Physical Sciences and Mathematics Commons^™

Complexity Reduction In State-Based Modeling, Martin Zwick

Systems Science Faculty Publications and Presentations

For a system described by a relation among qualitative variables (or quantitative variables "binned" into symbolic states), expressed either set-theoretically or as a multivariate joint probability distribution, complexity reduction (compression of representation) is normally achieved by modeling the system with projections of the overall relation. To illustrate, if ABCD is a four variable relation, then models ABC:BCD or AB:BC:CD:DA, specified by two triadic or four dyadic relations, respectively, represent simplifications of the ABCD relation. Simplifications which are lossless are always preferred over the original full relation, while simplifications which lose constraint are still preferred if the reduction of complexity more …

Weyl-Type Fields With Geodesic Lines Of Force, Brendan Guilfoyle

Publications

The static electrogravitational equations are studied and it is shown that an aligned type D metric which has a Weyl-type relationship between the gravitational and electric potential has shearfree geodesic lines of force. All such fields are then found and turn out to be the fields of a charged sphere, charged infinite rod and charged infinite plate. A further solution is also found with shearing geodesic lines of force. This new solution can have m > |e| or m < |e|, but cannot be in the Majumdar-Papapetrou class (in which m = |e|). It is algebraically general and has flat equipotential surfaces.

Construction Of Some Combinatorial Designs Arising Out Of Statistical Experiments., Tridib Kumar Dutta Dr.

Doctoral Theses

Chis dissertation considers construction of two kinds of combi natorial sesigns as used by statisticians: repeated measurements designs (RMDS) and symmetric balanced squares (SBSS). 1.1. REPEATED MEASUREMENTS DESIGNS The researchers need to perform experiments where each experimental unit receives some or all of the treatments in an appropriate sequence over a number of successive periods. These designs are known by several names in the statistical 1iterature: repeated measurements designs, crossover or changeover designs, (multiple) time series designs, and before-after designs. If there are n experimental units 1,2, ... n, t treatments and p periods 0,1, .. .p-1, applied, then an …

Symmetry And Tiling Groups For Genus 4 And 5, C. Ryan Vinroot

Mathematical Sciences Technical Reports (MSTR)

All symmetry groups for surfaces of genus 2 and 3 are known. In this paper, we classify symmetry groups and tiling groups with three branch points for surfaces of genus 4 and 5. Also, a class of symmetry groups that are not tiling groups is presented, as well as a class of odd order non-abelian tiling groups.

Attractors For Non-Compact Semigroups Via Energy Equations, Ioana Moise, Ricardo Rosa, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The energy-equation approach used to prove the existence of the global attractor by establishing the so-called asymptotic compactness property of the semigroup is considered, and a general formulation that can handle a number of weakly damped hyperbolic equations and parabolic equations on either bounded or unbounded spatial domains is presented. as examples, three specific and physically relevant problems are considered, namely the flows of a second-grade fluid, the flows of a Newtonian fluid in an infinite channel past an obstacle, and a weakly damped, forced Korteweg-de Vries equation on the whole line.

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.

The Sharp Sobolev Inequality And The Banchoff-Pohl Inequality On Surfaces, Ralph Howard

Faculty Publications

No abstract provided.

Quadrilaterals Subdivided By Triangles In The Hyperbolic Plane, Dawn M. Haney, Lori T. Mckeough

Mathematical Sciences Technical Reports (MSTR)

In this paper, we consider triangle-quadrilateral pairs in the hyperbolic plane which “kaleidoscopically” tile the plane simultaneously. These tilings are called divisible tilings or subdivided tilings. We restrict our attention to the simplest case of divisible tilings, satisfying the corner condition, in which a single triangle occurs at each vertexof the quadrilateral. All possible such divisible tilings are catalogued as well as determining the minimal genus surface on which the divisible tiling exists. The tiling groups of these surfaces are also determined.

On The Dynamics Of Stochastic Differential Systems (The Seventh Vilnius Conference On Probability Theory And Mathematical Statistics), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

We outline proofs of two stable-manifold theorems for stochastic differential systems with and without memory. The results are joint work with Michael Scheutzow.

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 …

Octary Codewords With Power Envelopes Of 3∗2M, Katherine M. Nieswand, Kara N. Wagner

Department of Math & Statistics Technical Report Series

This paper examines codewords of length 2^m in Z₈ with envelope power maxima of 3 ∗ 2^m. Using the general form for Golay pairs as a base, a general form is derived for the set of coset leaders that generate these codewords. From this general form it will be proven that there exists at least one element in the coset that achieves a power of 3 ∗ 2^m for each m-even and m-odd case.

Asymptotic Norming Properties And Related Themes., Sudeshna Basu Dr.

Doctoral Theses

In the first part of this chapter, we explain the main theme of this thesis. The second part consists of some of the notions and results used in subsequent discussions.It is a very familiar fact that a point outside a (bounded) closed convex set in a Banach space can be separated from the latter by a hyperplane. One can ask whether the separation can be effected by disjoint balls. This is a typical example of a ball separation property, study of which has become important in Banach space theory. In this thesis, we study several such properties along with some …

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, …

A Probabilistic Approach To Some Of Euler's Number Theoretic Identities, Don Rawlings

Mathematics

Probabilistic proofs and interpretations are given for the q-binomial theorem, q-binomial series, two of Euler's fundamental partition identities, and for q-analogs of product expansions for the Riemann zeta and Euler phi functions. The underlying processes involve Bernoulli trials with variable probabilities. Also presented are several variations on the classical derangement problem inherent in the distributions considered.

Review Of Visual Complex Analysis, By Tristan Needham, Frank A. Farris

Mathematics and Computer Science

Tristan Needham's Visual Complex Analysis will show you the field of complex analysis in a way you almost certainly have not seen before. Drawing on historical sources and adding his own insights, Needham develops the subject from the ground up, drawing attractive pictures at every step of the way. If you have time for a year course, full of fascinating detours, this is the perfect text; by picking and choosing, you could use it for a variety of shorter courses. I am tempted to hide the book from my own students, in order to appear the more clever for popping …

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).

Perturbation Results For Projecting A Point Onto A Linear Manifold, Jiu Ding

Faculty Publications

Some new results will be presented on the perturbation analysis for the orthogonal projection of a point onto a linear manifold. The obtained perturbation upper bound is with respect to the distance from the perturbed solution to the unperturbed manifold.

A Molecular Mechanics Simulation Of Cracks And Fractures In A Sheet Of Ice, Donald Greenspan

Mathematics Technical Papers

Rectangular, two dimensional sheets of ice molecules are both stressed and compressed. Computer examples compare dynamical responses when the plate has a slot or does not have a slot. The mechanisms for both crack and fracture development are clearly delineated on the molecular level.

Invariants Of Twist-Wise Flow Equivalence, Michael C. Sullivan

Articles and Preprints

Flow equivalence of irreducible nontrivial square nonnegative integer matrices is completely determined by two computable invariants, the Parry-Sullivan number and the Bowen-Franks group. Twist-wise flow equivalence is a natural generalization that takes account of twisting in the local stable manifold of the orbits of a flow. Two new invariants in this category are established.

The Solution Of Hypersingular Integral Equations With Applications In Acoustics And Fracture Mechanics, Richard S. St. John

Mathematics & Statistics Theses & Dissertations

The numerical solution of two classes of hypersingular integral equations is addressed. Both classes are integral equations of the first kind, and are hypersingular due to a kernel containing a Hadamard singularity. The convergence of a Galerkin method and a collocation method is discussed and computationally efficient algorithms are developed for each class of hypersingular integral equation.

Interest in these classes of hypersingular integral equations is due to their occurrence in many physical applications. In particular, investigations into the scattering of acoustic waves by moving objects and the study of dynamic Griffith crack problems has necessitated a computationally efficient technique …

Superconvergence In Iterated Solutions Of Integral Equations, Peter A. Padilla

Mathematics & Statistics Theses & Dissertations

In this thesis, we investigate the superconvergence phenomenon of the iterated numerical solutions for the Fredholm integral equations of the second kind as well as a class of nonliner Hammerstein equations. The term superconvergence was first described in the early 70s in connection with the solution of two-point boundary value problems and other related partial differential equations. Superconvergence in this context was understood to mean that the order of convergence of the numerical solutions arising from the Galerkin as well as the collocation method is higher at the knots than we might expect from the numerical solutions that are obtained …

Coupled Electrodynamic-Monte Carlo Simulations Of Nanoscale Gaas Terahertz Optical Mixers, Jiang Li

Electrical & Computer Engineering Theses & Dissertations

The concept of mixing or heterodyning has traditionally been used for microwaves and for radio frequency communications. However, the concept can easily be extended into the optical frequency regime. By doing so, the photomixing process can serve as a very versatile tool for both the generation of ultrahigh frequency (terahertz) and the detection of weak optical signals.

The aim of this thesis is to perform a theoretical study of the photomixing process inside GaAs devices as the non-linear elements. A coupled approach which combines the Monte Carlo simulation scheme for the carrier transport, with Maxwell's equation for the electrodynamics, has …

New Semiregular Divisible Difference Sets, James A. Davis

Department of Math & Statistics Faculty Publications

We modify and generalize the construction by McFarland (1973) in two different ways to construct new semiregular divisible difference sets (DDSs) with λ₁≠0. The parameters of the DDS fall into a family of parameters found in Jungnickel (1982), where his construction is for divisible designs. The final section uses the idea of a K-matrix to find DDSs with a nonelementary abelian forbidden subgroup.

On The Developement Of An Optical Character Recognition(Ocr) System For Printed Bangla Script., Umapada Pal Dr.

Doctoral Theses

This thesis concerns OCR development of machine printed text in an Indian lan- guage, Bangla (Bengali) which is the fourthmost popular language in the world and the secondmost popular language in India.1.1 Optical Character Recognition Optical Character Recognition (OCR) is a process of automatic computer recog- nition of characters in optically scanned and digitized pages of text. OCR is ene of the most fascinating and challenging areas of pattern recognition with various practical applications. It can contribute tremendously to the advancement of an automation process and can improve the interface between man and machine in many applications, including office automation …

Representations, Approximations, And Algorithms For Mathematical Speech Processing, Laura R. Suzuki

Theses and Dissertations

Representing speech signals such that specific characteristics of speech are included is essential in many Air Force and DoD signal processing applications. A mathematical construct called a frame is presented which captures the important time-varying characteristic of speech. Roughly speaking, frames generalize the idea of an orthogonal basis in a Hilbert space, Specific spaces applicable to speech are L₂(R) and the Hardy spaces H_p(D) for p> 1 where D is the unit disk in the complex plane. Results are given for representations in the Hardy spaces involving Carleson's inequalities (and its extensions), …

On Some Finitely Based Representations Of Semigroups, Nikolay Silkin

Department of Mathematics: Faculty Publications

In this paper we present a method of obtaining finitely based linear representations of possibly infinitely based semigroups.

Computational Geometry Column 33, Joseph O'Rourke

Computer Science: Faculty Publications

Several recent SIGGRAPH papers on surface simplification are described.

Optimized Preparation Of Quantum States By Conditional Measurements, G. Harel, G. Kurizki, Evangelos A. Coutsias, J. K. Mciver

Branch Mathematics and Statistics Faculty and Staff Publications

We introduce a general strategy for preparation of arbitrary quantum states via optimal control of repeated conditional measurements. The effectiveness of this strategy in generating finite Fock-state superpositions with a high level of confidence from experimentally accessible coherent states is demonstrated for the simple and well known Jaynes-Cummings model dynamics.

Units In Integral Group Rings For Direct Products, Richard M. Low

Dissertations

Given a finite group G and the ring of integers, one can form the integral group ring ZG . A natural problem to investigate is to find a description of the group of units for this ring ZG. Since the unit problem for integral group rings arises in the contexts of algebraic topology, number theory, and algebra, it is an important question to try to answer. For this reason, it has drawn the attention of researchers from diverse areas of mathematics.

Graham Higman (circa 1940) made substantial contributions to the solution of this problem, in the case where G was …

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

Dissertations

No abstract provided.