Mathematics Commons^™

On The Geometrisability Of Some Strongly Regular Graphs Related To Polar Spaces., Pratima Panigraphi Dr.

Doctoral Theses

GraphsA graph G = (VE) consists of a finite set V and a subset E of ). (Here () denotes the set of all 2-subsets of V.) Elements of Vare called the vertices and the elements of E are called the edges of the graph. So Vis the vertex set and E is the edge set of the graph G. Two vertices a, y are said to be adjacent if the pair {a, y} is an edge; otherwise they are non-adjacent. If two vertices are adjacent then each is called a neighbour of the other vertex.Sometimes the edges of a …

Static Interconnection Networks And Parallel Algorithms For Efficient Problem Solving., T. Krishnan Dr.

Doctoral Theses

There is nothing more difficult to take in hand, more perilous to conduct, or more uncertain in its success, than to take the lead in the introduction of a new order of things.

Wiener Tauberian Theorems On Semisimple Lie Group., Rudra Pada Sarkar Dr.

Doctoral Theses

In their celebrated study of Harmonic analysis on semi-simple Lie groups Ehrenpreis and Mautner [E-M] noticed that the analogue of the claasical Wiener Tauberian theorem resting on the unitary dual does not hold for semisimple Lle groups. A simple proof of this fact due to M. Duflo appears in (H). Ehrenpreis and Mautner went on in (E-M] to formulate the problem on the commutative Banach algebra of the SO2(R)-biinvariant functions in L1(SL2(R))1, and obtained two different versions of the theorem involving, this time, the dual of the Banach algebra which includes, beside the unitary dual of G, a part of …

Proper And Unit Bitolerance Orders And Graphs, Kenneth P. Bogart, Garth Isaak

Dartmouth Scholarship

We say any order ≺ is a tolerance order on a set of vertices if we may assign to each vertex x an interval I_x of real numbers and a real number t_x called a tolerance in such a way that x ≺ y if and only if the overlap of I_x and I_y is less than the minimum of t_x and t_y and the center of I_x is less than the center of I_y. An order is a bitolerance order if and only if there are intervals I_x and …

Identification And Characterization Of Gfrα-3, A Novel Co-Receptor Belonging To The Glial Cell Line-Derived Neurotrophic Receptor Family, Carolyn A. Worby, Quinn Vega, Hanna H.J. Chao, Audrey F. Seasholtz, Robert C. Thompson, Jack E. Dixon

Department of Mathematics Faculty Scholarship and Creative Works

A new family of neuronal survival factors comprised of glial cell line- derived neurotrophic factor (GDNF) and neurturin has recently been described (Kotzbauer, P. T., Lampe, P. A., Heuckeroth, R. O., Golden, J.P., Creedon, D. J., Johnson, E. M., Jr., and Milbrandt, J. (1997) Nature 384, 467-470). These molecules, which are related to transforming growth factor-β, are important in embryogenesis and in the survival of distinct neuronal populations. These molecules signal through a novel receptor system that includes the Ret receptor tyrosine kinase, a ligand (i.e. GDNF or neurturin), and an accessory glycosyl-phosphatidylinositol-linked molecule that is responsible for high affinity …

The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis

Department of Math & Statistics Technical Report Series

Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you've traveled less than 2πR. Does your path, γ, have to lie in some hemisphere?

This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that …

Recognizing Constant Curvature Discrete Groups In Dimension 3, J. W. Cannon, E. L. Swenson

Faculty Publications

We characterize those discrete groups Gwhich can act properly discontinuously, isometrically, and cocompactly on hyperbolic 3-space H^3 in terms of the combinatorics of the action of G on its space at infinity. The major ingredients in the proof are the properties of groups that are negatively curved (in the large) (that is, Gromov hyperbolic), the combinatorial Riemann mapping theorem, and the Sullivan-Tukia theorem on groups which act uniformly quasiconformally on the 2-sphere.

Positive Knots And Robinson's Attractor, Michael C. Sullivan

Articles and Preprints

We study knotted periodic orbits which are realized in an attractor of a certain ODE. These knots can be presented so as to have all positive crossings, but may not be restricted to positive braids.

New Families Of Semi-Regular Relative Difference Sets, James A. Davis, Jonathan Jedwab, Miranda Mowbray

Department of Math & Statistics Faculty Publications

We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose order can contain more than two distinct prime factors. For u greater than 2 these are the first such RDSs, and for u = 2 we obtain new examples.

Constructions Of Random Distributions Via Sequential Barycenters, Theodore P. Hill, Michael Monticino

Research Scholars in Residence

This article introduces and develops a constructive method for generating random probability measures with a prescribed mean or distribution of the means. The method involves sequentially generating an array of barycenters which uniquely defines a probability measure. Basic properties of the generated measures are presented, including conditions under which almost all the generated measures are continuous or almost all are purely discrete or almost all have finite support. Applications are given to models for average-optimal control problems and to experimental approximation of universal constants.

The Approximate Functional Formula For The Theta Function And Diophantine Gauss Sums, Evangelos A. Coutsias, N.D. Kazarinoff

Branch Mathematics and Statistics Faculty and Staff Publications

By introducing the discrete curvature of the polygonal line, and by exploiting the similarity of segments of the line, for small w, to Cornu spirals (C-spirals), we prove the precise renormalization formula. This formula, which sharpens Hardy and Littlewood's approximate functional formula for the theta function, generalizes to irrationals, as a Diophantine inequality, the well-known sum formula of Gauss. The geometrical meaning of the relation between the two limits is that the first sum is taken to a point of inflection of the corresponding C-spirals. The second sum replaces whole C-spirals of the first by unit vectors times scale and …

Some Harmonic N-Slit Mappings, Michael Dorff

Faculty Publications

The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, ∆, such that f = h+g where h(z) = (see PDF), g(z) = (see PDF) . SOH will denote the subclass with b1 = 0. We present a collection of n-slit mappings (n ≥ 2) and prove that the 2-slit mappings are in SH while for n ≥ 3 the mappings are in SOH. Finally we show that these mappings establish the sharpness of a previous theorem by Clunie and Sheil-Small while disproving a conjecture about the inner mapping radius.

On Lipschitzian, And Connected Matrices In: Linear Complementarity Problem., Sriparna Bandyopadhyay Dr.

Doctoral Theses

This dissertation deals with a number of questions related to the linear complementarity problem (LCP). Given A ∈ Rn*n and q ∈ Rnthe LCP is to find a vector z ∈ R" such that Az+q ≥0,≥ and 2'(Az + 9) = 0. There is a vast literature on LCP developed during the last four decades. LCP plays a crucial role in the study of Mathematical Progranming from the point of view of algorithms as well as applications. The questions on existence and multiplicity of solutions in LCP has led researchers to introduce and study a variety of matrix classes. Most …

On Subwavelet Sets., Eugen J. Ionascu

Faculty Bibliography

Abstract. In this note we give a characterization of subwavelet sets and show that any point x ∈ R\0 has a neighborhood which is contained in a regularized wavelet set.

On The Unitary Systems Affiliated With Orthonormal Wavelet Theory In N-Dimensions, Eugen J. Ionascu

Faculty Bibliography

We consider systems of unitary operators on the complex Hilbert space L2 (Rn) of the form U :=UDA , Tv1 , ..., Tvn :=[DmT l1 v1 }}} Tln vn : m, l1 , ..., ln # Z], where DA is the unitary operator corresponding to dilation by an n_n real invertible matrix A and Tv1 , ..., Tvn are the unitary operators corresponding to translations by the vectors in a basis [v1 , ..., vn] for Rn . Orthonormal wavelets are vectors in L2 (Rn ) which are complete wandering vectors for U in the sense that [U: U # …

Attractor Dimension Estimates For Two-Dimensional Shear Flows, Charles R. Doering, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We study the large time behavior of boundary and pressure-gradient driven incompressible fluid flows in elongated two-dimensional channels with emphasis on estimates for their degrees of freedom, i.e., the dimension of the attractor for the solutions of the Navier-Stokes equations. for boundary driven shear flows and flux driven channel flows we present upper bounds for the degrees of freedom of the form ca Re^3/2 where c is a universal constant, a denotes the aspect ratio of the channel (length/width), and Re is the Reynolds number based on the channel width and the imposed "outer" velocity scale. for fixed pressure …

Atomoicity Of Mappings, J. J. Charatonik, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

A mapping f:X→Y between continua X and Y is said to be atomic at a subcontinuumK of the domain X provided that f(K) is nondegenerate and K=f^-1(f(K)). The set of subcontinua at which a given mapping is atomic, considered as a subspace of the hyperspace of all subcontinua of X, is studied. The introduced concept is applied to get new characterizations of atomic and monotone mappings. Some related questions are asked.

Arc Approximation Property And Confluence Of Induced Mappings, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

We say that a continuum X has the arc approximation property if every subcontinuum K of X is the limit of a sequence of arcwise connected subcontinua of X all containing a fixed point of K. This property is applied to exhibit a class of continua Y such that confluence of a mapping f : X - Y implies confluence of the induced mappings 2^f : 2^x - @^y and C(f) : C(x) - C(y). The converse implications are studied and similar interrelations are considered for some other classes of mappings, related to confluent ones.

Quality Evaluation Methods – A Review, Boyan N. Dimitrov

Mathematics Publications

Quality is understood as a set of features that determine how a product fits to satisfy certain needs. Therefore, a set of measurements X1, X2,…, Xn characterizes each product, and also serves as information in evaluation of product's quality. Individual measurements Xi are quantitative (numerical) or qualitative (non-numerical) variables expressing the value of the ith index of quality. Evaluation of the overall level of quality, comparison of similar products, measuring and reporting quality improvement and other related problems need construction of some integral quality index Q in which all individual measurements are taken into account. Several proposals for integral quality …

Timing Analysis Of Targeted Hunter Searches, John W. Jones, David P. Roberts

Mathematics Publications

One can determine all primitive number fields of a given degree and discriminant with a finite search of potential defining polynomials. We develop an asymptotic formula for the number of polynomials which need to be inspected which reflects both archimedean and non-archimedean restrictions placed on the coefficients of a defining polynomial.

Exponential Dichotomy And Mild Solutions Of Nonautonomous Equations In Banach Spaces, Y. Latushkin, Timothy W. Randolph, R. Schnaubelt

Mathematics and Statistics Faculty Research & Creative Works

We prove that the exponential dichotomy of a strongly continuous evolution family on a Banach space is equivalent to the existence and uniqueness of continuous bounded mild solutions of the corresponding inhomogeneous equation. This result addresses nonautonomous abstract Cauchy problems with unbounded coefficients. The technique used involves evolution semigroups. Some applications are given to evolution families on scales of Banach spaces arising in center manifolds theory. © 1998 Plenum Publishing Corporation.

Some Harmonic N-Slit Mappings, Michael Dorff

Mathematics and Statistics Faculty Research & Creative Works

The class SH consists of univalent, harmonic, and sense-preserving functions f in the unit disk, Δ, such that f = h+ḡ where h(z) = z + ∑2∞ akzk g(z) = ∑1∞ bkzk. SHO will denote the subclass with b1 = 0. We present a collection of n-slit mappings (n ≥ 2) and prove that the 2-slit mappings are in SH while for n ≥ 3 the mappings are in SHO. Finally, we show that these mappings establish the sharpness of a previous theorem by Clunie and Sheil-Small while disproving a conjecture about the inner mapping radius. ©1998 American Mathematical Society.

A Study Of Optimization In Hilbert Space, John Awunganyi

Theses Digitization Project

No abstract provided.

State Sum Invariants Of Three Manifolds, Sharon Angela Newman-Gomez

Theses Digitization Project

No abstract provided.

Exceptional Objects, John Stillwell

Mathematics

No abstract provided.

A Study In Geometric Construction, Nichola Sue Mcclain

Theses Digitization Project

No abstract provided.

Using Symbolic Dynamical Systems: A Search For Knot Invariants, Russell Clark Wheeler

Theses Digitization Project

No abstract provided.

Spatial Estimates For Stochastic Flows In Euclidean Space, Salah-Eldin A. Mohammed, Michael K. R. Scheutzow

Articles and Preprints

We study the behavior for large |x| of Kunita-type stochastic flows φ(t, ω, x) on R^d, driven by continuous spatial semimartingales. For this class of flows we prove new spatial estimates for large |x|, under very mild regularity conditions on the driving semimartingale random field. It is expected that the results would be of interest for the theory of stochastic flows on noncompact manifolds as well as in the study of nonlinear filtering, stochastic functional and partial differential equations. Some examples and counterexamples are given.

Further Properties Of An Extremal Set Of Uniqueness, David E. Grow, Matt Insall

Mathematics and Statistics Faculty Research & Creative Works

Consider the circle group T = R mod 2_ as the interval [0, 1). Then each x 2 T has a binary expansion: x =P1 k=1 xk2−k where each xk is 0 or 1. Let S be the set of x with a binary expansionsuch that the number of 1's does not exceed the number of the leading zeros by more than one. The authors prove that the countable compact set S cannot be expressed as the union of a finite number of Dirichlet sets.

Interactions Of Topological Kinks In Two Coupled Rings Of Nonlinear Oscillators, A E. Duwel, C P. Heij, J C. Weisenfeld, Stephen M.K. Yeung, E Trias, S. J.K. Vardy, H. S.J. Van Der Zant, S H. Strogatz, T P. Orlando

Mathematics

Two discrete rings of nonlinear oscillators with topologically trapped kinks exhibit features due to coupling interactions between the rings. These interaction effects include phase locking between kinks in different rings, precession of the kink/antikink collision region, excitation of kink/antikink pairs, and time-dependent switching. We study these phenomena in simulations of two coupled discrete sine-Gordon equations, and in experiments on two inductively coupled rings of niobium Josephson junctions.