Physical Sciences and Mathematics Commons^™

Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng

Mathematics and Statistics Faculty Publications

A report of progress in linear and nonlinear partial differential equations, microlocal analysis, singular partial differential operators, spectral analysis and hyperfunction theory. The papers aretaken from a conference on partial differential equations and their applications, held in Wuhan.

On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for .

Reconstructing Subsets Of Reals, A. J. Radcliffe, A. D. Scott

Department of Mathematics: Faculty Publications

We consider the problem of reconstructing a set of real numbers up to translation from the multiset of its subsets of fixed size, given up to translation. This is impossible in general: for instance almost all subsets of Z contain infinitely many translates of every finite subset of Z. We therefore restrict our attention to subsets of R which are locally finite; those which contain only finitely many translates of any given finite set of size at least 2. We prove that every locally finite subset of R is reconstructible from the multiset of its 3-subsets, given up to …

Soliton Stability In A Z (2) Field Theory, J. J. P. Veerman, D. Bazeia, Fernando Moraes

Mathematics and Statistics Faculty Publications and Presentations

We investigate the stability of the coupled soliton solutions of a two-component Z(2) vector fieldmodel, in contraposition to similar solutions of a Z(2)×Z(2)model recently introduced. We demonstrate that the coupled soliton solutions of the Z(2) model are classically unstable.

Model Updating By Adding Known Masses And Stiffnesses, Philip D. Cha, Lisette G. De Pillis

All HMC Faculty Publications and Research

New approaches are developed to update the analytical mass and stiffness matrices of a system. By adding known masses to the structure of interest, measuring the modes of vibration of this mass-modified system, and finally using this set of new data in conjunction with the initial modal survey, the mass matrix of the structure can be corrected. A similar approach can also be used to update the stiffness matrix of the system by attaching known stiffnesses. Manipulating the mass and stiffness correction matrices into vector forms, the connectivity information can be enforced, thereby preserving the physical configuration of the system, …

Algebraic Geometric Codes Over Rings, Judy L. Walker

Department of Mathematics: Faculty Publications

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980’s. Recently, there has been an increased interest in the study of linear codes over finite rings. In this paper, we combine these two approaches to coding theory by introducing the study of algebraic geometric codes over rings. In addition to defining these new codes, we prove several results about their properties.

Geometrical Model For A Particle On A Rough Inclined Surface, Giovani L. Vasconcelos, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which the dynamics is described by a one-dimensional map. This map is studied in detail and it is shown to exhibit several dynamical regimes (steady state, chaotic behavior, and accelerated motion) as the model parameters vary. A phase diagram showing the corresponding domain of existence for these regimes is presented. The model is also found to be in good qualitative agreement …

A Unified Approach To Difference Sets With Gcd(V, N) > 1, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

The five known families of difference sets whose parameters (v, k, λ; n) satisfy the condition gcd(v,n) > 1 are the McFarland, Spence, Davis-Jedwab, Hadamard and Chen families. We survey recent work which uses recursive techniques to unify these difference set families, placing particular emphasis on examples. This unified approach has also proved useful for studying semi-regular relative difference sets and for constructing new symmetric designs.

The Cantor Set, Sam Alfred Pearsall

Theses Digitization Project

No abstract provided.

On 2-Reptiles In The Plane, Sze-Man Ngai, Víctor F. Sirvent, J. J. P. Veerman, Yang Wang

Mathematics and Statistics Faculty Publications and Presentations

We classify all rational 2-reptiles in the plane. We also establish properties concerning rational reptiles in the plane in general.

On The P-Connectedness Of Graphs – A Survey, Luitpold Babel, Stephan Olariu

Computer Science Faculty Publications

A graph is said to be p-connected if for every partition of its vertices into two non-empty, disjoint, sets some chordless path with three edges contains vertices from both sets in the partition. As it turns out, p-connectedness generalizes the usual connectedness of graphs and leads, in a natural way, to a unique tree representation for arbitrary graphs.

This paper reviews old and new results, both structural and algorithmic, about p-connectedness along with applications to various graph decompositions.

Polynomial Construction Of Complex Hadamard Matrices With Cyclic Core, C. H. Cooke, I. Heng

Mathematics & Statistics Faculty Publications

Conditions are given which are necessary and sufficient to ensure invariance of an M-sequence under periodic rearrangement. In conjunction with a certain uniformity property of polynomial coefficients, these conditions yield a simple method by which complex Hadamard matrices with cyclic core can be constructed. In such cases, a real p-ary linear cyclic error correcting code may be associated with the complex Hadamard matrix.

Algorithms For The Numerical Solution Of A Finite-Part Integral Equation, J. Tweed, R. St. John, M. H. Dunn

Mathematics & Statistics Faculty Publications

The authors investigate a hypersingular integral equation which arises in the study of acoustic wave scattering by moving objects. A Galerkin method and two collocation methods are presented for solving the problem numerically. These numerical techniques are compared and contrasted in three test problems.

Contraction Of The Model For The Bray-Liebhafsky Oscillatory Reaction By Eliminating Intermediate I2o, Zeljko D. Cupic

Zeljko D Cupic

No abstract provided.

Three-Dimensional Calculation Of Contaminant Transport In Groundwater At A Dover Afb Site, Tariq O. Hashim

Theses and Dissertations

Macroscale rate-limited sorption modeling was tested using a production transport code, the GMS/FEMWATER ground-water modeling package. The code (Version 1.1 of FEMWATER. dated 1 August 1995) was applied to a 3D conceptual model developed from a field site at Dover AFB, DE. A simulation was performed of a 200 hour contaminant injection pulse followed by clean water flushing. A moment analysis performed on the resulting breakthrough curve validated code self-consistency. Another injection pulse simulation showed that retardation temporally delays the breakthrough peak. Transport simulations of pulsed clean water pumping of the test cell with a prescribed initial contaminant distribution demonstrated …

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

Department of Math & Statistics Faculty Publications

An inverse problem for an 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 Cauchy data on a known portion of the boundary. The dynamics in the interior of the region are governed by a differential operator of parabolic type. Utilizing a unique continuation result for evolution operators, along with the method of eigenfunction expansions, it is shown that uniqueness holds for a large and physically reasonable class of Cauchy data pairs.

Validation Of Waimss Incident Duration Estimation Model, Wei Wu, Pushkin Kachroo, Kaan Ozbay

Electrical & Computer Engineering Faculty Research

This paper presents an effort to validate the traffic incident duration estimation model of WAIMSS (wide area incident management support system). Duration estimation model of WAIMSS predicts the incident duration based on an estimation tree which was calibrated using incident data collected in Northern Virginia. Due to the limited sample size, a full scale test of the distribution, mean and variance of incident duration was performed only for the root node of the estimation tree, white only mean tests were executed at all other nodes whenever a data subset was available. Further studies were also conducted on the model error …

Spectral Features Of The Stimulated Raman Backscattering Of Modulated Laser Pulses In A Plasma, Nikolai E. Andreev, Serguei Y. Kalmykov

Serge Youri Kalmykov

The characteristic features of the stimulated Raman backscattering of short modulated (multi-frequency) laser pulses in an underdense plasma are investigated. A laser pulse consisting of a given pair of spectral components with the frequency difference close to the double plasma frequency is studied in the weak mode coupling approximation. The scattering of the component with the higher frequency is shown to be a five-wave resonant process, and the conditions under which this process is totally suppressed are found. The scattering of the component with the lower frequency is an ordinary three-wave decay process without any suppression. When the difference between …

A Structural Result Of Irreducible Inclusions Of Type Iii Lambda Factors, Lambda Is An Element Of (0,1), Phan Loi

Mathematics and Statistics Faculty Publications

Given an irreducible inclusion of factors with finite index N ⊂ M, where M is of type III_λ1/m, N of type III_λ1/n, 0 < λ < 1, and m,n are relatively prime positive integers, we will prove that if N ⊂ M satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with N ⊂ M. Relations between N ⊂ M and a certain G-kernel on subfactors are also discussed.

Microwave Heating Of Fluid/Solid Layers : A Study Of Hydrodynamic Stability And Melting Front Propagation, John Gilchrist

Dissertations

In this work we study the effects of externally induced heating on the dynamics of fluid layers, and materials composed of two phases separated by a thermally driven moving front. One novel aspect of our study is in the nature of the external source, which is provided by the action of microwaves acting on dielectric materials. The main challenge is to model and solve systems of differential equations, which couple fluid dynamical motions (the Navie- Stokes equations for nonisothermal flows) and electromagnetic wave propagation (governed by Maxwell's equations).

When an electromagnetic wave impinges on a material, energy is generated within …

A Generalization Of Cayley Graphs For Finite Fields, Dawn M. Jones

Dissertations

A central question in the area of topological graph theory is to find the genus of a given graph. In particular, the genus parameter has been studied for Cayley graphs. A Cayley graph is a representation of a group and a fixed generating set for that group. A group is said to be planar if there is a generating set which produces a planar Cayley graph. We say that a group is toroidal if there is a generating set that produces a toroidal Cayley graph and if there are no generating sets which produce a planar Cayley graph. Characterizations for …

Maximally Disjoint Solutions Of The Set Covering Problem, David J. Rader, Peter L. Hammer

Mathematical Sciences Technical Reports (MSTR)

This paper is concerned with finding two solutions of a set covering problem that have a minimum number of variables in common. We show that this problem is NP­ complete, even in the case where we are only interested in completely disjoint solutions. We describe three heuristic methods based on the standard greedy algorithm for set covering problems. Two of these algorithms find the solutions sequentially, while the third finds them simultaneously. A local search method for reducing the overlap of the two given solutions is then described. This method involves the solution of a reduced set covering problem. Finally, …

Evolution Of Mixed-State Regions In Type-Ii Superconductors, Chaocheng Huang, Tom Svobodny

Mathematics and Statistics Faculty Publications

A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C^1+α(Ω₀) for all t > Ω, where Ω₀ is the initial vortex region that is assumed to be in C^1+α. Consequently, for any time t, the vortex region Ω_t is of C^1+α, and the vorticity is in C^α(Ω_t).

Isospectral Sets For Fourth-Order Ordinary Differential Operators, Lester Caudill, Peter A. Perry, Albert W. Schueller

Department of Math & Statistics Faculty Publications

Let L(p)u = D⁴u - (p₁u’)’ + p₂u be a fourth-order differential operator acting on L²[0; 1] with p ≡ (p1; p2) belonging to L²_ℝ[0, 1] x L²_ℝ[0, 1] and boundary conditions u(0) = u''(0) = u(1) = u''(1) = 0. We study the isospectral set of L(p) when L(p) has simple spectrum. In particular we show that for such p …

Trigonometric Transforms For Image Reconstruction, Thomas M. Foltz

Theses and Dissertations

This dissertation demonstrates how the symmetric convolution-multiplication property of discrete trigonometric transforms can be applied to traditional problems in image reconstruction with slightly better performance than Fourier techniques and increased savings in computational complexity for symmetric point spread functions. The fact that the discrete Fourier transform a circulant matrix provides an alternate way to derive the symmetric convolution-multiplication property for discrete trigonometric transforms. Derived in this manner, the symmetric convolution-multiplication property extends easily to multiple dimensions and generalizes to multidimensional asymmetric sequences. The symmetric convolution-multiplication property allows for linear filtering of degraded images via point-by-point multiplication in the transform domain …

Perturbed Hamiltonian System Of Two Parameters With Several Turning Points, Myeong Joon Ann

Dissertations

No abstract provided.

Bootstrapping Tsmars Models, Liangzhong Chen

Theses

We investigate bootstrap inference methods for nonlinear time series models obtained using Multivariate Adaptive Regression Splines for Time Series (TSMARS), for which theoretical properties are not currently known. We use two different methods of bootstrapping to obtain confidence intervals for the underlying nonlinear function and prediction intervals for future values, based on estimated TSMARS models for the bootstrapped data. We also explore the method of Bootstrap AGGregatING (Bagging), due to Breiman (1996), to investigate whether the residual and prediction mean squared errors from a fitted TSMARS model can be reduced by averaging across the values obtained from each of the …

Stability And Reconstruction For An Inverse Problem For The Heat Equations, Kurt M. Bryan, Lester Caudill

Mathematical Sciences Technical Reports (MSTR)

We examine the inverse problem of determining the shape of some unknown portion of the boundary of a region W from measurements of the Cauchy data for solutions to the heat equation on W. By suitably linearizing the inverse problem we obtain uniqueness and continuous dependence results. We propose an algorithm for recovering estimates of the unknown portion of the surface and use the insight gained from a detailed analysis of the inverse problem to regularize the inversion. Several computational examples are presented.

(A Note On)(2) The Shape Of The Erythrocyte, J. A. Adam

Mathematics & Statistics Faculty Publications

A note on the shape of the red blood cell is revisited, utilizing variational calculus to to find an extremum for the surface area of such a cell, using the volume as a constraint. A fairly significant error in the value of the volume is corrected, and the note concludes with a discussion of measures of cell shape (such as the sphericity index) which are more appropriate than the dimensional surface area to volume ratio.

Onset Of Superconductivity In Decreasing Fields For General Domains, Andrew J. Bernoff, Peter Sternberg

All HMC Faculty Publications and Research

Ginzburg–Landau theory has provided an effective method for understanding the onset of superconductivity in the presence of an external magnetic field. In this paper we examine the instability of the normal state to superconductivity with decreasing magnetic field for a closed smooth cylindrical region of arbitrary cross-section subject to a vertical magnetic field. We examine the problem asymptotically in the boundary layer limit (i.e., when the Ginzburg–Landau parameter, k, is large). We demonstrate that instability first occurs in a region exponentially localized near the point of maximum curvature on the boundary. The transition occurs at a value of the …