Mathematics Commons^™

On The Codifferential Of The Kähler Form And Cosymplectic Metrics On Maximal Flag Manifolds, Marlio Paredes, Sofia Pinzon

Turkish Journal of Mathematics

Using moving frames we obtain a formula to calculate the codifferential of the Kähler form on a maximal flag manifold. We use this formula to obtain some differential type conditions so that a metric on the classical maximal flag manifold be cosymplectic.

Traveling Wavefronts In A Single Species Model With Nonlocal Diffusion And Age-Structure, Xue-Shi Li, Guo Lin

Turkish Journal of Mathematics

This paper is concerned with the existence of monotone traveling wavefronts in a single species model with nonlocal diffusion and age-structure. We first apply upper and lower solution technique to prove the result if the wave speed is larger than a threshold depending only on the basic parameters. When the wave speed equals to the threshold, we show the conclusion by passing to a limit function.

Notes On Null Curves In Minkowski Spaces, Makoto Sakaki

Turkish Journal of Mathematics

We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the 4-dimensional Minkowski space. Also we characterize pseudo-spherical null curves in the n-dimensional Minkowski space in terms of the curvature functions.

The Linear Functionals On Fundamental Locally Multiplicative Topological Algebras, E. Ansari-Piri

Turkish Journal of Mathematics

In this paper we study the dual space of fundamental locally multiplicative topological algebras and prove some results for linear and multiplicative linear functionals on these algebras. An investigation on locally compactness of the carrier space of these algebras is the last part of this note.

Heteroclinic Solutions To An Asymptotically Autonomous Second-Order Equation, Gregory S. Spradlin

Mathematics - Daytona Beach

We study the differential equation ẍ(t) = a(t)V '(x(t)), where V is a double-well potential with minima at x = ±1 and a(t) →l > 0 as |t| → 1. It is proven that under certain additional assumptions on a, there exists a heteroclinic solution x to the differential equation with x(t) → -1 as t → -1 and x(t) → 1 as t → ∞. The assumptions allow l - a(t) to change sign for arbitrarily large values of |t|, and do not restrict the decay rate of |l -a(t)| as |t| → ∞ © 2010 Texas State University - …

On Baryon Number Non-Conservation In Two-Dimensional O(2n+1) Qcd, Tamar Friedmann

Mathematics Sciences: Faculty Publications

We construct a classical dynamical system whose phase space is a certain infinite dimensional Grassmannian manifold, and propose that it is equivalent to the large N limit of two-dimensional QCD with an O(2N + 1) gauge group. In this theory, we find that baryon number is a topological quantity that is conserved only modulo 2. We also relate this theory to the master field approach to matrix models.

Positive Solutions Of The (N-1, 1) Conjugate Boundary Value Problem, Bo Yang

Faculty Articles

We consider the (n - 1, 1) conjugate boundary value problem. Some upper estimates to positive solutions for the problem are obtained. We also establish some explicit sufficient conditions for the existence and nonexistence of positive solutions of the problem.

Signature Matrices: The Eigenvalue Problem, Valeria Aguirre Holguin

Open Access Theses & Dissertations

Dealing with matrices can give us a hard time, especially when their dimension is too big, but we also well know how valuable information a matrix may carry, and that is why we study them. When a matrix has a significant number of zeroes we realize how much easier all calculations are. For instance, the product will be simpler to calculate, the determinant, the inverse and even the eigenvalue problem. This thesis provides the description and behavior of a very special kind of matrices which we call signature matrices. A particular feature of these matrices lies in the fact that …

Incidence Functions, Yiyu Liao

Open Access Theses & Dissertations

In the mid 1960's, the incidence algebra was introduced in the seminal paper of Gian-Carlo Rota. He addressed the importance of the Mobius function in combinatorics. In particular, the incidence algebra of a locally finite poset plays an essentially unifying role in the theory of the Mobius function. One of the significant generalizations is the incidence algebra of a Mobius category introduced by Pierre Leroux. With the help from Mobius category, it was exciting to be able to extend the combinatorial results more broadly than just on posets. Before attempting to study this generalization of the Mobius function, we have …

Use Of Cognitive Constructs In Linear Algebra, Azucena Zamora

Open Access Theses & Dissertations

Thesis analyzed the presence of two cognitive entities-- modes of thinking and metonymies and metaphors- in the reasoning of three students enrolled in a first year matrix algebra course at a southwest university via the responses given to a set of eight questions asked during one-on-one interviews. The findings of our analysis shed light on the cognitive constructs that students employ to form their understanding of linear algebra concepts. Furthermore, our findings provide clues about the ways in which students move from one mode of thinking to another in the context of varying levels of exposure to graphical, algebraic, and …

General Flips And The Cd-Index, Daniel J. Wells

University of Kentucky Doctoral Dissertations

We generalize bistellar operations (often called flips) on simplicial manifolds to a notion of general flips on PL-spheres. We provide methods for computing the cd-index of these general flips, which is the change in the cd-index of any sphere to which the flip is applied. We provide formulas and relations among flips in certain classes, paying special attention to the classic case of bistellar flips. We also consider questions of "flip-connecticity", that is, we show that any two polytopes in certain classes can be connected via a sequence of flips in an appropriate class.

Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene

Publications and Research

The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities.In previous work [11,12] we described a numerical procedure for overcoming the Gibbs phenomenon called the Inverse Wavelet Reconstruction method (IWR). The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series. However, we only described the method standard wavelet series and …

Women And Math Performance: The Effects Of Stereotype Threat, Math Identity, And Gender Identity, Felicia W. Chu

Seton Hall University Dissertations and Theses (ETDs)

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The Influence Of Inclusion On Langauge Arts Literacy And Math Achievement On Non-Disabled Middle School Students, Faye Brady

Seton Hall University Dissertations and Theses (ETDs)

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On Osgood's Criterion For Classical Wave Equations And Nonlinear Shallow Water Wave Equations, Timothy Smith, Greg Spradlin

Publications

The problem on classical solutions for the wave equation and the BBM equation is considered. The equations are considered with a forcing term and sufficient conditions of solvability, existence and uniqueness are established.

On The Socles Of Characteristic Subgroups Of Abelian P-Groups, Brendan Goldsmith, Peter Danchev

Articles

Fully invariant subgroups of an Abelian p-group have been the object of a good deal of study, while characteristic subgroups have received somewhat less attention. Recently the socles of fully invariant subgroups have been studied and this led to the notion of a socle-regular group. The present work replaces the fully invariant subgroups with characteristic ones and leads in a natural way to the notion of a strongly socle-regular group. A surprising relationship, mirroring that between transitive and fully transitive groups, is obtained.

From Permutahedron To Associahedron, Colum Watt, Thomas Brady

Articles

For each finite real reflection group $W$, we identify a copy of the type-$W$ simplicial generalised associahedron inside the corresponding simplicial permutahedron. This defines a bijection between the facets of the generalised associahedron and the elements of the type-$W$ non-crossing partition lattice which is more tractable than previous such bijections. We show that the simplicial fan determined by this associahedron coincides with the Cambrian fan for $W$.

An Examination Of The Association Of Selected Toxic Metals With Total And Central Obesity Indices: Nhanes 99-02, Miguel A. Padilla, Mai Elobeid, Douglas M. Ruden, David B. Allison

Psychology Faculty Publications

It is conceivable that toxic metals contribute to obesity by influencing various aspects of metabolism, such as by substituting for essential micronutrients and vital metals, or by inducing oxidative stress. Deficiency of the essential metal zinc decreases adiposity in humans and rodent models, whereas deficiencies of chromium, copper, iron, and magnesium increases adiposity. This study utilized the NHANES 99-02 data to explore the association between waist circumference and body mass index with the body burdens of selected toxic metals (barium, cadmium, cobalt, cesium, molybdenum, lead, antimony, thallium, and tungsten). Some of the associations were significant direct relationships (barium and thallium), …

Algorithms For Upper Bounds Of Low Dimensional Group Homology, Joshua D. Roberts

University of Kentucky Doctoral Dissertations

A motivational problem for group homology is a conjecture of Quillen that states, as reformulated by Anton, that the second homology of the general linear group over R = Z[1/p; ζ_p], for p an odd prime, is isomorphic to the second homology of the group of units of R, where the homology calculations are over the field of order p. By considering the group extension spectral sequence applied to the short exact sequence 1 → SL₂ → GL₂ → GL₁ → 1 we show that the calculation of the homology …

Some Implications Of Chu's 10Ψ10 Generalization Of Bailey's 6Ψ6 Summation Formula, James Mclaughlin, Andrew Sills, Peter Zimmer

Mathematical Sciences: Faculty Publications

Lucy Slater used Bailey's 6ψ6 summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type.

In the present paper we apply the same techniques to Chu's 10ψ10 generalization of Bailey's formula to produce quite general Bailey pairs. Slater's Bailey pairs are then recovered as special limiting cases of these more general pairs.

In re-examining Slater's work, we find that her Bailey pairs are, for the most part, special cases of more general Bailey pairs containing one or more free parameters. Further, we also find new …