Mathematics Commons^™

Commutative Quartic P-Galois Extensions Over A Field Of Characteristic Not 2, Atsushi Nakajima

Turkish Journal of Mathematics

In [2], K. Kishimoto introduced the notion of P-Galois extensions and gave some fundamental properties of these extensions. P-Galois extensions relate Hopf Galois extensions, and the author treated these topics in [5]. Moreover, the cubic P-Galois extensions over a field were completely determined in [6]. Continuing [5] and [6], we classify commutative quartic P-Galois extensions over a field of characteristic not 2.

On A Class Of Para-Sakakian Manifolds, Ci̇han Özgür

Turkish Journal of Mathematics

In this study, we investigate Weyl-pseudosymmetric Para-Sasakian manifolds and Para-Sasakian manifolds satisfying the condition C \cdot S=0.

Maximal Oscillatory Singular Integrals With Kernels In L Log L(S^{N-1}), Ahmad Al-Salman

Turkish Journal of Mathematics

In this paper, we study the L^p mapping properties of a certain class of maximal oscillatory singular integral operators. We establish the L^p boundedness of our operators provided that their kernels belong to the natural space L log ^+L(S^{n-1}). Our result substantially improves a previously known result. Moreover, the approach developed in this paper can be applied to handle more general maximal oscillatory singular integral operators.

On Linear The Homeomorphism Between Function Spaces C_P(X) And C_{P,A}(X) \Times C_P (A), Sabri̇ Bi̇rli̇k

Turkish Journal of Mathematics

In this paper, we investigate a linear homeomorphism between function spaces C_p(X) and C_{p,A}(X) \times C_p(A) , where X is a normal space and A is a neighborhood retraction of X.

On Space Of Parabolic Potentials Associated With The Singular Heat Operator, Si̇nem Sezer, İlham A. Ali̇ev

Turkish Journal of Mathematics

Anisotropic spaces L_{p,\gamma}^{\alpha} of parabolic Bessel potentials, associated with the singular heat operator I-\Delta_{\gamma}+ \frac{\partial}{\partial t}, where \Delta_{\gamma} = \sum\limits_{k=1}^n \frac{\partial ^{2}}{\partial x_{k}^{2}} + \frac{2\gamma }{x_n}. \frac{\partial}{\partial x_n}, are introduced, and making use of special wavelet-type transform, a characterization of these spaces is obtained.

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.

The Stepping Stone Model, Ii: Genealogies And The Infinite Sites Model, Submitted, Iljana Zähle, J. Theodore Cox, Richard Durrett

Mathematics - All Scholarship

This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of Kingman’s coalescent. With DNA sequence data in mind, we investigate mutation patterns under the infinite sites model, which assumes that each mutation occurs at a new site. Our results suggest that the spatial structure of the human population contributes to the haplotype structure and a slower than expected decay of genetic correlation with distance revealed by …

The Backward Shift On HP, William T. Ross

Department of Math & Statistics Faculty Publications

In this semi-expository paper, we examine the backward shift operator

Bf := (f-f(0)/z

on the classical Hardy space H^p. Through there are many aspects of this operator worthy of study [20], we will focus on the description of its invariant subspaces by which we mean the closed linear manifolds Ɛ ⊂ H^p for which BƐ ⊂ Ɛ. When 1 < p < ∞, a seminal paper of Douglas, Shapiro, and Shields [8] describes these invariant subspaces by using the important concept of a pseudocontinuation developed earlier by Shapiro [26]. When p = 1, the description is the same [1] except that in the proof, one must be mindful of some technical considerations involving the functions of bounded mean oscillation.

Modeling The Evolution Of Inhomogeneities, Marek Elźanowski, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

A model of an anelastic evolution law of a defective continuum is discussed, emphasizing the role of the Clausius-Duhem inequality in selecting admissible processes.

Incompressible Finite Elements Via Hybridization. Part I: The Stokes System In Two Space Dimensions, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we introduce a new and efficient way to compute exactly divergence-free velocity approximations for the Stokes equations in two space dimensions. We begin by considering a mixed method that provides an exactly divergence-free approximation of the velocity and a continuous approximation of the vorticity. We then rewrite this method solely in terms of the tangential fluid velocity and the pressure on mesh edges by means of a new hybridization technique. This novel formulation bypasses the difficult task of constructing an exactly divergence-free basis for velocity approximations. Moreover, the discrete system resulting from our method has fewer degrees …

Nédélec Spaces In Affine Coordinates, Jay Gopalakrishnan, Luis E. García-Castillo, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

In this note, we provide a conveniently implementable basis for simplicial Nédélec spaces of any order in any space dimension. The main feature of the basis is that it is expressed solely in terms of the barycentric coordinates of the simplex.

Curvature Of The Weinhold Metric For Thermodynamical Systems With 2 Degrees Of Freedom, Manuel Santoro, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

In this work the curvature of Weinhold (thermodynamical) metric is studied in the case of systems with two thermodynamical degrees of freedom. Conditions for the Gauss curvature R to be zero, positive or negative are worked out. Signature change of the Weinhold metric and the corresponding singular behavior of the curvature at the phase boundaries are studied. Cases of systems with the constant C_v, including Ideal and Van der Waals gases, and that of Berthelot gas are discussed in detail.

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.

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 …

Kinetic Structure Simulations Of Nematic Polymers In Plane Couette Cells. Ii: In-Plane Structure Transitions, M. Gregory Forest, Ruhai Zhou, Qi Wang

Mathematics & Statistics Faculty Publications

Nematic, or liquid crystalline, polymer (LCP) composites are composed of large aspect ratio rod-like or platelet macromolecules. This class of nanocomposites exhibits tremendous potential for high performance material applications, ranging across mechanical, electrical, piezoelectric, thermal, and barrier properties. Fibers made from nematic polymers have set synthetic materials performance standards for decades. The current target is to engineer multifunctional films and molded parts, for which processing flows are shear-dominated. Nematic polymer films inherit anisotropy from collective orientational distributions of the molecular constituents and develop heterogeneity on length scales that are, as yet, not well understood and thereby uncontrollable. Rigid LCPs in …

Flowers Of Ice- Beauty, Symmetry, And Complexity: A Review Of The Snowflake: Winter's Secret Beauty, John A. Adam

Mathematics & Statistics Faculty Publications

(First paragraph) Growing up as a child in southern England, my early memories of snow include trudging home from school with my father, gazing at the seemingly enormous snowdrifts that smoothed the hedgerows, fields and bushes, while listening to the soft “scrunch” of the snow under my Wellington boots. In the country, snow stretching as far as I could see was not a particularly uncommon sight. The quietness of the land under a foot of snow seemed eerie. I cannot remember the first time I looked at snowflakes per se; my interests as a small child were primarily in their …

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 …

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.

Utilization Of Total Mass As A Control In Diffusion Processes, Mohamed Salman

Electronic Theses and Dissertations

As motivation for the mathematical problems considered in this work, consider a chamber in the form of a long linear transparent tube. We allow for the introduction or removal of material in a gaseous state at the ends of the tube. The material diffuses throughout the tube with or without reaction with other materials. By illuminating the tube on one side with a light source with a frequency range spanning the absorption range for the material and collecting the residual light that passes through the tube with photo-reception equipment, we can obtain a measurement of the total mass of material …

Decision Theory Classification Of High-Dimensional Vectors Based On Small Samples, David Bradshaw

Electronic Theses and Dissertations

In this paper, we review existing classification techniques and suggest an entirely new procedure for the classification of high-dimensional vectors on the basis of a few training samples. The proposed method is based on the Bayesian paradigm and provides posterior probabilities that a new vector belongs to each of the classes, therefore it adapts naturally to any number of classes. Our classification technique is based on a small vector which is related to the projection of the observation onto the space spanned by the training samples. This is achieved by employing matrix-variate distributions in classification, which is an entirely new …

Application Of Statistical Methods In Risk And Reliability, Astrid Heard

Electronic Theses and Dissertations

The dissertation considers construction of confidence intervals for a cumulative distribution function F(z) and its inverse at some fixed points z and u on the basis of an i.i.d. sample where the sample size is relatively small. The sample is modeled as having the flexible Generalized Gamma distribution with all three parameters being unknown. This approach can be viewed as an alternative to nonparametric techniques which do not specify distribution of X and lead to less efficient procedures. The confidence intervals are constructed by objective Bayesian methods and use the Jeffreys noninformative prior. Performance of the resulting confidence intervals is …

Queuing Systems With Multiple Fbm-Based Traffic Models, Mihaela Teodora Matache, Valentin Matache

Mathematics Faculty Publications

A multiple fractional Brownian motion (FBM)-based traffic model is considered. Various lower bounds for the overflow probability of the associated queueing system are obtained. Based on a probabilistic bound for the busy period of an ATM queueing system associated with a multiple FBM-based input traffic, a minimal dynamic buffer allocation function (DBAF) is obtained and a DBAF-allocation algorithm is designed. The purpose is to create an upper bound for the queueing system associated with the traffic. This upper bound, called a DBAF, is a function of time, dynamically bouncing with the traffic. An envelope process associated with the multiple FBM-based …

Asynchronous Random Boolean Network Model Based On Elementary Cellular Automata Rule 126, Mihaela Teodora Matache, Jack Heidel

Mathematics Faculty Publications

This paper considers a simple Boolean network with N nodes, each node’s state at time tbeing determined by a certain number k of parent nodes, which is fixed for all nodes. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. We make use of a Boolean rule that is a generalization of rule 126 of elementary cellular automata. We provide formulas for the probability of finding a node in state 1 at a time t for the class of asynchronous random Boolean networks (ARBN) in which only one node is updated at every time step, and …

A Short Proof Of A Characterization Of Inner Functions In Terms Of The Composition Operators They Induce, Valentin Matache

Mathematics Faculty Publications

The paper contains a new proof for the sufficiency in Joel H. Shapiro’s recent characterization of inner functions...

Operator Self-Similar Processes On Banach Spaces, Mihaela Teodora Matache, Valentin Matache

Mathematics Faculty Publications

Operator self-similar (OSS) stochastic processes on arbitrary Banach spaces are considered. If the family of expectations of such a process is a spanning subset of the space, it is proved that the scaling family of operators of the process under consideration is a uniquely determinedmultiplicative group of operators. If the expectation-function of the process is continuous, it is proved that the expectations of the process have power-growth with exponent greater than or equal to 0, that is, their norm is less than a nonnegative constant times such a power-function, provided that the linear space spanned by the expectations has category …

Geometry Of Jump Systems, Vadim Lyubashevsky, Chad Newell, Vadim Ponomarenko

Mathematics Faculty Research

A jump system is a set of lattice points satisfying a certain "two-step" axiom. We present a variety of results concerning the geometry of these objects, including a characterization of two-dimensional jump systems, necessary (though not sufficient) properties of higher-dimensional jump systems, and a characterization of constant-sum jump systems.

Navy Personnel Planning And The Optimal Partition, Allen G. Holder

Mathematics Faculty Research

One could argue that the Navy's most important resource is its personnel, and as such, workforce planning is a crucial task. We investigate a new model and solution technique that is designed to aid in optimizing the process of assigning sailors to jobs. This procedure attempts to achieve an increased level of sailor satisfaction by providing a list of possible jobs from which a sailor may choose. We show that the optimal partition provided by an interior-point algorithm is particularly useful when designing the job lists. This follows because a strictly complementary solution to the linear programming relaxation observes all …

Positive Operators And Maximum Principles For Ordinary Differential Equations, Paul W. Eloe

Mathematics Faculty Publications

We show an equivalence between a classical maximum principle in differential equations and positive operators on Banach Spaces. Then we shall exhibit many types of boundary value problems for which the maximum principle is valid. Finally, we shall present extended applications of the maximum principle that have arisen with the continued study of the qualitative properties of Green’s functions.

Gröbner Bases: A Natural Extension Of Gaussian Reduction And The Euclidean Algorithm (Abstract), Patrick Flinn

Kenneth C. Schraut Memorial Lectures

Gröbner bases can be used to answer fundamental questions concerning certain sets of polynomials. For example, when are two such sets equal? Given such a set and another polynomial, is this polynomial a member of that set? In this introduction to Gröbner bases, we motivate their salient features by considering the Euclidean algorithm and Gaussian row reduction of matrices from a slightly different point of view.

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 …