Impulsive Discontinuous Hyperbolic Partial Differential Equations Of Fractional Order On Banach Algebras,
2010
Florida Institute of Technology
Impulsive Discontinuous Hyperbolic Partial Differential Equations Of Fractional Order On Banach Algebras, Said Abbas, Ravi P. Agarwal, Mouffak Benchohra
Mathematics and System Engineering Faculty Publications
This article studies the existence of solutions and extremal solutions to partial hyperbolic differential equations of fractional order with impulses in Banach algebras under Lipschitz and Carathéodory conditions and certain monotonicity conditions.
Global Caccioppoli-Type And Poincar ´E Inequalities With Orlicz Norms,
2010
Florida Institute of Technology
Global Caccioppoli-Type And Poincar ´E Inequalities With Orlicz Norms, Ravi P. Agarwal, Shusen Ding
Mathematics and System Engineering Faculty Publications
We obtain global weighted Caccioppoli-type and Poincaré inequalities in terms of Orlicz norms for solutions to the nonhomogeneous A -harmonic equation d A(x,d)=B(x,d).
Some New Transformations For Bailey Pairs And Wp-Bailey Pairs,
2010
West Chester University of Pennsylvania
Some New Transformations For Bailey Pairs And Wp-Bailey Pairs, James Mclaughlin
Mathematics Faculty Publications
We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding relations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.
Foliations And Global Inversion,
2010
Trinity University
Foliations And Global Inversion, Eduardo C. Balreira
Mathematics Faculty Research
We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism f : M → Rn is bijective if and only if Hn−1(M) = 0 and the pre-image of every affine hyperplane is non-empty and acyclic. The proof is based on some geometric constructions involving foliations and tools from intersection theory. This topological result generalizes in finite dimensions the classical analytic theorem of Hadamard-Plastock, including its recent improvement by Nollet-Xavier. The main theorem also relates to a conjecture of the aforementioned authors, involving the well known …
Mathematics In Motion: Linear Systems Of Differential Equations On The Differential Analyzer,
2010
Marshall University
Mathematics In Motion: Linear Systems Of Differential Equations On The Differential Analyzer, Devon A. Tivener
Theses, Dissertations and Capstones
In this work, I will provide an introduction to the dierential analyzer, a machine designed to solve dierential equations through a process called mechanical integration. I will give a brief historical account of dierential analyzers of the past, and discuss the Marshall University Dierential Analyzer Project. The goal of this work is to provide an analysis of solutions of systems of dierential equations using a dierential analyzer. In particular, we are interested in the points at which these systems are in equilibrium and the behavior of solutions that start away from equilibrium. After giving a description of linear systems of …
Modeling Super-Spreading Events For Sars,
2010
Marshall University
Modeling Super-Spreading Events For Sars, Thembinkosi P. Mkhatshwa
Theses, Dissertations and Capstones
One of the intriguing characteristics of the 2003 severe acute respiratory syndrome (SARS) epidemics was the occurrence of super spreading events (SSEs). Super-spreading events for a specific infectious disease occur when infected individuals infect more than the average number of secondary cases. The understanding of these SSEs is critical to under- standing the spread of SARS. In this thesis, we present a modification of the basic SIR (Susceptible - Infected - Removed) disease model, an SIPR (Susceptible - Regular Infected - Super-spreader - Removed) model, which captures the effect of the SSEs.
On Residual Lifetimes Of K-Out-Of-N Systems With Nonidentical Components,
2010
Portland State University
On Residual Lifetimes Of K-Out-Of-N Systems With Nonidentical Components, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
In this article, mixture representations of survival functions of residual lifetimes of k-out-of-n systems are obtained when the components are independent but not necessarily identically distributed. Then we stochastically compare the residual lifetimes of k-out-of-n systems in one- and two-sample problems. In particular, the results extend some results in Li and Zhao [14], Khaledi and Shaked [13], Sadegh [17], Gurler and Bairamov [7] and Navarro, Balakrishnan, and Samaniego [16]. Applications in the proportional hazard rates model are presented as well.
Counting The Number Of Locally Convex Topologies On A Totally Ordered Finiate Set,
2010
Western Kentucky University
Counting The Number Of Locally Convex Topologies On A Totally Ordered Finiate Set, Thomas Tyler Clark
Mahurin Honors College Capstone Experience/Thesis Projects
We look at locally convex topologies on a totally ordered finite set. We determine a method of finding an upper bound on the number of such topologies on an n element. We show how this problem is related to Pascal’s Triangle and the Fibonacci Numbers. We explain an algorithm for determining the number of locally convex topologies consisting of nested intervals.
Derivatives Of The Dedekind Zeta Function Attached To A Complex Quadratic Field Extention,
2010
Western Kentucky University
Derivatives Of The Dedekind Zeta Function Attached To A Complex Quadratic Field Extention, Nathan Salazar
Mahurin Honors College Capstone Experience/Thesis Projects
The Riemann Zeta Function is a function of vital importance in the study of number theory and other branches of mathematics. This is primarily due to its intrinsic link with the prime numbers of the ring of integers. The value of the Riemann Zeta Function at 0 and the values of the first few derivatives at 0 have been determined by various mathematicians. Apostol obtained a closed expression for the nth derivative of the Riemann Zeta Function at 0 that generalized previously known results. For higher derivatives, his result is useful for numerical computations. The Dedekind Zeta Function is a …
Generalized Complex Hamiltonian Torus Actions: Examples And Constraints,
2010
Georgia Southern University
Generalized Complex Hamiltonian Torus Actions: Examples And Constraints, Thomas Baird, Yi Lin
Department of Mathematical Sciences Faculty Publications
Consider an effective Hamiltonian torus action T×M→M on a topologically twisted,generalized complex manifold M of dimension 2n. We prove that the rank(T)≤n−2 and that the topological twisting survives Hamiltonian reduction. We then construct a large new class of such actions satisfying rank(T)=n−2, using a surgery procedure on toric manifolds.
Fejér Polynomials And Control Of Nonlinear Discrete Systems,
2010
Odessa National Polytechnic University
Fejér Polynomials And Control Of Nonlinear Discrete Systems, Dmitriy Dmitrishin, Paul Hagelstein, Anna Khamitova, Anatolii Korenovskyi, Alexander M. Stokolos
Department of Mathematical Sciences Faculty Publications
We consider optimization problems associated to a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing T-cycles of a differentiable function f : R → R of the form x(k + 1) = f(x(k)) + u(k) where u(k) = (a1−1)f(x(k))+a2f(x(k−T))+· · ·+aN f(x(k−(N −1)T)) , with a1 + · · · + aN = 1. Following an approach of Morgul, we associate to each periodic orbit of f, N ∈ N, and a1, . . . …
Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity,
2010
University of Richmond
Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, William T. Ross, Joseph A. Cima, Stephan Ramon Garcia, Warren R. Wogen
Department of Math & Statistics Faculty Publications
A truncated Toeplitz operator Aᵩ : KƟ → KƟ is the compression of a Toeplitz operator Tᵩ : H2 → H2 to a model space KƟ := H2 ⊖ ƟH2. For Ɵ inner, let TƟ denote the set of all bounded truncated Toeplitz operators on KƟ. Our main result is a necessary and sufficient condition on inner functions Ɵ1 and Ɵ2 which guarantees that TƟ1 and TƟ2 are spatially isomorphic. (i.e., UTƟ1 = TƟ2 U for some unitary U : KƟ1 …
Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators,
2010
University of Richmond
Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen
Department of Math & Statistics Faculty Publications
We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.
The Norm Of A Truncated Toeplitz Operator,
2010
University of Richmond
The Norm Of A Truncated Toeplitz Operator, William T. Ross, Stephan Ramon Garcia
Department of Math & Statistics Faculty Publications
We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the H2 and H∞ norms of functions in model spaces.
[Introduction To] Ordinary And Particial Differential Equations: An Introduction To Dynamical Systems,
2010
University of Richmond
[Introduction To] Ordinary And Particial Differential Equations: An Introduction To Dynamical Systems, John W. Cain, Angela M. Reynolds
Bookshelf
Differential equations arise in a variety of contexts, some purely theoretical and some of practical interest. As you read this textbook, you will find that the qualitative and quantitative study of differential equations incorporates an elegant blend of linear algebra and advanced calculus. This book is intended for an advanced undergraduate course in differential equations. The reader should have already completed courses in linear algebra, multivariable calculus, and introductory differential equations.
Review: The Semi-Dynamical Reflection Equation: Solutions And Structure Matrices,
2010
Pomona College
Review: The Semi-Dynamical Reflection Equation: Solutions And Structure Matrices, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Support Varieties And Representation Type Of Small Quantum Groups,
2010
University of South Alabama
Support Varieties And Representation Type Of Small Quantum Groups, Jorg Feldvoss, Sarah Witherspoon
University Faculty and Staff Publications
In this paper, we provide a wildness criterion for any finite dimensional Hopf algebra with finitely generated cohomology. This generalizes a result of Farnsteiner to not necessarily cocommutative Hopf algebras over ground fields of arbitrary characteristic. Our proof uses the theory of support varieties for modules, one of the crucial ingredients being a tensor product property for some special modules. As an application, we prove a conjecture of Cibils stating that small quantum groups of rank at least two are wild.
Tme Volume 7, Number 1,
2010
University of Montana
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum,
2010
CUNY Kingsborough Community College
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 …
The Maximum Rectilinear Crossing Number Of The Petersen Graph,
2010
CUNY Kingsborough Community College
The Maximum Rectilinear Crossing Number Of The Petersen Graph, Elie Feder, Heiko Harborth, Steven Herzberg, Sheldon Klein
Publications and Research
We prove that the maximum rectilinear crossing number of the Petersen graph is 49. First, we illustrate a picture of the Petersen graph with 49 crossings to prove the lower bound. We then prove that this bound is sharp by carefully analyzing the ten Cs's which occur in the Petersen graph and their properties.
