Physical Sciences and Mathematics Commons^™

An Oscillation Theorem For Discrete Eigenvalue Problems, Martin Bohner, Ondřej Došlý, Werner Kratz

Mathematics and Statistics Faculty Research & Creative Works

In this paper we consider problems that consist of symplectic difference systems depending on an eigenvalue parameter, together with self-adjoint boundary conditions. Such symplectic difference systems contain as important cases linear Hamiltonian difference systems and also Sturm-Liouville difference equations of second and of higher order. The main result of this paper is an oscillation theorem that relates the number of eigenvalues to the number of generalized zeros of solutions.

The Connective K-Theory Of Finite Groups, Robert R. Bruner, John Greenlees

Mathematics Faculty Research Publications

This paper is devoted to the connective K homology and cohomology of finite groups G. We attempt to give a systematic account from several points of view. In Chapter 1, following Quillen [50, 51], we use the methods of algebraic geometry to study the ring ku^*(BG) where ku denotes connective complex K-theory. We describe the variety in terms of the category of abelian p-subgroups of G for primes p dividing the group order. As may be expected, the variety is obtained by splicing that of periodic complex K-theory and that of integral ordinary homology, however the way these parts fit …

Optimal Control Of Neutral Functional-Differential Inclusions, Boris S. Mordukhovich, Lianwen Wang

Mathematics Research Reports

This paper deals with optimal control problems for dynamical systems governed by constrained functional-differential inclusions of neutral type. Such control systems contain time-delays not only in state variables but also in velocity variables, which make them essentially more complicated than delay-differential (or differential-difference) inclusions. Our main goal is to derive necessary optimality conditions for general optimal control problems governed by neutral functional-differential inclusions with endpoint constraints. While some results are available for smooth control systems governed by neutral functional-differential equations, we are not familiar with any results for neutral functional-differential inclusions, even with smooth cost functionals in the absence of …

Nonlinear Equations And Wavelets, Andrei Ludu

Andrei Ludu

No abstract provided.

Radial Basis Function Interpolation: Numerical And Analytical Developments, Grady Wright

Grady Wright

The Radial Basis Function (RBF) method is one of the primary tools for interpolating multidimensional scattered data. The methods' ability to handle arbitrarily scattered data, to easily generalize to several space dimensions, and to provide spectral accuracy have made it particularly popular in several different types of applications. Some of the more recent of these applications include cartography, neural networks, medical imaging, and the numerical solution of partial differential equations (PDEs). In this thesis we study three issues with the RBF method that have received very little attention in the literature.

First, we focus on the behavior of RBF interpolants …

Relations Between $\Lambda{\Rm Bv}$ And ${\Rm Bv}(P(N)\Uparrow\Infty)$ Classes Of Functions, Ushangi Goginava

Ushangi Goginava

No abstract provided.

On The Uniform Convergence And $L$-Convergence Of Double Fourier Series With Respect To The Walsh-Kaczmarz System, Ushangi Goginava

Ushangi Goginava

No abstract provided.

Evaluation Of Dedekind Sums, Eisenstein Cocycles, And Special Values Of L-Functions, Pe Gunnells, R Sczech

Paul Gunnells

We define higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums as well as Zagier's sums, and we show how to compute them effectively using a generalization of the continued-fraction algorithm. We present two applications. First, we show how to express special values of partial zeta functions associated to totally real number fields in terms of these sums via the Eisenstein cocycle introduced by R. Sczech. Hence we obtain a polynomial time algorithm for computing these special values. Second, we show how to use our techniques to compute certain special values of the Witten zeta function, and we compute some …

Sensorimotor Coordination And The Structure Of Space, Gin Mccollum

Gin McCollum

Embedded in neural and behavioral organization is a structure of sensorimotor space. Both this embedded spatial structure and the structure of physical space inform sensorimotor control. This paper reviews studies in which the gravitational vertical and horizontal are crucial. The mathematical expressions of spatial geometry in these studies indicate methods for investigating sensorimotor control in freefall.

In freefall, the spatial structure introduced by gravitation – the distinction between vertical and horizontal – does not exist. However, an astronaut arriving in space carries the physiologically-embedded distinction between horizontal and vertical learned on earth. The physiological organization based on this distinction collapses …

Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang

Yi Li

We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.

Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao

Yi Li

No abstract provided.

On The Location Of Critical Points Of Polynomials, Branko Ćurgus, Vania Mascioni

Mathematics Faculty Publications

Given a polynomial p of degree n ≥ 2 and with at least two distinct roots let Z(p) = { z: p(z) = 0}. For a fixed root α ∈ Z(p) we define the quantities ω(p, α) := min (formula) and (formula). We also define ω (p) and τ (p) to be the corresponding minima of ω (p,α) and τ (p,α) as α runs over Z(p). Our main results show that the ratios τ (p,α)/ω (p,α) and τ (p)/ω (p) are bounded above and below by constants that only depend on the degree of p. In particular, …

Continuous Embeddings, Completions And Complementation In Krein Spaces, Branko Ćurgus, H. Langer

Mathematics Faculty Publications

Let the Krein space (A,[^. , ^. ]_A) be continuously embedded in the Krein space (K,[^.,^.]_K )_^. A unique self-adjoint operator A in K can be associated with(A,[^. , ^. ]_A) via the adjoint of the inclusion mapping of A in K. Then (A,[^. , ^. ]_A) is a Krein space completion of R(A) equipped with an A-inner product. In general this completion is not unique. If, additionally, the embedding of A …

Birkhoff-Kellogg Theorems On Invariant Directions For Multimaps, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

We establish Birkhoff-Kellogg type theorems on invariant directions for a general class of maps. Our results, in particular, apply to Kakutani, acyclic, O'Neill, approximable, admissible, and script U signCK maps.

Common Fixed Point Theorems For A Pair Of Countably Condensing Mappings In Ordered Banach Spaces, Bapurao C. Dhage, Donal O'Regan, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

In this paper some common fixed point theorems for a pair of multivalued weakly isotone mappings on an ordered Banach space are proved.

A Non-Markovian Queueing System With A Variable Number Of Channels, Hong-Tam T. Rosson, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

In this paper we study a queueing model of type GI/M/m̃a/∞ with m parallel channels, sonic of which may suspend their service at specified random moments of time. Whether or not this phenomenon occurs depends on the queue length. The queueing process, which we target, turns out to be semi-regenerative, and we fully explore this utilizing semi-regenerative techniques. This is contrary to the more traditional supplementary variable approach and the less popular approach of combination semi-regenerative and supplementary variable technique. We pass to the limiting distribution of the continuous time parameter process through the embedded Markov chain for which we …

Mimeomatroids, Vadim Ponomarenko

Mathematics Faculty Research

A mimeomatroid is a matroid union of a matroid with itself. We develop several properties of mimeomatroids, including a generalization of Rado's theorem, and prove a weakened version of a matroid conjecture by Rota[2].

Direct Paths Of Wavelets, Eugen J. Ionascu

Faculty Bibliography

We associate a von Neumann algebra with each pair of complete wandering vectors for a unitary system. When this algebra is nonatomic, there is a norm–continuous path of a simple nature connecting the original pair of wandering vectors. We apply this technique to wavelet theory and compute the above von Neumann algebra in some special cases. Results from selection theory and ergodic theory lead to nontrivial examples where both atomic and nonatomic von Neumann algebras occur.

A Continuation Of The Discussion On Cross Symmetry Of Solutions, Paul W. Eloe, Qin Sheng

Mathematics Faculty Publications

In this paper we continue to explore cross-symmetry properties of the solutions of second-order nonlinear boundary value problems on time scales. Dynamic equations under delta and nabla differentiations are considered. It is proven that, by introducing a proper companion problem, the solution of a dynamic equation is cross-symmetric to the solution of the companion problem. Proper jump functions on time scales are utilized. Computational examples are given to further illustrate our conclusions.

A First Course In Computer Science: Languages And Goals, Dennis C. Smolarski

Mathematics and Computer Science

The College Board Advanced Placement exam in computer science will use the language Java starting in fall 2003. The language chosen for this exam is based on the language commonly taught in introductory computer science courses at the university level. This article reviews the purpose of an introductory course and the various suggestions for the curriculum of introductory courses published by the Association for Computing Machinery. It then proposes that such a course stress foundational concepts over specific language syntax, and then provides a list of such foundational concepts and related topics. Based on this fundamental curriculum, the article recommends …

Septic Fields With Discriminant ±2A3B, John W. Jones, David P. Roberts

Mathematics Publications

We classify septic number fields which are unramified outside of {∞,2,3} by a targeted Hunter search; there are exactly 10 such fields, all with Galois group S₇. We also describe separate computations which strongly suggest that none of these fields come from specializing septic genus zero three-point covers.

Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang

Mathematics and Statistics Faculty Publications

We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.

Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao

Mathematics and Statistics Faculty Publications

No abstract provided.

An Algebraic Characterization Of Projective-Planar Graphs, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G∗ on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homology groups.

Multiple Positive Solutions For A Class Of Quasilinear Elliptic Boundary-Value Problems, Kanishka Perera

Mathematics and System Engineering Faculty Publications

Using variational arguments we prove some nonexistence and multiplicity results for positive solutions of a class of elliptic boundary-value problems involving the p-Laplacian and a parameter.

Existence Theory For Single And Multiple Solutions To Semipositone Discrete Dirichlet Boundary Value Problems With Singular Dependent Nonlinearities, Daqing Jiang, Lili Zhang, Donal O'Regan, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

In this paper we establish the existence of single and multiple solutions to the semipositone discrete Dirichlet boundary value problem {Δ²y(i - 1) + μf(i, y(i)) = 0, i ∈ {1, 2, ..., T} y(0) = y(T + 1) = 0, where μ > 0 is a constant and our nonlinear term f(i, u) may be singular at u = 0.

Necessary And Sufficient Condition That The Limit Of Stieltjes Transforms Is A Stieltjes Transform, Jeffrey S. Geronimo, Theodore P. Hill

Research Scholars in Residence

The pointwise limit S of a sequence of Stieltjes transforms (S_n) of real Borel probability measures (P_n) is itself the Stieltjes transform of a Borel p.m. P if and only if iy S(iy) →−1as y →∞, in which case P_n converges to P in distribution. Applications are given to several problems in mathematical physics.

A Characterization Of Primitive Polynomials Over Finite Fields, Robert W. Fitzgerald

Articles and Preprints

No abstract provided.

Vertex-Magic Labeling Of Trees And Forests, I. D. Gray, J. Macdougall, John P. Mcsorley, Walter D. Wallis

Articles and Preprints

A vertex-magic total labeling of a graph G(V,E) is a one-to-one map λ from E ∪ V onto the integers {1, 2, . . . , |E| + |V|} such that

λ(x) + Σ λ(xy) where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite different from the conjectured behavior of edge-magic total labelings …

The Euler Line In Non-Euclidean Geometry, Elena Strzheletska

Theses Digitization Project

The main purpose of this thesis is to explore the conditions of the existence and properties of the Euler line of a triangle in the hyperbolic plane. Poincaré's conformal disk model and Hermitian matrices were used in the analysis.ʹ