Mathematics Commons^™

A Kinetic Model For Semidilute Bacterial Suspensions, Shawn D. Ryan, Leonid Berlyand, Brian M. Haines, D. A. Karpeev

Mathematics and Statistics Faculty Publications

Suspensions of self-propelled microscopic particles, such as swimming bacteria, exhibit collective motion leading to remarkable experimentally observable macroscopic properties. Rigorous mathematical analysis of this emergent behavior can provide significant insight into the mechanisms behind these experimental observations; however, there are many theoretical questions remaining unanswered. In this paper, we study a coupled PDE/ODE system first introduced in the physics literature and used to investigate numerically the effective viscosity of a bacterial suspension. We then examine the kinetic theory associated with the coupled system, which is designed to capture the long-time behavior of a Stokesian suspension of point force dipoles (infinitesimal …

Integrable Models For Shallow Water With Energy Dependent Spectral Problems, Rossen Ivanov, Tony Lyons

Articles

We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependence on the spectral parameter. The corresponding hierarchy of integrable equations includes the Kaup–Boussinesq equation. We formulate the inverse problem as a Riemann–Hilbert problem with a Z₂ reduction group. The soliton solutions are explicitly obtained.

On Some New Inequalities For Convex Functions, Mevlüt Tunç

Turkish Journal of Mathematics

In the present paper we establish some new integral inequalities analogous to the well known Hadamard's inequality by using a fairly elementary analysis.

The Wright Message, 2012-2013, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- Department Head
-- Around Wright Hall
-- 2012 - 2013 Tenure-Stream Faculty
-- New Faculty
-- Retiring Faculty: Larry Leutzinger
-- In Memory of Bonnie Litwiller
-- John & Marla Peterson: Making an Impact
-- The 2012 Hari Shankar Lecture
-- Internal UNI Awards
-- Projects and Grants
-- Student Spotlight: Melinda McDowell & Duncan Wright
-- Recent winners of the Purple and Old Gold Award
-- Alumni Spotlight: Karla Digmann, Kamilla Svajgl, & Suzanne Shontz
-- Math Day 2012
-- Squigonometry
-- Student Organizations
-- News from KME
-- …

Verifying Harder's Conjecture For Classical And Siegel Modular Forms, Davia Sulon

Honors Theses

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form.

Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.

Unitary Equivalence To A Truncated Toeplitz Operator: Analytic Symbols, William T. Ross, Stephan Ramon Garcia, Daniel E. Poore

Department of Math & Statistics Faculty Publications

Unlike Toeplitz operators on H², truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension < 3 is unitarily equivalent to a direct sum of truncated Toeplitz operators.

Generalizing Amdahl’S Law For Power And Energy, Rong Ge, Kirk W. Cameron

Mathematics, Statistics and Computer Science Faculty Research and Publications

Extending Amdahl's law to identify optimal power-performance configurations requires considering the interactive effects of power, performance, and parallel overhead.

Categoricity And Topological Graphs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let X be a topological graph, with arcs joined only at end points. If Y is any locally connected metrizable compactum that is co-elementarily equivalent to X, then Y is homeomorphic to X. In particular, X and Y are homeomorphic if some lattice base for one is elementarily equivalent to some lattice base for the other.

A Zeta Function For Juggling Sequences, Carsten Elsner, Dominic Klyve, Erik R. Tou

Mathematics Faculty Scholarship

We give a new generalization of the Riemann zeta function to the set of b-ball juggling sequences. We develop several properties of this zeta function, noting among other things that it is rational in b^−s. We provide a meromorphic continuation of the juggling zeta function to the entire complex plane (except for a countable set of singularities) and completely enumerate its zeroes. For most values of b, we are able to show that the zeroes of the b-ball zeta function are located within a critical strip, which is closely analogous to that of the Riemann zeta function.

On \Alpha-Skew Mccoy Modules, Jian Cui, Jianlong Chen

Turkish Journal of Mathematics

Let \alpha be a ring endomorphism. Extending the notions of McCoy modules and \alpha-skew McCoy rings, we introduce the notion of \alpha-skew McCoy modules, which can also be regarded as a generalization of \alpha-skew Armendariz modules. A number of illustrative examples are given. Various properties of these modules are developed, and equivalent conditions for \alpha-skew McCoy modules are established. Furthermore, we study the relationship between a module and its polynomial module.

Generalization Of Some Properties Of Banach Algebras To Fundamental Locally Multiplicative Topological Algebras, Ali Zohri, Ali Jabbari

Turkish Journal of Mathematics

In this article we generalized some properties of Banach algebras, to a new class of topological algebras namely fundamental and fundamental locally multiplicative topological algebras (abbreviated by FLM). Also the new notion of sub-multiplicatively metrizable topological algebra is given and some well known spectral properties of Banach algebras are generalized to such kind of algebras.

Hamiltonian Sets Of Polygonal Paths In 4-Valent Spatial Graphs, Tilahun Abay Muche

USF Tampa Graduate Theses and Dissertations

Spatial graphs with 4–valent rigid vertices and two single valent endpoints, called assembly graphs, model DNA recombination processes that appear in certain species of ciliates. Recombined genes are modeled by certain types of paths in an assembly graph that make a ”oper pendicular ” turn at each 4–valent vertex of the graph called polygonal paths. The assembly number of an assembly graph is the minimum number of polygonal paths that visit each vertex exactly once. In particular, an assembly graph is called realizable if the graph has a Hamiltonian polygonal path.

An assembly graph ɣ^{^} obtained from a given …

Integrable Couplings Of The Kaup-Newell Soliton Hierarchy, Mengshu Zhang

USF Tampa Graduate Theses and Dissertations

By enlarging the spatial and temporal spectral problems within a certain Lie algebra, a hierarchy of integrable couplings of the Kaup-Newell soliton equations is constructed. The recursion operator of the resulting hierarchy of integrable couplings is explicitly computed. The integrability of the new coupling hierarchy is exhibited by showing the existence of infinitely many commuting symmetries.

Multi-Time Scales Stochastic Dynamic Processes: Modeling, Methods, Algorithms, Analysis, And Applications, Jean-Claude Pedjeu

USF Tampa Graduate Theses and Dissertations

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model is formulated and it leads to a system of multi-time scale stochastic differential equations. The classical Picard-Lindel\"{o}f successive approximations scheme is expended to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this generates to a problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations. To illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are exhibited. Without loss in generality, …

Stochastic Hybrid Dynamic Systems: Modeling, Estimation And Simulation, Daniel Siu

USF Tampa Graduate Theses and Dissertations

Stochastic hybrid dynamic systems that incorporate both continuous and discrete dynamics have been an area of great interest over the recent years. In view of applications, stochastic hybrid dynamic systems have been employed to diverse fields of studies, such as communication networks, air traffic management, and insurance risk models. The aim of the present study is to investigate properties of some classes of stochastic hybrid dynamic systems.

The class of stochastic hybrid dynamic systems investigated has random jumps driven by a non-homogeneous Poisson process and deterministic jumps triggered by hitting the boundary. Its real-valued continuous dynamic between jumps is described …

Simulation Study On Using Moment Functions For Sufficient Dimension Reduction , Lipu Tian

Dissertations, Master's Theses and Master's Reports - Open

No abstract provided.

Dual Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Dual numbers was first introduced by W.K. Clifford in 1873. This nice concept has lots of applications; to screw systems, modeling plane joint, iterative methods for displacement analysis of spatial mechanisms, inertial force analysis of spatial mechanisms etc. In this book the authors study dual numbers in a special way. The main aim of this book is to find rich sources of new elements g such that g2 = 0. The main sources of such new elements are from Zn, n a composite number. We give algebraic structures on them. This book is organized into six chapters. The final chapter …

Exploring The Extension Of Natural Operations On Intervals, Matrices And Complex Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

This book extends the natural operations defined on intervals, finite complex numbers and matrices. The intervals [a, b] are such that a ≤ b. But the natural class of intervals [a, b] introduced by the authors are such that a ≥ b or a need not be comparable with b. This way of defining natural class of intervals enables the authors to extend all the natural operations defined on reals to these natural class of intervals without any difficulty. Thus with these natural class of intervals working with interval matrices like stiffness matrices finding eigenvalues takes the same time as …

Continuous And Smooth Images Of Sets, Krzysztof Ciesielski

Faculty & Staff Scholarship

This note shows that if a subset S of R is such that some continuous function f from R to R has the property "f[S] contains a perfect set," then some infinitely many times differentiable function g (from R to R) has the same property. Moreover, if f[S] is nowhere dense, then the g can have the stronger property "g[S] is perfect." The last result is used to show that it is consistent with ZFC (the usual axioms of set theory) that for each subset S of R of cardinality continuum there exists an infinitely many times differentiable function …

Functions Continuous On Twice Differentiable Curves, Discontinuous On Large Sets, Krzysztof Ciesielski

Faculty & Staff Scholarship

We provide a simple construction of a function F:R²-->R discontinuous on a perfect set P, while having continuous restrictions F|C for all twice differentiable curves C. In particular, F is separately continuous and linearly continuous. While it has been known that the projection \pi[P] of any such set P onto a straight line must be meager, our construction allows \pi[P] to have arbitrarily large measure. In particular, P can have arbitrarily large 1-Hausdorff measure, which is the best possible result in this direction, since any such P has Hausdorff dimension at most 1.