Physical Sciences and Mathematics Commons^™

Fixed Point Theory For Mönch-Type Maps Defined On Closed Subsets Of Fréchet Spaces: The Projective Limit Approach, Ravi P. Agarwal, Donal O'Regan, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

New Leray-Schauder alternatives are presented for Mönch-type maps defined between Fréchet spaces. The proof relies on viewing a Fréchet space as the projective limit of a sequence of Banach spaces.

Multiple Positive Solutions Of Singular Discrete P-Laplacian Problems Via Variational Methods, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

We obtain multiple positive solutions of singular discrete p-Laplacian problems using variational methods.

Comparing Distribution Functions Via Empirical Likelihood, Yichuan Zhao, Ian W. Mckeague

Mathematics and Statistics Faculty Publications

This paper develops empirical likelihood based simultaneous confidence bands for differences and ratios of two distribution functions from independent samples of right-censored survival data. The proposed confidence bands provide a flexible way of comparing treatments in biomedical settings, and bring empirical likelihood methods to bear on important target functions for which only Wald-type confidence bands have been available in the literature. The approach is illustrated with a real data example.

One-Dimensional Dynamical Systems And Benford's Law, Arno Berger, Leonid A. Bunimovich, Theodore P. Hill

Research Scholars in Residence

Near a stable fixed point at 0 or ∞, many real-valued dynamical systems follow Benford's law: under iteration of a map T the proportion of values in {x, T(x), T²(x), ... , Tⁿ(x)} with mantissa (base b) less than t tends to log_bt for all t in [1,b) as n→ ∞, for all integer bases b>1. In particular, the orbits under most power, exponential, and rational functions (or any successive combination thereof), follow Benford's law for almost all sufficiently large initial values. For linearly-dominated systems, convergence to Benford's distribution …

Voice Authenticationa Study Of Polynomial Representation Of Speech Signals, John Strange

Electronic Theses and Dissertations

A subset of speech recognition is the use of speech recognition techniques for voice authentication. Voice authentication is an alternative security application to the other biometric security measures such as the use of fingerprints or iris scans. Voice authentication has advantages over the other biometric measures in that it can be utilized remotely, via a device like a telephone. However, voice authentication has disadvantages in that the authentication system typically requires a large memory and processing time than do fingerprint or iris scanning systems. Also, voice authentication research has yet to provide an authentication system as reliable as the other …

Factors Of Dickson Polynomials Over Finite Fields, Robert W. Fitzgerald, Joseph L. Yucas

Articles and Preprints

We give new descriptions of the factors of Dickson polynomials over finite fields.

Highly Degenerate Quadratic Forms Over Finite Fields Of Characteristic 2, Robert W. Fitzgerald

Articles and Preprints

Let K/F be an extension of finite fields of characteristic two. We consider quadratic forms written as the trace of xR(x), where R(x) is a linearized polynomial. We show all quadratic forms can be so written, in an essentially unique way. We classify those R, with coefficients 0 or 1, where the form has a codimension 2 radical. This is applied to maximal Artin-Schreier curves and factorizations of linearized polynomials.

Sums Of Gauss Sums And Weights Of Irreducible Codes, Robert W. Fitzgerald, Joseph L. Yucas

Articles and Preprints

We develop a matrix approach to compute a certain sum of Gauss sums which arises in the study of weights of irreducible codes. A lower bound on the minimum weight of certain irreducible codes is given.

Symbolic Dynamics And Its Applications, Michael C. Sullivan

Articles and Preprints

Book review of Symbolic Dynamics and its Applications, edited by Susan Williams, AMS.

Equivariant Flow Equivalence Of Shifts Of Finite Type By Matrix Equivalence Over Group Rings, Mike Boyle, Michael C. Sullivan

Articles and Preprints

Let G be a finite group. We classify G-equivariant flow equivalence of non-trivial irreducible shifts of finite type in terms of

(i) elementary equivalence of matrices over ZG and

(ii) the conjugacy class in ZG of the group of G-weights of cycles based at a fixed vertex.

In the case G = Z/2, we have the classification for twistwise flow equivalence. We include some algebraic results and examples related to the determination of E(ZG) equivalence, which involves K₁(ZG).

Twistwise Flow Equivalence And Beyond..., Michael C. Sullivan

Articles and Preprints

An expository account of recent progress on twistwise flow equivalence. There is a new result in the appendix. (Appendix joint with Mike Boyle.)

Knots On A Positive Template Have A Bounded Number Of Prime Factors., Michael C. Sullivan

Articles and Preprints

Templates are branched 2-manifolds with semi-flows used to model "chaotic" hyperbolic invariant sets of flows on 3-manifolds. Knotted orbits on a template correspond to those in the original flow. Birman and Williams conjectured that for any given template the number of prime factors of the knots realized would be bounded. We prove a special case when the template is positive; the general case is now known to be false.

Real Numbers With Polynomial Continued Fraction Expansions, James Mclaughlin, Nancy Wyshinski

Mathematics Faculty Publications

In this paper we show how to apply various techniques and theorems (including Pincherle’s theorem, an extension of Euler’s formula equating infinite series and continued fractions, an extension of the corresponding transformation that equates infinite products and continued fractions, extensions and contractions of continued fractions and the Bauer-Muir transformation) to derive infinite families of in-equivalent polynomial continued fractions in which each continued fraction has the same limit. This allows us, for example, to construct infinite families of polynomial continued fractions for famous constants like π and e, ζ(k) (for each positive integer k ≥ 2), various special functions evaluated at …

Domination Graphs Of Tournaments And Other Digraphs, Deborah J. Bergstrand, L. M. Friedler

Mathematics & Statistics Faculty Works

No abstract provided.

Existence, Uniqueness And Constructive Results For Delay Differential Equations, Paul W. Eloe, Youssef N. Raffoul, Christopher C. Tisdell

Mathematics Faculty Publications

Here, we investigate boundary-value problems (BVPs) for systems of second-order, ordinary, delay-differential equations. We introduce some differential inequalities such that all solutions (and their derivatives) to a certain family of BVPs satisfy some a priori bounds. The results are then applied, in conjunction with topological arguments, to prove the existence of solutions. We then apply earlier abstract theory of Petryshyn to formulate some constructive results under which solutions to BVPs for systems of second-order, ordinary, delay-differential equations are A-solvable and may be approximated via a Galerkin method. Finally, we provide some differential inequalities such that solutions to our equations are …

Convergent Sequences Of Composition Operators, Valentin Matache

Mathematics Faculty Publications

Composition operators Cφ on the Hilbert Hardy space H² over the unit disk are considered.

Powers Of A Matrix And Combinatorial Identities, James Mclaughlin, B. Sury

Mathematics Faculty Publications

In this article we obtain a general polynomial identity in k variables, where k ≥ 2 is an arbitrary positive integer. We use this identity to give a closed-form expression for the entries of the powers of a k × k matrix. Finally, we use these results to derive various combinatorial identities.

The Relative Growth On Information In Two-Dimensional Partitions, K. Dajani, M. De Vries, Aimee S.A. Johnson

Mathematics & Statistics Faculty Works

Let ... ∈ [0, 1)^sup 2^. In this paper we find the rate at which knowledge about the partition elements ... lies in for one sequence of partitions determines the partition elements it lies in for another sequence of partitions. This rate depends on the entropy of these partitions and the geometry of their shapes, and gives a two-dimensional version of Lochs' theorem.

A Property Of Weak Convergence Of Positive Contractions Of Von Neumann Algebras, Farrukh Mukhamedov, Seyi̇t Temi̇r

Turkish Journal of Mathematics

In the present paper we prove that the mixing property of positive L^1-contraction of finite von Neumann algebras implies the property of complete mixing.

Julian Cecil Stanley Papers, Zach S. Henderson Library, Special Collections

Finding Aids

This collection consists of the research materials of Johns Hopkins professor of psychology, Julian C. Stanley. Materials range from 1950-2005 and include his published reprints, abstracts, reports, letters, and seminar papers. The collection also includes reviews of research materials and articles by prominent psychologists in similar fields.

Find this collection in the University Libraries' catalog.

Srt Division Algorithms As Dynamical Systems, Mark Mccann, Nicholas Pippenger

All HMC Faculty Publications and Research

Sweeney--Robertson--Tocher (SRT) division, as it was discovered in the late 1950s, represented an important improvement in the speed of division algorithms for computers at the time. A variant of SRT division is still commonly implemented in computers today. Although some bounds on the performance of the original SRT division method were obtained, a great many questions remained unanswered. In this paper, the original version of SRT division is described as a dynamical system. This enables us to bring modern dynamical systems theory, a relatively new development in mathematics, to bear on an older problem. In doing so, we are able …

The Closed Topological Vertex Via The Cremona Transform, Jim Bryan, Dagan Karp

All HMC Faculty Publications and Research

We compute the local Gromov-Witten invariants of the "closed vertex", that is, a configuration of three rational curves meeting in a single triple point in a Calabi-Yau threefold. The method is to express the local invariants of the vertex in terms of ordinary Gromov-Witten invariants of a certain blowup of CP^3 and then to compute those invariants via the geometry of the Cremona transformation.

Interval Neutrosophic Sets And Logic; Theory And Applications In Computing, Haibin Wang, Florentin Smarandache, Yan-Qing Zhang, Rajshekhar Sunderraman

Branch Mathematics and Statistics Faculty and Staff Publications

This book presents the advancements and applications of neutrosophics. Chapter 1 first introduces the interval neutrosophic sets which is an instance of neutrosophic sets. In this chapter, the definition of interval neutrosophic sets and set-theoretic operators are given and various properties of interval neutrosophic set are proved. Chapter 2 defines the interval neutrosophic logic based on interval neutrosophic sets including the syntax and semantics of first order interval neutrosophic propositional logic and first order interval neutrosophic predicate logic. The interval neutrosophic logic can reason and model fuzzy, incomplete and inconsistent information. In this chapter, we also design an interval neutrosophic …

Quantum Quasi-Paradoxes And Quantum Sorites Paradoxes, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

There can be generated many paradoxes or quasi-paradoxes that may occur from the combination of quantum and non-quantum worlds in physics. Even the passage from the micro-cosmos to the macro-cosmos, and reciprocally, can generate unsolved questions or counter-intuitive ideas. We define a quasi-paradox as a statement which has a prima facie self-contradictory support or an explicit contradiction, but which is not completely proven as a paradox. We present herein four elementary quantum quasi-paradoxes and their corresponding quantum Sorites paradoxes, which form a class of quantum quasi-paradoxes.

Today's Take On Einstein’S Relativity: Proceedings Of The Conference Of 18 Feb 2005, Florentin Smarandache, Homer B. Tilton

Branch Mathematics and Statistics Faculty and Staff Publications

Non Sequiturs in Relativity Four in number at this point Dr. Smith of "Lost in Space" had a knack of easing out of binds that he'd gotten himself into. Dr. Einstein was a little like that. Einstein originally declared that the distortions of special relativity reflect real changes to the objects being remotely observed, then reconsidered. The first non sequitur is quoted here from Sachs:[1] In a lecture that Einstein gave to the Prussian Academy of Sciences in 1921, he said the following: "Geometry predicates nothing about relations of real things, but only geometry together with the purport of physical …

Fuzzy And Neutrosophic Analysis Of Women With Hiv/Aids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Fuzzy theory is one of the best tools to analyze data, when the data under study is an unsupervised one, involving uncertainty coupled with imprecision. However, fuzzy theory cannot cater to analyzing the data involved with indeterminacy. The only tool that can involve itself with indeterminacy is the neutrosophic model. Neutrosophic models are used in the analysis of the socio-economic problems of HIV/AIDS infected women patients living in rural Tamil Nadu. Most of these women are uneducated and live in utter poverty. Till they became seriously ill they worked as daily wagers. When these women got admitted in the hospital …

N-Algebraic Structures And S-N-Algebraic Structures, Florentin Smarandache, Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, for the first time we introduce the notions of Ngroups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. We expect the reader to be well versed in group theory and have at least basic knowledge about Smarandache groupoids, Smarandache loops, Smarandache semigroups and bialgebraic structures and Smarandache bialgebraic structures. The book is organized into six chapters. The first chapter gives the basic notions of S-semigroups, S-groupoids and S-loops thereby making the book self-contained. Chapter two introduces N-groups and their Smarandache analogues. In chapter three, Nloops and Smarandache N-loops are introduced and analyzed. Chapter four …

Introduction To Bimatrices, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable component of each other. The study of bialgebraic structures led to the invention of new notions like birings, Smarandache birings, bivector spaces, linear bialgebra, bigroupoids, bisemigroups, etc. But most of these are abstract algebraic concepts except, the bisemigroup being used in …

Properties Of One-Point Completions Of A Noncompact Metrizable Space, Melvin Henriksen, Ludvík Janoš, R. G. Woods

All HMC Faculty Publications and Research

If a metrizable space X is dense in a metrizable space Y, then Y is called a metric extension of X. If T₁ and T₂ are metric extensions of X and there is a continuous map of T₂ into T₁ keeping X pointwise fixed, we write T₁ ≤ T₂. If X is noncompact and metrizable, then (M(X),≤) denotes the set of metric extensions of X, where T₁ and T₂ are identified if T₁ ≤ T₂ and T₂ ≤ T₁, i.e., if there is a homeomorphism of …

C(X) Can Sometimes Determine X Without X Being Realcompact, Melvin Henriksen, Biswajit Mitra

All HMC Faculty Publications and Research

As usual C(X) will denote the ring of real-valued continuous functions on a Tychonoff space X. It is well-known that if X and Y are realcompact spaces such that C(X) and C(Y ) are isomorphic, then X and Y are homeomorphic; that is C(X) determines X. The restriction to realcompact spaces stems from the fact that C(X) and C(uX) are isomorphic, where uX is the (Hewitt) realcompactifcation of X. In this note, a class of locally compact spaces X that includes properly the class of locally compact realcompact spaces is exhibited such that C(X) determines X. The problem of getting …