Physical Sciences and Mathematics Commons^™

Quotient F-Modules, Ayşe Uyar

Turkish Journal of Mathematics

Let L be an f-module over f-algebra A. Then L^{\sim} is a cf-module over the f-algebra (A^{\sim})^{\sim}_n. Quotient f-modules are studied and subsequently a connection between Z(L^{\sim}) and [A^{\sim})^{\sim}_n]_{\hat{e}} is investigated.

Submanifolds Of Riemannian Product Manifolds, Mehmet Atçeken

Turkish Journal of Mathematics

In this paper, we study the geometry of the semi-invariant submanifolds of a Riemannian product manifold. Fundamental properties of these type submanifolds such as the integrability of the distributions D, D^{\bot} and mixed-geodesic property are studied. Finally, necessary and sufficient conditions are given on a semi-invariant submanifold of Riemannian product manifold to be D-geodesic and D^{\bot}-geodesic.

Exterior Differential Systems With Symmetry, Ian M. Anderson, Mark E. Fels

Mathematics and Statistics Faculty Publications

We use the theory of reduction of exterior differential systems with symmetry to study the problem of using a symmetry group of a differential equation to find noninvariant solutions.

Coffee To Go! Modeling Thermoclines In Multivariable Calculus, Andrea Bruder, Brynja R. Kohler

Mathematics and Statistics Faculty Publications

While mathematical modeling is an integral process in applied mathematics, students rarely encounter genuine modeling opportunities in their calculus courses. Here we introduce a laboratory experience as a natural starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients in lakes or the atmosphere, where temperature depends on both a temporal and spatial variable. Students create, observe, and collect temperature data of their own, graph the data, and develop mathematical models to fit the data. We require students to write a report about their findings. This …

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

Branch Mathematics and Statistics Faculty and Staff Publications

The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic models and so on. This book has for the first time, introduced a new algebraic structure called linear bialgebra, which is also a very powerful algebraic tool that can yield itself to applications. With the recent introduction of bimatrices (2005) we have ventured in this book to introduce new concepts like linear bialgebra and Smarandache neutrosophic linear bialgebra and also give the applications of these algebraic …

Minimal Modules Over Valuation Domains, Brendan Goldsmith, P. Zanardo

Articles

Let R be a valuation domain. We say that a torsion-free R-module is minimal if it is isomorphic to all its submodules of finite index. Here, the usual concept of finite index for groups is replaced by the more appropriate (for module theory) definition: a submodule H of the module G is said to be of finite index in G if the quotient G/H is a finitely presented torsion module. We investigate minimality in various settings and show inter alia that over a maximal valuation domain, all torsion-free modules are minimal. Constructions of non-minimal modules are given by utilizing realization …

The Simultaneous Onset And Interaction Of Taylor And Dean Instabilities In A Couette Geometry, C. P. Hills, A. P. Bassom

Articles

The fluid flow between a pair of coaxial circular cylinders generated by the uniform rotation of the inner cylinder and an azimuthal pressure gradient is susceptible to both Taylor and Dean type instabilities. The flow can be characterised by two parameters: a measure of the relative magnitude of the rotation and pressure effects and a non-dimensional Taylor number. Neutral curves associated with each instability can be constructed but it has been suggested that these curves do not cross but rather posses `kinks'. Our work is based in the small gap, large wavenumber limit and considers the simultaneous onset of Taylor …

On The Integrability Of A Class Of Nonlinear Dispersive Wave Equations, Rossen Ivanov

Articles

We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases coincide with the Camassa-Holm and Degasperis-Procesi equations.

Simplex Codes Over The Ring \Sum_{N=0}^Su^N F_2, Mohammed M. Al-Ashker

Turkish Journal of Mathematics

In this paper, we introduce simplex linear codes over the ring \sum_{n=0}^{n=s}u^n F_2 of types \alpha and \beta, where u^{s+1}=0. And we determine their properties. These codes are an extension and generalization of simplex codes over the ring Z_{2^s}.

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 Rough Singular Integrals Along Surfaces On Product Domains, Ahmad Al-Salman, Ali A. Al-Jarrah

Turkish Journal of Mathematics

In this paper, we study a class of singular integrals along surfaces on product domains with kernels in L(log L)^2(S^{n-1} \times S^{m-1}). We formulate a general theorem concerning the L^p boundedness of these operators. As a consequence of this theorem we establish L^p estimates of several classes of operators whose L^p boundedness in the one parameter setting is known. The condition L(log L)^2(B^{n-1} \times S^{m-1}) is known to be an optimal size condition

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.

The Use And Influence Of Technology In Mathematics Education, Ma. Louise Antonette N. De Las Peñas, Wei-Chi Yang

Mathematics Faculty Publications

The use of various types of technologies in the classroom and examinations is growing rapidly and is strongly influencing teaching and learning practices. In this paper, we will look at particular situations on how various technologies such as numerically capable calculators, graphics calculators, and technological tools that are CAS enabled or have CAS with Dynamic Geometry, impact students' learning. We also discuss briefly the educational opportunities that are made available by the emergence of graphics calculators with capabilities of handling electronic learning activities, such as Casio’s Class Pad (see [1]) and Casio’s 9860 graphics calculator.

Symmetrically Generated Groups, Benny Nguyen

Theses Digitization Project

This thesis constructs several groups entirely by hand via their symmetric presentations. In particular, the technique of double coset enumeration is used to manually construct J₃ : 2, the automorphism group of the Janko group J₃, and represent every element of the group as a permutation of PSL₂ (16) : 4, on 120 letters, followed by a word of length at most 3.

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.

Estimating Load-Sharing Properties In A Dynamic Reliability System, Paul H. Kvam, Edsel A. Peña

Department of Math & Statistics Faculty Publications

An estimator for the load-share parameters in an equal load-share model is derived based on observing k-component parallel systems of identical components that have a continuous distribution function F (˙) and failure rate r (˙). In an equal load-share model, after the first of k components fails, failure rates for the remaining components change from r (t) to γ1r (t), then to γ2r (t) after the next failure, and so on. On the basis of observations on n independent and identical systems, a semiparametric estimator of the component baseline …

Shuffle Up And Deal; Should We Have Jokers Wild? (Abstract), Kristen Lampe

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

From the Interactive Media Lab at the University of Florida to the Poker News blog to the Christian Science Monitor, everyone is talking about the rise in poker’s popularity.

Sixth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics

Kenneth C. Schraut Memorial Lectures

No abstract provided.

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.

Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt

Theses Digitization Project

Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.

Numbers Of Generators Of Ideals In Local Rings And A Generalized Pascal's Triangle, Lucia Riderer

Theses Digitization Project

This paper defines generalized binomial coefficients and shows that they can be used to generate generalized Pascal's Triangles and have properties analogous to binomial coefficients. It uses the generalized binomial coefficients to compute the Dilworth number and the Sperner number of certain rings.

A Topological Approach To Nonlinear Analysis, Wendy Ann Peske

Theses Digitization Project

A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed point theorem to Schauder's fixed point theorem, and Picard's theorem.

The Solvability Of Polynomials By Radicals: A Search For Unsolvable And Solvable Quintic Examples, Robert Lewis Beyronneau

Theses Digitization Project

This project centers around finding specific examples of quintic polynomials that were and were not solvable. This helped to devise a method for finding examples of solvable and unsolvable quintics.

Farrell's Spider, Jeremiah Farrell, Ivan Moscovich

Scholarship and Professional Work - LAS

Puzzle game featured in Ivan Moscovich's magnetic puzzle pack:

Place the 18 discs on the web so that the sum of the numbers on each of the three hexagons and on each of the three ribs equals 57.

Monotone Periodic Orbits For Torus Homeomorphisms, Kamlesh Parwani

Kamlesh Parwani

Let f be a homeomorphism of the torus isotopic to the identity and suppose that there exists a periodic orbit with a non-zero rotation vector (p/q,r/q), then f has a topologically monotone periodic orbit with the same rotation vector.

Point Evaluation And Hardy Space On A Homogeneous Tree, Daniel Alpay, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We consider stationary multiscale systems as defined by Basseville, Benveniste, Nikoukhah and Willsky. We show that there are deep analogies with the discrete time non stationary setting as developed by the first author, Dewilde and Dym. Following these analogies we define a point evaluation with values in a C*–algebra and the corresponding “Hardy space” in which Cauchy’s formula holds. This point evaluation is used to define in this context the counterpart of classical notions such as Blaschke factors.

On Additive Almost Continuous Functions Under Cpaprismgame, Krzysztof Ciesielski

Faculty & Staff Scholarship

We prove that the Covering Property Axiom CPA_prism^game, which holds in the iterated perfect set model, implies that there exists an additive discontinuous almost continuous function f from R to R whose graph is of measure zero. We also show that, under CPA_prism^game, there exists a Hamel basis H for which the set E⁺(H), of all linear combinations of elements from H with positive rational coefficients, is of measure zero. The existence of both of these examples follows from Martin's axiom, while it is unknown whether either of them can be constructed …

Gender Differences In Reading And Math Scores On The Pennsylvania System Of School Assessment Grade Five And Grade Eight Tests, Steven J. Rush

Seton Hall University Dissertations and Theses (ETDs)

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On An Extension Of Abel-Gontscharoff's Expansion Formula, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Scholarship

We present a constructive generalization of Abel-Gontscharoff’s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for the constructing the basis functions of the interpolants are given.