Mathematics Commons^™

Numerical Methods For Fluid-Structure Interaction - A Review, Gene Hou, Jin Wang, Anita Layton

Mechanical & Aerospace Engineering Faculty Publications

The interactions between incompressible fluid flows and immersed structures are nonlinear multi-physics phenomena that have applications to a wide range of scientific and engineering disciplines. In this article, we review representative numerical-methods based on conforming and non-conforming meshes that are currently available for computing fluid-structure interaction problems, with an emphasis on some of the recent developments in the field. A goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interactions

Interpolating Blaschke Products And Angular Derivatives, Eva A. Gallardo-Gutierrez, Pamela Gorkin

Faculty Journal Articles

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H-infinity[(b) over bar : b has finite angular derivative everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Natural Product Xn On Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce a new product on matrices called the natural product. ...

Thus by introducing natural product we can find the product of column matrices and product of two rectangular matrices of same order. Further this product is more natural which is just identical with addition replaced by multiplication on these matrices. Another fact about natural product is this enables the product of any two super matrices of same order and with same type of partition. We see on supermatrices products cannot be defined easily which prevents from having any nice algebraic structure on the collection …

On A Pair Of Identities From Ramanujan's Lost Notebook, James Mclaughlin, Andrew Sills

Mathematics Faculty Publications

Using a pair of two variable series-product identities recorded by Ramanujan in the lost notebook as inspiration, we find some new identities of similar type. Each identity immediately implies an infinite family of Rogers-Ramanujan type identities, some of which are well-known identities from the literature. We also use these identities to derive some general identities for integer partitions.

A Reciprocity Relation For Wp-Bailey Pairs, James Mclaughlin, Peter Zimmer

Mathematics Faculty Publications

We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Other consequences include new proofs of some classical identities due to Jacobi, Ramanujan and others, and indeed extend these identities to identities involving particular specializations of arbitrary WP-Bailey pairs.

A Hardy-Ramanujan-Rademacher-Type Formula For (R,S)-Regular Partitions, James Mclaughlin, Scott Parsell

Mathematics Faculty Publications

Let pr,s(n) denote the number of partitions of a positive integer n into parts containing no multiples of r or s, where r > 1 and s > 1 are square-free, relatively prime integers. We use classical methods to derive a Hardy-Ramanujan-Rademacher-type infinite series for pr,s(n).

Quantum Algorithms For: Quantum Phase Estimation, Approximation Of The Tutte Polynomial And Black-Box Structures, Hamad Ahmadi

Electronic Theses and Dissertations

In this dissertation, we investigate three different problems in the field of Quantum computation. First, we discuss the quantum complexity of evaluating the Tutte polynomial of a planar graph. Furthermore, we devise a new quantum algorithm for approximating the phase of a unitary matrix. Finally, we provide quantum tools that can be utilized to extract the structure of black-box modules and algebras. While quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT) ) is highly constrained by the requirement of high-precision controlled phase shift …

On The Class Rsi Of J-Contractive Functions Intertwining Solutions Of Linear Differential Equations, Daniel Alpay, Andrey Melnikov, Victor Vinnikov

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we extend and solve in the class of functions RSI mentioned in the title, a number of problems originally set for the class RS of rational functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned self-adjoint matrix. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on the one-to-one correspondence between elements in a given subclass of RSI and elements in RS. Another important tool in the arguments is a new result pertaining to the classical tangential …

Cotorsion Pairs In C(R-Mod), Diego Bravo, Edgar E. Enochs, Alina Iacob, Overtoun M. G. Jenda, Juan Rada

Mathematical Sciences: Faculty Publications

In [8] Salce introduced the notion of a co-torsion pair (A, B) in the category of abelian groups. But his definitions and basic results carry over to more general abelian categories and have proved useful in a variety of settings. In this article we will consider complete cotorsion pairs (C, D)in the category C(R-Mod) of complexes of left R-modules over some ring R.If(C, D) is such a pair, and if C is closed un-der taking suspensions, we will show when we regard K(C) and K(D) as subcategories of the homotopy category K(R-Mod), then the embedding functors K(C) → K(R-Mod) and …

Weighted Generalized Beta Distribution Of The Second Kind, Yuan Ye, Broderick O. Oluyede, Marvis Pararai

Mathematical Sciences: Faculty Publications

In this paper, a new class of weighted generalized beta distribution of the second kind (WGB2) is presented. The construction makes use of the "conservability approach" which includes the size or length-biased distribution as a special case. The class of WGB2 is used as descriptive models for the distribution of income. The results that are presented generalizes the generalized beta distribution of second kind (GB2). The properties of these distributions including behavior of hazard functions, moments, variance, coefficients of variation, skewness and kurtosis are obtained. The moments of other weighted distributions that are related to WGB2 are obtained. Other important …

Rational Approximation On Compact Nowhere Dense Sets, Christopher Mattingly

Theses and Dissertations--Mathematics

For a compact, nowhere dense set X in the complex plane, C, define R^p(X) as the closure of the rational functions with poles off X in L^p(X, dA). It is well known that for 1 ≤ p < 2, R^p(X) = L^p(X) . Although density may not be achieved for p > 2, there exists a set X so that R^p(X) = L^p(X) for p up to a given number greater than 2 but not after. Additionally, when p > 2 we shall establish that the support of the annihiliating and …

Proof-Of-Concept For A Green Energy Linear Program For Optimizing Deployments, James M. Taylor, Betty Love

Mathematics Faculty Proceedings & Presentations

The US military has spent billions of dollars and sacrificed many lives in the effort to bring electrical power services and the fuel that drives the generators to forward-deployed bases in Afghanistan and Iraq over the past 10 years. In an effort to reduce some of these tremendous costs, the US military has considered using alternative energy sources to generate electricity and reduce costs and exposure of fuel truck convoys. While some research [10] has used detailed software packages to model the electrical demand and renewable energy production tradeoffs in this environment, the impact of operational constraints is not readily …

Numerical Ranges Of Composition Operators With Inner Symbols, Valentin Matache

Mathematics Faculty Publications

Operators on function paces acting by composition to the right with a fixed self-map φ of some set are called composition operators with the symbol φ. In this paper, composition operators on the Hilbert Hardy space over the unit disk are considered. The numerical ranges of composition operators with inner symbol of parabolic automorphic type of hyperbolic type are shown to be circular.

High Order Les For Supersonic Ramp Flow Control With Mvg, Yonghua Yan

Mathematics Dissertations - Archive

An implicitly implemented large eddy simulation by using the fifth order bandwidth-optimized WENO scheme is applied to make comprehensive studies on ramp flows with and without control at Mach 2.5 and Re=5760. Flow control in the form of microramp vortex generators (MVG) is applied. The results show that MVG can distinctly reduce the separation zone at the ramp corner and lower the boundary layer shape factor under the condition of the computation. A series of new findings are obtained about the MVG-ramp flow including the three-dimensional vortex structure generated by MVG. The mechanism about the formation vortex ring structure and …

Effects Of Vector Migration On Sylvatic Trypanosoma Cruzi Transmission, Britnee A. Crawford

Mathematics Dissertations - Archive

Vector-borne diseases have had a major impact on global health concerns since their discovery in the 1800's. A vector-borne disease is one transmitted to human or animal host via an invertebrate vector (usually an insect). Chagas' disease, caused by the parasite Trypanosoma cruzi, is transmitted via insect vectors from the Triatoma family. Although human infection with Chagas' is of importance, the disease is maintained in sylvatic (in the wild) transmission cycles. This study examines the effects of vector migration on the spread of T. cruzi in certain sylvatic cycles in the southeastern U.S. and Mexico from several angles. First, a …

Coming Out Of The Dungeon: Mathematics And Role-Playing Games, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

After hiding it for many years, I have a confession to make.

Throughout middle school and high school my friends and I would gather almost every weekend, spending hours using numbers, probability, and optimization to build models that we could use to simulate almost anything.

That’s right. My big secret is simple. I was a high school mathematical modeler.

Of course, our weekend mathematical models didn’t bear any direct relationship to the models we explored in our mathematics and science classes. You would probably not even recognize our regular gatherings as mathematical exercises. If you looked into the room, you’d …

Minimality And Duality Of Tail-Biting Trellises For Linear Codes, Elizabeth A. Weaver

Theses and Dissertations--Mathematics

Codes can be represented by edge-labeled directed graphs called trellises, which are used in decoding with the Viterbi algorithm. We will first examine the well-known product construction for trellises and present an algorithm for recovering the factors of a given trellis. To maximize efficiency, trellises that are minimal in a certain sense are desired. It was shown by Koetter and Vardy that one can produce all minimal tail-biting trellises for a code by looking at a special set of generators for a code. These generators along with a set of spans comprise what is called a characteristic pair, and we …

Hilbert Polynomials And Strongly Stable Ideals, Dennis Moore

Theses and Dissertations--Mathematics

Strongly stable ideals are important in algebraic geometry, commutative algebra, and combinatorics. Prompted, for example, by combinatorial approaches for studying Hilbert schemes and the existence of maximal total Betti numbers among saturated ideals with a given Hilbert polynomial, three algorithms are presented. Each of these algorithms produces all strongly stable ideals with some prescribed property: the saturated strongly stable ideals with a given Hilbert polynomial, the almost lexsegment ideals with a given Hilbert polynomial, and the saturated strongly stable ideals with a given Hilbert function. Bounds for the complexity of our algorithms are included. Also included are some applications for …

Analytic And Topological Combinatorics Of Partition Posets And Permutations, Jiyoon Jung

Theses and Dissertations--Mathematics

In this dissertation we first study partition posets and their topology. For each composition c we show that the order complex of the poset of pointed set partitions is a wedge of spheres of the same dimension with the multiplicity given by the number of permutations with descent composition c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module of a border strip associated to the composition. We also study the filter of pointed set partitions generated by knapsack integer partitions. In the second half of this dissertation we study descent …

The Hydrodynamic Flow Of Nematic Liquid Crystals In R3, Jay Lawrence Hineman

Theses and Dissertations--Mathematics

This manuscript demonstrates the well-posedness (existence, uniqueness, and regularity of solutions) of the Cauchy problem for simplified equations of nematic liquid crystal hydrodynamic flow in three dimensions for initial data that is uniformly locally L³(R³) integrable (L³_U(R³)). The equations examined are a simplified version of the equations derived by Ericksen and Leslie. Background on the continuum theory of nematic liquid crystals and their flow is provided as are explanations of the related mathematical literature for nematic liquid crystals and the Navier–Stokes equations.

2012 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

A Meshless Numerical Solution Of The Family Of Generalized Fifth-Order Korteweg-De Vries Equations, Syed Tauseef Mohyud-Din, Elham Negahdary, Muhammad Usman

Mathematics Faculty Publications

In this paper we present a numerical solution of a family of generalized fifth-order Korteweg-de Vries equations using a meshless method of lines. This method uses radial basis functions for spatial derivatives and Runge-Kutta method as a time integrator. This method exhibits high accuracy as seen from the comparison with the exact solutions.

Existence And Uniqueness Conditions For A Class Of (K+4j)-Point N-Th Order Boundary Value Problems, Paul W. Eloe, Johnny Henderson, Rahmat Ali Khan

Mathematics Faculty Publications

No abstract provided.

A Leggett-Williams Type Theorem Applied To A Fourth Order Problem, Richard Avery, Paul Eloe, Johnny Henderson

Mathematics Faculty Publications

We apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a fourth order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach spstce. Inequalities that extend the notion of concavity to fourth order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.

Bounded Solutions Of Almost Linear Volterra Equations, Muhammad Islam, Youssef Raffoul

Mathematics Faculty Publications

Fixed point theorem of Krasnosel’skii is used as the primary mathematical tool to study the boundedness of solutions of certain Volterra type equations. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold.

Creating Macroscopes With Technology And Analytics: New Possibilities In Our Lives – The Important Role Of Tomorrow’S Mathematics Professionals (Abstract), Lilian S. Wu

Kenneth C. Schraut Memorial Lectures

Our world is increasingly computerized, interconnected, and instrumented with sensors. Massive amounts of data are being captured in computer systems about our natural environment and man-made engineered structures, processes, and systems. But it is necessary to make sense out of all this data. With new computer methods computers can in effect become macroscopes, enabling us to see the world portrayed by our data.

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

Kenneth C. Schraut Memorial Lectures

No abstract provided.

On Hall Magnetohydrodynamics: X-Type Neutral Point And Parker Problem, Kyle Reger

Electronic Theses and Dissertations

The framework for the Hall magnetohydrodynamic (MHD) model for plasma physics is built up from kinetic theory and used to analytically solve problems of interest in the field. The Hall MHD model describes fast magnetic reconnection processes in space and laboratory plasmas. Specifically, the magnetic reconnection process at an X-type neutral point, where current sheets form and store enormous amounts of magnetic energy which is later released as magnetic storms when the sheets break up, is investigated. The phenomena of magnetic flux pile-up driving the merging of antiparallel magnetic fields at an ion stagnation-point flow in a thin current sheet, …

Improving Student Learning In Undergraduate Mathematics, Gabrielle Rejniak

Electronic Theses and Dissertations

The goal of this study was to investigate ways of improving student learning, par- ticularly conceptual understanding, in undergraduate mathematics courses. This study focused on two areas: course design and animation. The methods of study were the following: Assessing the improvement of student conceptual understanding as a result of team project-based learning, individual inquiry-based learning and the modi ed empo- rium model; and Assessing the impact of animated videos on student learning with the emphasis on concepts. For the first part of our study (impact of course design on student conceptual understanding) we began by comparing the following three groups …

Instability In A Generalized Keller–Segel Model, Patrick De Leenheer, Jay Gopalakrishnan, Erica Zuhr

Mathematics and Statistics Faculty Publications and Presentations

We present a generalized Keller–Segel model where an arbitrary number of chemical compounds react, some of which are produced by a species, and one of which is a chemoattractant for the species. To investigate the stability of homogeneous stationary states of this generalized model, we consider the eigenvalues of a linearized system. We are able to reduce this infinite dimensional eigenproblem to a parametrized finite dimensional eigenproblem. By matrix theoretic tools, we then provide easily verifiable sufficient conditions for destabilizing the homogeneous stationary states. In particular, one of the sufficient conditions is that the chemotactic feedback is sufficiently strong. Although …