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2007

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Articles 361 - 390 of 541

Full-Text Articles in Mathematics

An Example Of An Indecomposable Module Without Non-Zero Hollow Factor Modules, Christian Lomp Jan 2007

An Example Of An Indecomposable Module Without Non-Zero Hollow Factor Modules, Christian Lomp

Turkish Journal of Mathematics

A module M is called hollow-lifting if every submodule N of M such that M/N is hollow contains a direct summand D \subseteq N such that N/D is a small submodule of M/D. A module M is called lifting if such a direct summand D exists for every submodule N. We construct an indecomposable module M without non-zero hollow factor modules, showing that there are hollow-lifting modules which are not lifting. The existences of such modules had been left open in a recent work by N. Orhan, D. Keskin-Tütüncü and R. Tribak [2].

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A Generalization Of Ankeny And Rivlin's Result On The Maximum Modulus Of Polynomials Not Vanishing In The Interior Of The Unit Circle, V. K. Jain Jan 2007

A Generalization Of Ankeny And Rivlin's Result On The Maximum Modulus Of Polynomials Not Vanishing In The Interior Of The Unit Circle, V. K. Jain

Turkish Journal of Mathematics

For an arbitrary entire function f(z), let M(f,r) = max_{ z =r} f(z) . For a polynomial p(z) of degree n, it is known that M(p,R) \leq R^n M(p,1), R > 1. By considering the polynomial p(z) with no zeros in z < 1, Ankeny and Rivlin obtained the refinement M(p,R) \leq {(R^n+1)/2}M(p,1), R > 1. By considering the polynomial p(z) with no zeros in z < k, (k \geq 1) and simultaneously thinking of s^{\rm th} derivative (0 \leq s < n) of the polynomial, we have obtained the generalization \begin{displaymath} M(p^{(s)},R) \leq \left\{\begin{array}{l} (1/2){\frac{d^s}{dR^s}(R^n + k^n)}(2/(1+k))^nM(p,1), R \geq k,\ (1/(R^s+k^s))[{\frac{d^s}{dx^s}(1+x^n)}_{x=1}]((R+k)/(1+k))^nM(p,1), 1 \leq R \leq k,\end{array}\right. of Ankeny and Rivlin's result.

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Efficient Inversion Of The Cone Beam Transform For A General Class Of Curves, Mikhail Kapralov Jan 2007

Efficient Inversion Of The Cone Beam Transform For A General Class Of Curves, Mikhail Kapralov

Electronic Theses and Dissertations

We extend an efficient cone beam transform inversion formula, proposed earlier for helices, to a general class of curves. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much in a certain sense, and do not admit lines which are tangent to C at one point and intersect C at another point. A domain U is found where reconstruction is possible with a filtered backprojection type algorithm. Results of numerical experiments demonstrate very good image quality. The algorithm developed is useful for image reconstruction in …

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Spectral Problems For Operator Pencils In Non-Separated Root Zones, Mahi̇r Hasanov Jan 2007

Spectral Problems For Operator Pencils In Non-Separated Root Zones, Mahi̇r Hasanov

Turkish Journal of Mathematics

Variational principles for real eigenvalues of self-adjoint operator pencils in non-separated root zones are studied.

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Shellability Of Noncrossing Partition Lattices, Colum Watt, Thomas Brady, Christos Athanasiadis Jan 2007

Shellability Of Noncrossing Partition Lattices, Colum Watt, Thomas Brady, Christos Athanasiadis

Articles

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank at least three.

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An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins Jan 2007

An Upperbound On The Ropelength Of Arborescent Links, Larry Andrew Mullins

Theses Digitization Project

This thesis covers improvements on the upperbounds for ropelength of a specific class of algebraic knots.

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Stone's Representation Theorem, Ion Radu Jan 2007

Stone's Representation Theorem, Ion Radu

Theses Digitization Project

The thesis analyzes some aspects of the theory of distributive lattices, particularly two representation theorems: Birkhoff's representation theorem for finite distributive lattices and Stone's representation theorem for infinite distributive lattices.

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Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah Jan 2007

Mordell-Weil Theorem And The Rank Of Elliptical Curves, Hazem Khalfallah

Theses Digitization Project

The purpose of this thesis is to give a detailed group theoretic proof of the rank formula in a more general setting. By using the proof of Mordell-Weil theorem, a formula for the rank of the elliptical curves in certain cases over algebraic number fields can be obtained and computable.

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The Q-Exponential Generating Function For Permutations By Consecutive Patterns And Inversions, Don Rawlings Jan 2007

The Q-Exponential Generating Function For Permutations By Consecutive Patterns And Inversions, Don Rawlings

Mathematics

The inverse of Fedou's insertion-shift bijection is used to deduce a general form for the q-exponential generating function for permutations by consecutive patterns (overlaps allowed) and inversion number from a result due to Jackson and Goulden for enumerating words by distinguished factors. Explicit q-exponential generating functions are then derived for permutations by the consecutive patterns 12…m, 12…(m−2)m(m−1), 1m(m−1)…2, and by the pair of consecutive patterns (123,132).

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Primary Decomposition Of Ideals In A Ring, Sola Oyinsan Jan 2007

Primary Decomposition Of Ideals In A Ring, Sola Oyinsan

Theses Digitization Project

The concept of unique factorization was first recognized in the 1840s, but even then, it was still fairly believed to be automatic. The error of this assumption was exposed largely through attempts to prove Pierre de Fermat's, 1601-1665, last theorem. Once mathematicians discovered that this property did not always hold, it was only natural for them to try to search for the strongest available alternative. Thus began the attempt to generalize unique factorization. Using the ascending chain condition on principle ideals, we will show the conditions under which a ring is a unique factorization domain.

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Minimal Surfaces, Maria Guadalupe Chaparro Jan 2007

Minimal Surfaces, Maria Guadalupe Chaparro

Theses Digitization Project

The focus of this project consists of investigating when a ruled surface is a minimal surface. A minimal surface is a surface with zero mean curvature. In this project the basic terminology of differential geometry will be discussed including examples where the terminology will be applied to the different subjects of differential geometry. In addition the focus will be on a classical theorem of minimal surfaces referred to as the Plateau's Problem.

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Tutte Polynomial In Knot Theory, David Alan Petersen Jan 2007

Tutte Polynomial In Knot Theory, David Alan Petersen

Theses Digitization Project

This thesis reviews the history of knot theory with an emphasis on the diagrammatic approach to studying knots. Also covered are the basic concepts and notions of graph theory and how these two fields are related with an example of a knot diagram and how to associate it to a graph.

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Construction Of Finite Homomorphic Images, Jane Yoo Jan 2007

Construction Of Finite Homomorphic Images, Jane Yoo

Theses Digitization Project

The purpose of this thesis is to construct finite groups as homomorphic images of progenitors.

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Dissipative Solitons In The Cubic-Quintic Complex Ginzburg-Landau Equation:Bifurcations And Spatiotemporal Structure, Ciprian Mancas Jan 2007

Dissipative Solitons In The Cubic-Quintic Complex Ginzburg-Landau Equation:Bifurcations And Spatiotemporal Structure, Ciprian Mancas

Electronic Theses and Dissertations

Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic--quintic Ginzburg--Landau equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non--integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are …

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A "Sound" Approach To Fourier Transforms: Using Music To Teach Trigonometry, Bruce Kessler Jan 2007

A "Sound" Approach To Fourier Transforms: Using Music To Teach Trigonometry, Bruce Kessler

Mathematics Faculty Publications

If a large number of educated people were asked, ``What was your most exciting class?'', odds are that very few of them would answer ``Trigonometry.'' The subject is generally presented in a less-than-exciting fashion, with the repeated caveat that ``you'll need this when you take calculus,'' or ``this has lots of applications'' without ever really seeing many of them. This manuscript addresses how the author is trying to change this tradition by exposing casual students from kindergarten to college to Joseph Fourier's secret, that nearly any function can be built out of sine and cosine curves. And music serves as …

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Strokes Of Existence: The Connection Of All Things, Mari Gorman Jan 2007

Strokes Of Existence: The Connection Of All Things, Mari Gorman

Graduate Student Publications and Research

Acted or real—and all life is real whether one is acting or not—the common denominator and consistent, ubiquitous reality of life and all behavior is that it manifests in the form of relationships on all scales. But what is a relationship? Until now, the answer to this question has not been sufficiently known. As a result of many years of empirical research that began with the aim of discovering what is going on in a gifted actor when s/he is playing a character that can be observed and experienced as a living, intuitive being, and based on the knowledge that …

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Eighth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics Jan 2007

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

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Unbounded Regions Of Infinitely Logconcave Sequences, David Uminsky, Karen Yeats Jan 2007

Unbounded Regions Of Infinitely Logconcave Sequences, David Uminsky, Karen Yeats

Mathematics

We study the properties of a logconcavity operator on a symmetric, unimodal subset of finite sequences. In doing so we are able to prove that there is a large unbounded region in this subset that is ∞-logconcave. This problem was motivated by the conjecture of Boros and Moll in [1] that the binomial coefficients are ∞-logconcave.

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On Graded Secondary Modules, Shahabaddin Ebrahimi Atani, F. Farzalipour Jan 2007

On Graded Secondary Modules, Shahabaddin Ebrahimi Atani, F. Farzalipour

Turkish Journal of Mathematics

Let G be a group with identity e, and let R be a G-graded commutative ring. Here we study the graded primary submodules of a G-graded R-module and examine when graded submodules of a graded representable module are graded representable. A number of results concerning of these class of submodules are given.

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Potts Model With Two Competing Binary Interactions, Nasir Ganikhodjaev, Hasan Akin, Seyi̇t Temi̇r Jan 2007

Potts Model With Two Competing Binary Interactions, Nasir Ganikhodjaev, Hasan Akin, Seyi̇t Temi̇r

Turkish Journal of Mathematics

The Potts model on a Cayley tree in the presence of competing two binary interactions and magnetic field is considered. We exactly solve a problem of phase transitions for the model,namely we calculate critical surface such that there is a phase transition above it,and a single Gibbs state found elsewhere.

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Locally Finite Simple Moufang Loops, J. I. Hall Jan 2007

Locally Finite Simple Moufang Loops, J. I. Hall

Turkish Journal of Mathematics

A Moufang loop is a binary system that satisfies a particular weak form of the associative law. Doro and Glauberman observed that there is a direct connection between simple Moufang loops and simple groups with triality. Using this correspondence, Liebeck proved that nonassociative finite simple Moufang loops arise from split octonion algebras over finite fields. We extend Liebeck's theorem to the case of locally finite simple Moufang loops.

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Graphics With Tikz, Andrew Mertz, William Slough Jan 2007

Graphics With Tikz, Andrew Mertz, William Slough

Faculty Research and Creative Activity

Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a thin line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cover a wide spectrum of use and provide a starting point for exploration.

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Graphics With Pgf And Tikz, Andrew Mertz, William Slough Jan 2007

Graphics With Pgf And Tikz, Andrew Mertz, William Slough

Faculty Research and Creative Activity

Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a fine line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cover a wide spectrum of use and provide a starting point for exploration.

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Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler Jan 2007

Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We consider the differentiability of weak solutions of linear parabolic equations with respect to parameters and initial data. under natural assumptions, it is shown that solutions possess as much differentiability with respect to the data as do the terms appearing in the equation. The derivatives are shown to satisfy the appropriate sensitivity equations. The theoretical results are illustrated with an example.

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Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner Jan 2007

Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

By means of Riccati transformation techniques we establish some oscillation criteria for the second order Emden-Fowler dynamic equation on a time scale. Such equations contain the classical Emden-Fowler equation as well as their discrete counterparts. The classical oscillation results of Atkinson (in the superlinear case) and Belohorec (in the sublinear case) are extended in this paper to Emden-Fowler dynamic equations on any time scale.

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Closed Geodesics On Orbifolds Of Revolution, Joseph E. Borzellino, Christopher R. Jordan-Squire, Gregory C. Petrics, D. Mark Sullivan Jan 2007

Closed Geodesics On Orbifolds Of Revolution, Joseph E. Borzellino, Christopher R. Jordan-Squire, Gregory C. Petrics, D. Mark Sullivan

Mathematics

Using the theory of geodesics on surfaces of revolution, we show that any two-dimensional orbifold of revolution homeomorphic to S2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert's theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert's result does not hold in the wider class of closed surfaces with …

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Distances Between Composition Operators, Valentin Matache Jan 2007

Distances Between Composition Operators, Valentin Matache

Mathematics Faculty Publications

Composition operators Cϕ induced by a selfmap ϕ of some set S are operators acting on a space consisting of functions on S by composition to the right with ϕ, that is Cϕf = f ◦ ϕ. In this paper, we consider the Hilbert Hardy space H2 on the open unit disk and find exact formulas for distances kCϕ − Cψk between composition operators. The selfmaps ϕ and ψ involved in those formulas are constant, inner, or analytic selfmaps of the unit disk fixing the origin.

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Promoting Undergraduate Research In Mathematics At The University Of Nebraska – Lincoln, Judy L. Walker, Glenn Ledder, Richard Rebarber, Gordon S. Woodward Jan 2007

Promoting Undergraduate Research In Mathematics At The University Of Nebraska – Lincoln, Judy L. Walker, Glenn Ledder, Richard Rebarber, Gordon S. Woodward

Department of Mathematics: Faculty Publications

The Department of Mathematics at the University of Nebraska – Lincoln (UNL) has several programs which promote undergraduate research in a variety of ways. Two of these are summer programs which draw from a national applicant pool: The Nebraska REU in Applied Mathematics (Section 1) is a traditional NSF-funded REU site, and Nebraska IMMERSE (Section 2) offers a summer “bridge” program (with a research bent) for students about to start graduate school in mathematics. IMMERSE is a relatively new program, started in 2004 as part of the department’s Mentoring through Critical Transition Points (MCTP) grant from NSF. The MCTP grant …

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Teaching Time Savers: Is Homework Grading On Your Nerves?, Lisette G. De Pillis, Michael E. Orrison Jr. Jan 2007

Teaching Time Savers: Is Homework Grading On Your Nerves?, Lisette G. De Pillis, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

You have probably heard it said that we learn mathematics best when we do mathematics, or that mathematics is not a spectator sport. For most of our students, this means that their mathematics courses will involve a fair amount of homework. This homework is often used to evaluate individual student progress, but it can also be used, for example, as a catalyst for discussion, to emphasize a point made in class, and to identify common misunderstandings throughout the class as a whole. There is, however, the matter of grading homework.

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Domain Relaxation In Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Jacob R. Wintersmith '06, Lu Zou Jan 2007

Domain Relaxation In Langmuir Films, James C. Alexander, Andrew J. Bernoff, Elizabeth K. Mann, J. Adin Mann Jr., Jacob R. Wintersmith '06, Lu Zou

All HMC Faculty Publications and Research

We report on theoretical studies of molecularly thin Langmuir films on the surface of a quiescent subfluid and qualitatively compare the results to both new and previous experiments. The film covers the entire fluid surface, but domains of different phases are observed. In the absence of external forcing, the compact domains tend to relax to circles, driven by a line tension at the phase boundaries. When stretched (by a transient applied stagnation-point flow or by stirring), a compact domain elongates, creating a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape will then relax slowly …

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