phenomena at the monument. Diurnal variation in shadow directions and lengths are analysed for their potential use in the Bronze Age to indicate the passage of seasonal time. Computer-aided simulations are developed from a photogrammetric survey to accurately show how three of the largest monoliths, located closest to the tomb entrance and archaeologically coded GC1, GC-1 and GC-2, cast their shadows onto the vertical face of the entrance kerbstone, coded K1. The phenomena occur at …

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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 …

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Sets Of Typical Subsamples, Joel Atkins, G.J Sherman Sep 1990

Sets Of Typical Subsamples, Joel Atkins, G.J Sherman

Mathematical Sciences Technical Reports (MSTR)

A group theoretic condition on a set of subsamples of a random sample from a continuous random variable symmetric about 0 is shown to be sufficient to provide typical values for 0.

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