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1998

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Articles 1 - 30 of 109

Full-Text Articles in Mathematics

On The Basic Representation Theorem For Convex Domination Of Measures, J. Elton, Theodore P. Hill Dec 1998

On The Basic Representation Theorem For Convex Domination Of Measures, J. Elton, Theodore P. Hill

Research Scholars in Residence

A direct, constructive proof is given for the basic representation theorem for convex domination of measures. The proof is given in the finitistic case (purely atomic measures with a finite number of atoms), and a simple argument is then given to extend this result to the general case, including both probability measures and finite Borel measures on infinite-dimensional spaces. The infinite-dimensional case follows quickly from the finite-dimensional case with the use of the approximation property.

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Fan-Type Conditions For Collapsible Graphs, Zhi-Hong Chen Dec 1998

Fan-Type Conditions For Collapsible Graphs, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

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Stability And Reconstruction For An Inverse Problem For The Heat Equation, Kurt Bryan, Lester Caudill Nov 1998

Stability And Reconstruction For An Inverse Problem For The Heat Equation, Kurt Bryan, Lester Caudill

Department of Math & Statistics Faculty Publications

We examine the inverse problem of determining the shape of some unknown portion of the boundary of a region Ω from measurements of the Cauchy data for solutions to the heat equation on Ω. 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.

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Interior Blowup In A Convection-Diffusion Equation, Christopher P. Grant Nov 1998

Interior Blowup In A Convection-Diffusion Equation, Christopher P. Grant

Faculty Publications

This paper addresses the qualitative behavior of a nonlinear convection-diffusion equation on a smooth bounded domain in Rn, in which the strength of the convection grows superlinearly as the density increases. While the initial-boundary value problem is guaranteed to have a local-in-time solution for smooth initial data, it is possible for this solution to be extinguished in nite time. We demonstrate that the way this may occur is through nite-time "blow up," i.e., the unboundedness of the solution in arbitrarily small neighborhoods of one or more points in the closure of the spatial domain. In special circumstances, such as the …

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A Continuum Analysis Of The Chemotactic Signal Seen By Dictyostelium Discoideum, J. C. Dallon, H. G. Othmer Oct 1998

A Continuum Analysis Of The Chemotactic Signal Seen By Dictyostelium Discoideum, J. C. Dallon, H. G. Othmer

Faculty Publications

We develop a mathematical model of cell-to-cell-signalling in Dictyostelium discoideum that predicts the cAMP signal seen by individual cells in early aggregation. The model employs two cells on a plane and is designed to predict the space-time characteristics of both the extracellular cAMP signal seen by one cell when a nearby cell relays, and the intracellular cAMP response produced by the stimulus in the receiving cell. The effect of membrane bound phosphodiesterase is studied and it is shown that cells can orient effectively even in its absence. Our results give a detailed picture of how the spatio-temporal characteristics of the …

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Finding Cyclic Redundancy Check Polynomials For Multilevel Systems, James A. Davis, Miranda Mowbray, Simon Crouch Oct 1998

Finding Cyclic Redundancy Check Polynomials For Multilevel Systems, James A. Davis, Miranda Mowbray, Simon Crouch

Department of Math & Statistics Faculty Publications

This letter describes a technique for finding cyclic redundancy check polynomials for systems for transmission over symmetric channels which encode information in multiple voltage levels, so that the resulting redundancy check gives good error protection and is efficient to implement. The codes which we construct have a Hamming distance of 3 or 4. We discuss a way to reduce burst error in parallel transmissions and some tricks for efficient implementation of the shift register for these polynomials. We illustrate our techniques by discussing a particular example where the number of levels is 9, but they are applicable in general.

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On The Dynamics Of Stochastic Differential Equations (Ellis B. Stouffer Colloquium, University Of Kansas), Salah-Eldin A. Mohammed Oct 1998

On The Dynamics Of Stochastic Differential Equations (Ellis B. Stouffer Colloquium, University Of Kansas), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

We formulate and outline a proof of the Local Stable Manifold Theorem for stochastic differential equations (SDE's) in Euclidean space (joint work with M. Scheutzow). This is a central result in dynamical systems with noise. Starting with the existence of a stochastic flow for an SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of a hyperbolic stationary solution. For Stratonovich noise, the stable and unstable manifolds are dynamically characterized using forward and backward solutions of the anticipating SDE.

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Rank One And Loosely Bernoulli Actions In Zᵈ, Aimee S.A. Johnson, A. A. Şahin Oct 1998

Rank One And Loosely Bernoulli Actions In Zᵈ, Aimee S.A. Johnson, A. A. Şahin

Mathematics & Statistics Faculty Works

We define rank one for Zᵈ actions and show that those rank one actions with a certain tower shape are loosely Bernoulli for d greater than or equal to 1. We also construct a zero entropy Z² loosely Bernoulli action with a zero entropy, ergodic, non-loosely Bernoulli one-dimensional subaction.

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Cohomology Of Polynomials Under An Irrational Rotation, Lawrence W. Baggett, Herbert A. Medina, Kathy D. Merrill Oct 1998

Cohomology Of Polynomials Under An Irrational Rotation, Lawrence W. Baggett, Herbert A. Medina, Kathy D. Merrill

Mathematics Faculty Works

A new description of cohomology of functions under an irrational rotation is given in terms of symmetry properties of the functions on subintervals of [0, 1]. This description yields a method for passing information about the cohomology classes for a given irrational to the cohomology classes for an equivalent irrational.

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Complexity Reduction In State-Based Modeling, Martin Zwick Oct 1998

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 …

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Weyl-Type Fields With Geodesic Lines Of Force, Brendan Guilfoyle Sep 1998

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.

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The A-Hypergeometric System Associated With A Monomial Curve, Eduardo Cattani, Carlos D’Andrea, Alicia Dickenstein Sep 1998

The A-Hypergeometric System Associated With A Monomial Curve, Eduardo Cattani, Carlos D’Andrea, Alicia Dickenstein

Mathematics and Statistics Department Faculty Publication Series

No abstract provided.

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Symmetry And Tiling Groups For Genus 4 And 5, C. Ryan Vinroot Sep 1998

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.

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Attractors For Non-Compact Semigroups Via Energy Equations, Ioana Moise, Ricardo Rosa, Xiaoming Wang Sep 1998

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.

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A Structural Result Of Irreducible Inclusions Of Type Iii Lambda Factors, Lambda Is An Element Of (0,1), Phan Loi Sep 1998

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 IIIλ1/m, N of type IIIλ1/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.

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The Sharp Sobolev Inequality And The Banchoff-Pohl Inequality On Surfaces, Ralph Howard Sep 1998

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

Faculty Publications

No abstract provided.

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Quadrilaterals Subdivided By Triangles In The Hyperbolic Plane, Dawn M. Haney, Lori T. Mckeough Aug 1998

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.

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On The Dynamics Of Stochastic Differential Systems (The Seventh Vilnius Conference On Probability Theory And Mathematical Statistics), Salah-Eldin A. Mohammed Aug 1998

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.

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Octary Codewords With Power Envelopes Of 3∗2M, Katherine M. Nieswand, Kara N. Wagner Jul 1998

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 2m in Z8 with envelope power maxima of 3 ∗ 2m. 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 ∗ 2m for each m-even and m-odd case.

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Maximally Disjoint Solutions Of The Set Covering Problem, David J. Rader, Peter L. Hammer Jul 1998

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, …

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A Probabilistic Approach To Some Of Euler's Number Theoretic Identities, Don Rawlings Jul 1998

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.

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Invariants Of Twist-Wise Flow Equivalence, Michael C. Sullivan Jul 1998

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.

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Perturbation Results For Projecting A Point Onto A Linear Manifold, Jiu Ding Jul 1998

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.

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Review Of Visual Complex Analysis, By Tristan Needham, Frank A. Farris Jul 1998

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 …

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Evolution Of Mixed-State Regions In Type-Ii Superconductors, Chaocheng Huang, Tom Svobodny Jul 1998

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 C1+α(Ω0) for all t > Ω, where Ω0 is the initial vortex region that is assumed to be in C1+α. Consequently, for any time t, the vortex region Ωt is of C1+α, and the vorticity is in Cα(Ωt).

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New Semiregular Divisible Difference Sets, James A. Davis Jun 1998

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.

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A Basis Theorem For Perfect Sets, Marcia J. Groszek, Theodore A. Slaman Jun 1998

A Basis Theorem For Perfect Sets, Marcia J. Groszek, Theodore A. Slaman

Dartmouth Scholarship

We show that if there is a nonconstructible real, then every perfect set has a nonconstructible element, answering a question of K. Prikry. This is a specific instance of a more general theorem giving a sufficient condition on a pair M ⊂ N of models of set theory implying that every perfect set in N has an element in N which is not in M.

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On Some Finitely Based Representations Of Semigroups, Nikolay Silkin Jun 1998

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.

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Computational Geometry Column 33, Joseph O'Rourke Jun 1998

Computational Geometry Column 33, Joseph O'Rourke

Computer Science: Faculty Publications

Several recent SIGGRAPH papers on surface simplification are described.

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Optimized Preparation Of Quantum States By Conditional Measurements, G. Harel, G. Kurizki, Evangelos A. Coutsias, J. K. Mciver Jun 1998

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.

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