Mathematics Commons^™

Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu

Mathematics Faculty Publications and Presentations

We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2-norm (Occam's Inversion) and L1-norm (TV Regularization). We forward model Rayleigh waves using a finite-element method instead of the conventional technique based on a recursion formula and root-finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam's Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not penalize discontinuities. …

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 H_n−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 …

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.

Positive Solutions For A System Of Singular Second Order Nonlocal Boundary Value Problems, Naseer Ahmad Asif, Paul W. Eloe, Rahmat Ali Khan

Mathematics Faculty Publications

Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type (see PDF for details) are obtained. The nonlinearities (see PDF) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. … An example is provided to illustrate the results.

Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth

Mathematics Faculty Publications

We study the existence of continuous periodic solutions of a neutral delay integral equation of advanced type. In the analysis we employ three fixed point theorems: Banach, Krasnosel'skii, and Krasnosel'skii-Schaefer. Krasnosel'skii-Schaefer fixed point theorem requires an a priori bound on all solutions. We employ a Liapunov type method to obtain such bound.

The Topology Of Incidence Pseudographs, Thomas R. James, Reinhard Klette

Mathematics Faculty Scholarship

Incidence pseudographs model a (re°exive and symmetric) inci- dence relation between sets of various dimensions, contained in a count- able family. Work by Klaus Voss in 1993 suggested that this general discrete model allows to introduce a topology, and some authors have done some studies into this direction in the past (also using alternative discrete models such as, for example, abstract complexes or orders on sets of cells). This paper provides a comprehensive overview about the topology of incidence pseudographs. This topology has various appli- cations, such as in modeling basic data in 2D or 3D digital picture analysis, or …

Curve Interpolation And Coding Theory, Darren B. Glass

Math Faculty Publications

Whether it is downloading files from the Internet, having conversations between cell phones, or sending information from a laptop to a printer, we often want to transmit data in situations where we need to worry about interference from other signals that may cause errors in the transmission. The branch of mathematics known as coding theory is dedicated to finding ways to tell when these are errors in transmission and, when possible, how to correct those errors. The goal of coding theory is to build as much redundancy as possible into a message without greatly increasing its length. [excerpt]

Review: Nontangential Limits In Pt(Μ)-Spaces And The Index Of Invariant Subgroups, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Review: Common Cyclic Vectors For Unitary Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Recognizing Graph Theoretic Properties With Polynomial Ideals, Jesus A. De Loera, Christopher J. Hillar, Peter N. Malkin, Mohamed Omar

All HMC Faculty Publications and Research

Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of the polynomial method and show how the algorithmic theory of polynomial ideals can be used to detect k-colorability, unique Hamiltonicity, and automorphism rigidity of graphs. Our techniques are diverse and involve Nullstellensatz certificates, linear algebra over finite fields, Gröbner bases, toric algebra, convex programming, and real algebraic geometry.

The Marshall Differential Analyzer: A Visual Interpretation Of Mathematics, Bonita A. Lawrence, Richard P. Merritt, Devon A. Tivener

Undergraduate Mathematics Day: Past Content

Mechanical integration is an idea dating back to the late 1800's discovered by James Thomson, brother of Lord Kelvin. This idea was then expanded to build a calculating machine, called a differential analyzer, by Vannevar Bush (M.I.T) in 1929. The Marshall University Differential Analyzer Team has followed in the footsteps of Dr. Bush and a gentleman named Dr. Arthur Porter, who was the first to build a differential analyzer in England when he was a student of Dr. Douglas Hartree. He built his machine of Meccano components, the British version of Erector Set. In the early days of Arthur Porter's …

Lifting Module Maps Between Different Noncommutative Domain Algebras, Jonathan Von Stroh

Electronic Theses and Dissertations

The classical Carathéodory interpolation problem is the following: let n be a natural number, a₀, a₁, . . . , a_N be complex numbers, and D the unit disk. When does there exist an analytic function F : D → C and complex numbers a_N+1, a_N+2, . . . such that F(z) = a₀ + a₁z + a₂z² + . . . + a_Nz^N + a_N+1z^N+1 + . . . and ||F||_∞ < 1? In 1967, Sarason used operator theory techniques to give an elegant solution to the Carathéodory interpolation problem. In 1968, Sz.-Nagy and Foias extended Sarason's approach into a commutant lifting theorem. Both the theorem and the technique of the proof have become standard tools in control theory. In particular, the commutant lifting theorem approach lends itself to a wide range of generalizations. This thesis concerns one such generalization.

Arias presented generalizations of the original …

Snort: A Combinatorial Game, Keiko Kakihara

Theses Digitization Project

This paper focuses on the game Snort, which is a combinatorial game on graphs. This paper will explore the characteristics of opposability through examples. More fully, we obtain some neccessary conditions for a graph to be opposable. Since an opposable graph guarantees a second player win, we examine graphs that result in a first player win.

Symmetric Generators Of Order 3, Stewart Contreras

Theses Digitization Project

The main purpose of this project is to construct finite homomorphic images of infinite semi-direct products.

Symmetric Generation, Dung Hoang Tri

Theses Digitization Project

In this thesis we construct finite homorphic images of infinite semi-direct products, 2*n : N, where 2*n is a free product of n copies the cyclic group of permutations on n letter.

An Investigation Of Kurosh's Theorem, Keith Anthony Earl

Theses Digitization Project

The purpose of this project will be an exposition of the Kurosh Theorem and the necessary and suffcient condition that A must be algebraic and satisfy a P.I. to be locally finite.

U-Singularity And T-Topos Theoretic Entropy, Goro C. Kato

Mathematics

We will give descriptions of u-singularities as we introduce the notion of t-topos theoretic entropies. The unifying methodology for a u-singularity is the universal mapping property of an inverse or direct limit. The qualitative, conceptual, and structural analyses of u-singularities are given in terms of inverse and direct limits of micro decompositions of a presheaf and coverings of an object in t-site in the theory of temporal topos.

Gronwall-Ouiang-Type Integral Inequalities On Time Scales, Ailian Liu, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We present several Gronwall-OuIang-type integral inequalities on time scales. Firstly, an OuIang inequality on time scales is discussed. Then we extend the Gronwall-type inequalities to multiple integrals. Some special cases of our results contain continuous Gronwall-type inequalities and their discrete analogues. Several examples are included to illustrate our results at the end.

Weyl-Titchmarsh Theory For Hamiltonian Dynamic Systems, Shurong Sun, Shaozhu Chen, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale T , which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for T= ℝ and T= ℤ within one theory and to explain the discrepancies between these two theories. This paper extends the Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian dynamic systems. These investigations are part of a larger program which includes the following: (i) M(λ) theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for …

Urcohomologies And Cohomologies Of N -Complexes, Naoya Hiramatsu, Goro Kato

Mathematics

For a general sequence of objects and morphisms, we construct two N-complexes. Then we can define cohomologies (i, k)-type of the N-complexes not only on a diagonal region but also in the triangular region. We obtain an invariant defined on a general sequence of objects and morphisms. For a short exact sequence of N-complexes, we get the associated long exact sequence generalizing the classical long exact sequence. Lastly, several properties of the vanishing cohomologies of N-complexes are given.