Physical Sciences and Mathematics Commons^™

A Dual Approach To Constrained Interpolation From A Convex Subset Of Hilbert Space, Frank Deutsch, Wu Li, Joseph D. Ward

Mathematics & Statistics Faculty Publications

Many interesting and important problems of best approximationare included in (or can be reduced to) one of the followingtype: in a Hilbert spaceX, find the best approximationPK(x) to anyx∈Xfrom the setK≔C∩A−1(b),whereCis a closed convex subset ofX,Ais a bounded linearoperator fromXinto a finite-dimensional Hilbert spaceY, andb∈Y. The main point of this paper is to show thatPK(x)isidenticaltoPC(x+A*y …

Continuities Of Metric Projection And Geometric Consequences, Robert Huotari, Wu Li

Mathematics & Statistics Faculty Publications

We discuss the geometric characterization of a subset K of a normed linear space via continuity conditions on the metricprojection onto K. The geometric properties considered includeconvexity, tubularity, and polyhedral structure. The continuityconditions utilized include semicontinuity, generalized stronguniqueness and the non-triviality of the derived mapping. Infinite-dimensional space with the uniform norm we show thatconvexity is equivalent to rotation-invariant almost convexityand we characterize those sets every rotation of which has continuousmetric projection. We show that polyhedral structure underliesgeneralized strong uniqueness of the metric projection.

Superconvergence Of The Iterated Collocation Methods For Hammerstein Equations, Hideaki Kaneko, Richard D. Noren, Peter A. Padilla

Mathematics & Statistics Faculty Publications

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [16] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 18].

Scattering From Stellar Acoustic-Gravity Potentials: Ii. Phase Shifts Via The First Born Approximation, J. A. Adam, I. Mckaig

Mathematics & Statistics Faculty Publications

Using the first Born approximation, properties of the scattering phase shift are investigated for waves that are scattered by a schematic representation of a large-scale “stellar potential,” i.e., one for which the star itself is viewed as the potential inducing a phase shift in an incoming wave. In particular, the phase shift properties are examined as functions of the relative wavenumber (α) and the azimuthal wavenumber (l), high l-values being of interest in helioseismology.

The Hadamard Matroid And An Anomaly In Its Single Element Extensions, C. H. Cooke

Mathematics & Statistics Faculty Publications

A nonstandard vector space is formulated, whose bases afford a representation of what is called a Hadamard matroid, M_p. For prime p, existence of M_p is equivalent to the existence of both a classical Hadamard matrix H(p,p) and a certain affine resolvable, balanced incomplete block design AR(p). An anomaly in the representable single element extension of a Hadamard matroid is discussed.

Global Attractors From The Explosion Of Singular Cycles, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

Résumé:

Nous présentons dans cette Note des résultats récents concernant l’existence et les bifurcations d’un nouvel attracteur global chaotique.

Algebraic Fiberings Of Grassmann Varieties, R. J. D. Ferdinands, R. E. Schultz

University Faculty Publications and Creative Works

No abstract provided.

Nonlinear Liquid Drop Model. Cnoidal Waves, Andrei Ludu

Andrei Ludu

No abstract provided.

An Investigation Of Instantaneous Plume Rise From Rocket Exhaust, Paul F. Sand

Theses and Dissertations

Rocket launches at Vandenburg Air Force Base and Cape Canaveral Air Station produce exhaust clouds containing several toxic by-products, including HC1 and A12O3. These clouds rise to atmospheric stabilization heights, and then start dispersing and diffusing through the air. Upon reaching the ground, concentration levels of the toxins may present a human health risk. To predict these risks and concentration levels, range officials use a computer program titled the Rocket Effluent Exhaust Diffusion Model (REEDM). The version currently in use has been shown to underpredict the stabilization height of the exhaust cloud. This thesis examines the theory and algorithms used …

Integrity Of Digraphs, Robert Charles Vandell

Dissertations

The vertex-integrity of a digraph D, denoted I(D), is defined to be the minimum over aIII subsets X of the vertex set of D for the quantity IXI + m(D - X), w here IXI is the number of vertices in X and m(D - X) is the maximum order of a strong component in the digraph D - X. In a like manner, the arc-integrity of the digraph D, denoted I’(D), is defined to be the minimum over all subsets Y of the arc set of D for the quantity IYI + m(D - Y), where IYI is the …

Roll The Bones: "A Study Of Random Events Using Interactive Simulation", Jason Saint

Honors Capstone Projects and Theses

No abstract provided.

Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li

Yi Li

In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)_μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)_μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ∈(0, μ*) and 2<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ_**⩽μ**<μ* such that problem (∗)_{μ …}

Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li

Mathematics and Statistics Faculty Publications

In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)_μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)_μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ∈(0, μ*) and 2<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ_**⩽μ**<μ* such that problem (∗)_{μ …}

Uniqueness For A Boundary Identification Problem In Thermal Imaging, Kurt M. Bryan, Lester F. Caudill

Mathematical Sciences Technical Reports (MSTR)

An inverse problem for a parabolic initial-boundary value problem is considered. The goal is to determine an unknown portion of the boundary of a region in Rⁿ from measurements of Dirichlet data on a known portion of the boundary. It is shown that under reasonable hypotheses uniqueness results hold.

Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury

Mathematics and Statistics Faculty Publications

The term ''self-consistency'' was introduced in 1989 by Hastie and Stuetzle to describe the property that each point on a smooth curve or surface is the mean of all points that project orthogonally onto it. We generalize this concept to self-consistent random vectors: a random vector Y is self-consistent for X if E[X|Y] = Y almost surely. This allows us to construct a unified theoretical basis for principal components, principal curves and surfaces, principal points, principal variables, principal modes of variation and other statistical methods. We provide some general results on self-consistent random variables, give …

Positive Solutions For A Semilinear Elliptic Problem With Critical Exponent, Ismail Ali, Alfonso Castro

All HMC Faculty Publications and Research

No abstract provided in article.

Controlling Experiment-Wise Type I Error Of Meta-Analysis In The Solomon Four-Group Design, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Abstract. Stouffer=s Z, a meta-analytic technique, was proposed by W. Braver and Braver (1988) for analyzing data collected from a Solomon Four-group Design. Sawilowsky, Kelley, Blair, and Markman (1994) showed that this technique produces inflated Type I error rates. Recommendations are made to control the false positive inflation of their procedure.

Characteristic Spatial Quadratures For Discrete Ordinates Neutral Particle Transport On Arbitrary Tetrahedral Meshes, Charles R. Brennan

Theses and Dissertations

Characteristic spatial quadratures for discrete ordinates calculations on meshes of arbitrary tetrahedra are derived and tested, including the step (SC), linear (LC), and exponential (EC) characteristic quadratures and variants that assume constant distributions on cell faces. Tetrahedral meshes accurately model curved surfaces with few cells. A split cell approach subdivides tetrahedra along the streaming direction, reducing the transport to one dimension. Assumed forms of the cell source and entering flux distributions have sufficient parameters to match the zeroth and first spatial moments. These parameters are determined by analytically inverting a linear system (LC), or by numerical inversion using Newton's method …

An Inverse Problem In Thermal Imaging, Kurt Bryan, Lester Caudill

Department of Math & Statistics Faculty Publications

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied in both the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

The Exponential Stability Of A Coupled Hyperbolic/Parabolic System Arising In Structural Acoustics, George Avalos

Department of Mathematics: Faculty Publications

We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE’s which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domain Ω, coupled to a “parabolic–like” beam equation holding on ∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our result is an analog of a recent result by Lasiecka and Triggiani which shows the exponential stability of the wave equation via Neumann feedback control, and like that work, depends upon a trace regularity estimate for solutions of hyperbolic …

Droplet Evaporation And Deformations In An Amplitude Modulated Ultrasonic Field, Nihad E. Daidzic, Rene Stadler, Adrian Melling

Aviation Department Publications

The aim of the report presented is the measurements of droplet oscillations.

Stability Analysis Of A Model For The Defect Structure Of Yba2cu3ox, Gregory Kozlowski, Tom Svobodny

Physics Faculty Publications

Unusual microstructures of YBa₂Cu₃O_x (123) crystals have been observed. These structures have been shown to pass very high transport currents. A model of the solidification of 123 from a melt with Y₂BaCuO₅ (211) inclusions indicates that the stability of the 123 interface can depend on the sizes of the 211 inclusions. The observed formations are interpreted in the light of this instability.

Effects Of Vascularization On Lymphocyte/Tumor Cell Dynamics: Qualitative Features, J. A. Adam

Mathematics & Statistics Faculty Publications

By adapting a pre-existing model to include the effects of vascularization within a tumor or multicell spheroid, a predator-prey system describing the cell populations of a solid tumor and reactive lymphocytes is formulated. The paper serves as a review of the minimal deterministic approach to tumor-host immune system interactions while examining, in a qualitative manner, the modifications to the dynamics induced by a simple representation of the vascularized tumor. In addition, the possibility of limit-cycle behavior is studied by regarding each of six parameters present in the model as a bifurcation parameter. Thus, in principle, well-defined and periodic oscillations in …

Effective Behavior Of Clusters Of Microscopic Cracks Inside A Homogeneous Conductor, Kurt M. Bryan, Michael Vogelius

Mathematical Sciences Technical Reports (MSTR)

We study the effective behaviour of a periodic array of microscopic cracks inside a homoge­neous conductor. Special emphasis is placed on a rigorous study of the case in which the corresponding effective conductivity becomes nearly singular, due to the fact that adjacent cracks nearly touch. It is heuristically shown how thin clusters of such extremely close cracks may macroscopically appear as a single crack. The results have implications for our earlier work on impedance imaging.

On An Investment-Consumption Model With Transaction Costs, Marianne Akian, José Luis Menaldi, Agnès Sulem

Mathematics Faculty Research Publications

This paper considers the optimal consumption and investment policy for an investor who has available one bank account paying a fixed interest rate and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption. Dynamic programming leads to a variational inequality for the value function. Existence and uniqueness of a viscosity solution are proved. The variational inequality is solved by using a numerical algorithm based on policies, iterations, and multigrid methods. Numerical results are displayed …

Optimal Starting-Stopping Problems For Markov-Feller Processes, Jose-Luis Menaldi, Maurice Robin, Min Sun

Mathematics Faculty Research Publications

By means of nested inequalities in semigroup form we give a characterization of the value functions of the starting-stopping problem for general Markov-Feller processes. Next, we consider two versions of constrained problems on the nal state or on the final time. The plan is as follows:

1. Introduction
2. Nested variational inequalities
3. Solution of optimal starting-stopping problem
4. Problems with constraints

References.

Orthogonalization Process Or Finding A Basic Feasible Solution (Bfs), G.R. Jahanshahloo, S. Abbasbandy

Saeid Abbasbandy

For finding an optimal solution in L.P., combination of orthogonality and simplex method is used. It seems that the number of iteration is reduced with respect to new algorithm in [1].

Exp For Windows, Version 4.0 A Software Review, Donn E. Miller-Harnish

Mathematics and System Engineering Faculty Publications

No abstract provided.

Exact Multiplicity Results For Boundary Value Problems With Nonlinearities Generalizing Cubic, Philip Korman, Yi Li, Tiancheng Ouyang

Mathematics and Statistics Faculty Publications

No abstract provided.

A Center-Unstable Manifold Theorem For Parametrically Excited Surface Waves, Larry Turyn

Mathematics and Statistics Faculty Publications

When fluid in a rectangular tank sits upon a platform which is oscillating with sufficient amplitude, surface waves appear in the ''Faraday resonance.'' Scientists and engineers have done bifurcation analyses which assume that there is a center manifold theory using a finite number of excited spatial modes. We establish such a center manifold theorem for Xiao-Biao Lin's model in which potential flow is assumed but an artificial dissipation term is included in the system of partial differential equations on the free surface. We use interpolation spaces developed by da Prate and Grisvard, establish maximal regularity for a family of evolution …