Applied Mathematics Commons^™

Some Properties Of Hereditarily Indecomposable Chainable Continua, Thomas John Kacvinsky

Masters Theses

"In 1920, B. Knaster and C. Kuratowski raised the question of whether each homogeneous plane continuum is a simple closed curve. In 1921, S. Mazurkiewicz raised the question of whether each subcontinuum of Euclidean n-space which is homeomorphic to each of its subcontinua is necessarily an arc. In that same year, B. Knaster and C. Kuratowski raised the question of whether there exists a nondegenerate hereditarily indecomposable continuum.

The third question was answered in the affirmative in 1922 by B. Knaster, when he constructed a nondegenerate hereditarily indecomposable subcontinuum of the plane.

The second question was answered in 1947 by …

Convolution And Fourier-Feynman Transforms, Chull Park, David Skough

Department of Mathematics: Faculty Publications

In this paper, for a class of funtionals on Wiener space of the form F(x) = exp{∫^T₀ f(t, x(t)) dt}, we show that the Fourier-Feynman transform of the convolution product is a product of Fourier-Feynman transforms. This allows us to compute the transform of the convolution product without computing the convolution product.

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.

The Laws Of Complexity & The Complexity Of Laws: The Implications Of Computational Complexity Theory For The Law, Eric Kades

Faculty Publications

No abstract provided.

Hausdorff Dimension Of Boundaries Of Self-Affine Tiles In R N, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We present a new method to calculate the Hausdorff dimension of a certain class of fractals: boundaries of self-affine tiles. Among the interesting aspects are that even if the affine contraction underlying the iterated function system is not conjugated to a similarity we obtain an upper- and and lower-bound for its Hausdorff dimension. In fact, we obtain the exact value for the dimension if the moduli of the eigenvalues of the underlying affine contraction are all equal (this includes Jordan blocks). The tiles we discuss play an important role in the theory of wavelets. We calculate the dimension for a …

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

University Faculty Publications and Creative Works

No abstract provided.

Limiting Spheroid Size As A Function Of Growth Factor Source Location, J. A. Adam, K. Y. Ward

Mathematics & Statistics Faculty Publications

Solutions C(r) of the time-independent nonhomogeneous diffusion equation for three different piecewise-uniform source terms are used to examine the limiting size of multicell spheroids using a simple model which reproduces concentration-dependent mitotic behavior. A condition is derived under which nontrivial solutions do not exist (in all three cases), and a condition for the existence of a unique nontrivial solution is established for the case of growth-modifying factor (GMF) production throughout the spheroid. Qualitative behavior of the limiting size is established as a function of various physiological parameters. Of fundamental importance is the assumed GMF concentration threshold θ, …

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.

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.

Antiplane Shear Of A Strip Containing A Staggered Array Of Rigid Line Inclusions, G. Kerr, G. Melrose, J. Tweed

Mathematics & Statistics Faculty Publications

Motivated by the increased use of fibre-reinforced materials, we illustrate how the effective elastic modulus of an isotropic and homogeneous material can be increased by the insertion of rigid inclusions. Specifically we consider the two-dimensional antiplane shear problem for a strip of material. The strip is reinforced by introducing two sets of ribbon-like, rigid inclusions perpendicular to the faces of the strip. The strip is then subjected to a prescribed uniform displacement difference between its faces, see Figure 1. it should be noted that the problem posed is equivalent to that of the uniform antiplane shear problem for an infinite …

Time-Optimal Tree Computations On Sparse Meshes, D. Bhagavathi, V. Bokka, H. Gurla, S. Olariu, J. L. Schwing

Computer Science Faculty Publications

The main goal of this work is to fathom the suitability of the mesh with multiple broadcasting architecture (MMB) for some tree-related computations. We view our contribution at two levels: on the one hand, we exhibit time lower bounds for a number of tree-related problems on the MMB. On the other hand, we show that these lower bounds are tight by exhibiting time-optimal tree algorithms on the MMB. Specifically, we show that the task of encoding and/or decoding n-node binary and ordered trees cannot be solved faster than Ω(log n) time even if the MMB has an infinite …

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 …

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 …

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

Honors Capstone Projects and Theses

No abstract provided.

Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke

Mechanical & Aerospace Engineering Theses & Dissertations

The control of payload swing in industrial gantry cranes is a topic of widespread interest. In this thesis, the control of the swing of a payload idealized by a point mass assumption is investigated utilizing s, compact robotics matrix/vector representation of the dynamical model. In this form, this particular system can be viewed as sn underactuated manipulator with equal numbers of active and passive degrees of freedom. The full three dimensional model is developed and linearized by modelling the cable as a single thread of fiexible wire and the degree of dynamic coupling between the active and passive coordinates is …

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.

A Study Of The Numerical Implementation Of Multidisciplinary Design Optimization Strategies, Rodney A. Taylor

Mechanical & Aerospace Engineering Theses & Dissertations

Design optimization provides an organized, systematic, and efficient method for obtaining design improvements based upon a specified measure of design performance. In the multidisciplinary design optimization (MDO) environment efficient optimization techniques allow complex designs to be improved by managing conflicting disciplinary design goals so as to improve the global design. This thesis studies the implementation issues surrounding MDO techniques and strategies. To facilitate this investigation two testbed problems have been selected for study. These problems consider two approaches to the conceptual design of an aeroelastic wing. The first approach is based on an idealized, two-dimensional representation of an airfoil under …

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.

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.

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 …

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.

Bounds On Squares Of Two-Sets, Daniel Slilaty, Jeffrey Vanderkam

Mathematics and Statistics Faculty Publications

Let G be a finite group and let pi(G) denote the proportion of (x, y) ∈ G2 for which the set {x2,xy,yx,y2} has cardinality i. We show that either 0 < pi(G) + p2(G) ≤ 1/2 or pi(G) + p2(G) = 1, and that either p4(G) = 0 or 5/32 ≤ p4(G) ≤ 1. Each of the preceding inequalities are the best possible.

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.

The Steady Boundary Layer Due To A Fast Vortex, Andrew J. Bernoff, Harald J. H. M. Van Dongen, Seth Lichter

All HMC Faculty Publications and Research

A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherently unsteady. Here we show that for a vortex convected by a uniform shear flow, there is a steady solution when the speed of the vortex c_v is sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (c_v→∞) and numerically …