Applied Mathematics Commons^™

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 …

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.

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.

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.

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn

Mathematics Faculty Publications

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring Axiom.

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 …

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.

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 .

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.

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.

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.