Physical Sciences and Mathematics Commons^™

Pre-1994 Journal Articles, David Bressoud

David Bressoud

No abstract provided.

First Excess Levels Of Vector Processes, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

This paper analyzes the behavior of a point process marked by a two-dimensional renewal process with dependent components about some fixed (two-dimensional) level. The compound process evolves until one of its marks hits (i.e. reaches or exceeds) its associated level for the first time. The author targets a joint transformation of the first excess level, first passage time, and the index of the point process which labels the first passage time. The cases when both marks are either discrete or continuous or mixed are treated. For each of them, an explicit and compact formula is derived. Various applications to stochastic …

Random Fixed Point Theorems For Nonexpansive And Contractive-Type Random Operators On Banach Spaces, Ismat Beg, Naseer Shahzad

Mathematics and System Engineering Faculty Publications

The existence of random fixed points for nonexpansive and pseudocontractive random multivalued operators defined on unbounded subsets of a Banach space is proved. A random coincidence point theorem for a pair of compatible random multivalued operators is established.

The Complexity Of Local Stratification, Peter Cholak, Howard A. Blair

College of Engineering and Computer Science - Former Departments, Centers, Institutes and Projects

The class of locally stratified logic programs is shown to be Π 1 1-complete by the construction of a reducibility of the class of infinitely branching nondeterministic finite register machines.

Some Conjectures Concerning Triangular Numbers, Bruce Brandt

Journal of the Minnesota Academy of Science

Strong empirical evidence supports conjectures that certain number patterns always hold. These patterns concern the function cr, defined by the equation cr(n) = n - m2, m2 being the nearest square to n, on the domain of the triangular numbers. Triangular squares or triangular numbers of the form m2+m are also mentioned in most of the conjectures. One of the conjectures, for example, is that the sum of cr over the triangular numbers up to a triangular square is 0. Some of these patterns can be described by strings of symbols, such as "S" and "L," formed by first writing …

Supplement To "Some Conjectures Concerning Triangular Numbers", Bruce Brandt

Journal of the Minnesota Academy of Science

In a previous paper (1), I stated many conjectures about triangular numbers. Since submitting that paper I have discovered many more results, including generalizations, which are presented here.

Counting Order Classes Of Triple Products In Finite Groups, Scott Annin, Jennifer Ziebarth

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group and let W_G denote the proportion of triples, (.x:, y , z) , i n G3 for which x yz , x zy, y x z, zx y , yzx , and z y x have the same order. The following results are established.

i) G is abelian if, and only if, W_G = 1.

ii) W_G can be arbitrarily close to 1.

iii) Additional estimates on W_G

Nothing In Moderation, Everything In Excess: A New Weighted Statistic On Permutations, Ann Marie Paulukonis

Honors Theses, 1963-2015

The major index is a well-known statistic on permutations which is computed by summing the positions of descents in a permutation. Instead of considering descents, this paper investigates what happens when excedances are weighted by position in a permutation. Several theorems are presented concerning various symmetries of the resulting distribution.

On The Noninterpolation Of Polyhedral Maps, Adrian Riskin, D.W. Barnette

Mathematics

In this paper we show that if attention is restricted to polyhedral embeddings of graphs, no theorem analogous to the Duke interpolation theorem for 2-cell embeddings is true. We also give two interesting classes of graphs: (i) a class in which the members have polyhedral embeddings in the torus and also in orientable manifolds of arbitrarily high genus, (ii) and another in which the members have polyhedral embeddings in the projective plane and also in orientable and nonorientable manifolds of arbitrarily low Euler characteristic.

Fault-Tolerant Circuit-Switching Networks, Nicholas Pippenger, Geng Lin

All HMC Faculty Publications and Research

The authors consider fault-tolerant circuit-switching networks under a random switch failure model. Three circuit-switching networks of theoretical importance—nonblocking networks, rearrangeable networks, and superconcentrators—are studied. The authors prove lower bounds for the size (the number of switches) and depth (the largest number of switches on a communication path) of such fault-tolerant networks and explicitly construct such networks with optimal size Θ( n (log n)² ) and depth Θ( log n ).

Review: J.M. Aarts And T. Nishiura, Dimension And Extensions (Amsterdam, London, New York, And Tokyo, 1993), Melvin Henriksen

All HMC Faculty Publications and Research

Reviewed work: J. M. Aarts and T. Nishiura. Dimension and extensions. North-Holland Math. Library, Amsterdam, London, New York, and Tokyo, 1993, xii + 331 pp., $106.50. ISBN 0444897402.

Finite Amplitude Convection Between Stress-Free Boundaries; Ginzburg-Landau Equations And Modulation Theory, Andrew J. Bernoff

All HMC Faculty Publications and Research

The stability theory for rolls in stress-free convection at finite Prandtl number is affected by coupling with low wavenumber two-dimensional mean-flow modes. In this work, a set of modified Ginzburg-Landau equations describing the onset of convection is derived which accounts for these additional modes. These equations can be used to extend the modulation equations of Zippelius & Siggia describing the breakup of rolls, bringing their stability theory into agreement with the results of Busse & Bolton.

Advection Of A Passive Scalar By A Vortex Couple In The Small-Diffusion Limit, Joseph F. Lingevitch, Andrew J. Bernoff

All HMC Faculty Publications and Research

We study the advection of a passive scalar by a vortex couple in the small-diffusion (i.e. large Péclet number, Pe) limit. The presence of weak diffusion enhances mixing within the couple and allows the gradual escape of the scalar from the couple into the surrounding flow. An averaging technique is applied to obtain an averaged diffusion equation for the concentration inside the dipole which agrees with earlier results of Rhines & Young for large times. At the outer edge of the dipole, a diffusive boundary layer of width O(Pe^−½) forms; asymptotic matching to the interior …

A Qualitative Study Of Planar Elastic Deformations, Stephen Thomas Wentworth

Theses Digitization Project

No abstract provided.

Linear Codes And Error-Correction, Karen Brown

Presidential Scholars Theses (1990 – 2006)

The process of encoding information for transmission from one source to another is a vital process in many areas of science and technology. Whenever coded information is sent, there arises a certain possibility that an error will occur, either during transmission or in decoding. Therefore, it is imperative to develop methods to detect and correct errors in a code. The study of coding theory is a "new" area of mathematics which is relatively undeveloped.

This paper focuses on the properties of linear codes -and their corresponding methods of error-correction. To simplify the issue, only binary block codes are studied; hence …

Fixed Point Theorems For Non-Self Maps I, Troy L. Hicks, Unda Marie Sauga

Mathematics and Statistics Faculty Research & Creative Works

Suppose f:C→X where C is a closed subset of X. Necessary and sufficient conditions are given for f to have a fixed point. All results hold when X is complete metric space. Several results hold in a much more general setting. © 1994, Hindawi Publishing Corporation. All rights reserved.

Asymptotic Behavior Of Solutions Of Model Problems For A Coupled System, S. Shao

Mathematics and Statistics Faculty Publications

We study the asymptotic behavior of solutions of model problems for a coupled system. By consistent use of a priori estimates and asymptotic analysis, we present here an more efficient approach which provides precise descriptions of the asymptotic behabior of solutions of this system. Our results amplify and extend earlier results of Dorr, Patter, and Shampine and their treatment of this system. Meanwhile, the stability of the steady-state solutions of the corresponding time-dependent system is discussed.

Periodic Orbits For Hamiltonian Systems In Cotangent Bundles, Christophe Golé

Mathematics Sciences: Faculty Publications

We prove the existence of at least cl(Af) periodic orbits for certain time-dependent Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold M. These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on M. We discretize the variational problem by decomposing the time-1 map into a product of "symplectic twist maps". A second theorem deals with homotopically non-trivial orbits of negative curvature.

Irreducible Polynomials Over A Finite Field Zp, Brian Holbrook

Honors Theses, 1963-2015

The topic of my thesis was counting irreducible polynomials. I began with some preliminary material including relevant theorems discovered in various math textbooks and data generated by a computer program that I wrote. I then used this data to calculate formulas for the number of polynomials which had zeroes in a field Zp of sufficiently low degree. Next, I explained why it would not be practical to use the formulas for lower degrees to synthesize formulas for high degrees. However, I was able to generate a new formula using a different counting technique: the inclusion-exclusion principle. Finally, I discussed the …

Triangles, Triangles And, Yes, More Triangles: Explorations In Euclidean Ramsey Theory, Kathleen Wilson

Honors Theses, 1963-2015

Several important general theorems of Euclidean Ramsey Theory are presented with an emphasis on trying to prove or disprove the 1973 conjecture of Erdös et al. that for all triangles, except for equilateral triangles, it is possible to find a monochromatic coloring of the vertices in any two colorings of the plane. Further investigation included looking at triangles in greater dimensions.

A Mathematical Analysis Of A Small Corporation: This Stuff Really Works?, Wade Olson

Honors Theses, 1963-2015

This thesis is a mathematical analysis of Foam Enterprises, a small corporation in the Twin Cities. Through interaction with the,. I heard of several problems occurring at that time which were being dealt with in a mathematical fashion. The first involves the profitability of two main clients of Foam Enterprises. The second deals with the production capacity of the two current plants and the distribution of products to customers. Each problem was then described in detail. The general mathematical approaches were stated for each problem and important circumstances which could affect the procedure were given. In turn, the results of …

Operator Equations And Invariant Subspaces, Valentin Matache

Mathematics Faculty Publications

Banach space operators acting on some fixed space X are considered. If two such operators A and B verify the condition A² = B² and if A has non-trivial hyperinvariant subspaces, then B has nontrivial invariant subspaces. If A and B commute and satisfy a special type of functional equation, and if A is not a scalar multiple of the identity, the author proves that if A has nontrivial invariant subspaces, then so does B.

Density Of The Numerators Or Denominators Of A Continued Fraction, Seyed J. Vafabakhsh

UNF Graduate Theses and Dissertations

Let A = {a_n}^∞_{n = 1} be a sequence of positive integers. There are two related sequences P_n and Q_n obtained from A by taking partial convergents out of the number [0; a₁, a₂, ..., a_n, ...], where P_n and Q_n are the numerators and denominators of the finite continued fraction [0; a₁, a₂, ...,a_n].

Let P(n) be the largest positive integer k , such that P_k ≤ n. The sequence Q(n …

A Study Of The Two Major Causes Of Neonatal Deaths: Perinatal Conditions And Congenital Anomalies, Felipe Lorenzo-Luaces

UNF Graduate Theses and Dissertations

Infant mortality is a public health concern in the United states. We concentrate on neonatal mortality for its high accountability of infant mortality. In this paper we study the neonatal mortality of Florida's 1989 live birth cohort.

The data has been analyzed for two major causes of deaths: perinatal conditions and congenital anomalies. We use the KAPLAN-MEIER method to estimate the survival probabilities. For each cause, data were fit to the Weibull models and Extreme Value models to estimate the parameters of the survival curves. The results indicate that primary factors for each cause of neonatal deaths are very low …

Statistical Analysis Of Survival Data, Rexanne Marie Bruno

UNF Graduate Theses and Dissertations

The terminology and ideas involved in the statistical analysis of survival data are explained including the survival function, the probability density function, the hazard function, censored observations, parametric and nonparametric estimations of these functions, the product limit estimation of the survival function, and the proportional hazards estimation of the hazard function with explanatory variables.

In Appendix A these ideas are applied to the actual analysis of the survival data for 54 cervical cancer patients.

A Relationship Between The Fibonacci Sequence And Cantor's Ternary Set, John David Samons

UNF Graduate Theses and Dissertations

The Fibonacci sequence and Cantor's ternary set are two objects of study in mathematics. There is much theory published about these two objects, individually. This paper provides a fascinating relationship between the Fibonacci sequence and Cantor's ternary set. It is a fact that every natural number can be expressed as the sum of distinct Fibonacci numbers. This expression is unique if and only if no two consecutive Fibonacci numbers are used in the expression--this is known as Zekendorf's representation of natural numbers. By Zekendorf's representation, a function F from the natural numbers into [0,0.603] will be defined which has the …

Hankel Transforms In Generalized Fock Spaces, John Schmeelk

Mathematics and Applied Mathematics Publications

A classical Fock space consists of functions of the form,ϕ↔(ϕ0,ϕ1,…,ϕq),where ϕ0∈ℂ and ϕq∈Lp(ℝq), q≥1. We will replace the ϕq, q≥1 with test functions having Hankel transforms. This space is a natural generalization of a classical Fock space as seen by expanding functionals having abstract Taylor Series. The particular coefficients of such series are multilinear functionals having distributions as their domain. Convergence requirements set forth are somewhat in the spirit of ultra differentiable functions and ultra distribution theory. The Hankel transform oftentimes implemented in Cauchy problems will be introduced into this setting. A theorem will be proven relating the convergence of …

Multiage Classrooms: A New Way To Learn Math, Martha Taylor Dever, Randy Zila, Noel N. Mansano

Teacher Education and Leadership Faculty Publications

No abstract provided.

Boundary And Interior Layer Behavior In A Time-Dependent Singularly Perturbed System, S. Shao

Mathematics and Statistics Faculty Publications

No abstract provided.

An Invariant Subspace Problem For P = 1 Bergman Spaces On Slit Domains, William T. Ross

Department of Math & Statistics Faculty Publications

In this paper, we characterize the z-invariant subspaces that lie between the Bergman spaces A¹(G) and A¹(G/K), where G is a bounded region in the complex plane and K is a compact subset of a simple arc of class C¹.