Physical Sciences and Mathematics Commons^™

Preface

Communications on Stochastic Analysis

No abstract provided.

General Equilibrium Asset Pricing Under Regime Switching, Robert J Elliott, Hong Miao, Jin Yu

Communications on Stochastic Analysis

No abstract provided.

A Decomposition Of Multiple Wiener Integrals By The Lévy Process And Lévy Laplacian, Atsushi Ishikawa

Communications on Stochastic Analysis

No abstract provided.

Errata: Existence And Uniqueness Of Solutions To The Backward Stochastic Lorenz System (Cosa, Vol. 1, No. 3 (2007) 473–483) [Mr2403863], P Sundar, Hong Yin

Communications on Stochastic Analysis

No abstract provided.

Limits Of Bifractional Brownian Noises, Makoto Maejima, Ciprian A Tudor

Communications on Stochastic Analysis

No abstract provided.

A Class Of Extreme X-Harmonic Functions, John Verzani

Communications on Stochastic Analysis

No abstract provided.

Applicability Of Multiplicative Renormalization Method For A Certain Function, Izumi Kubo, Hui-Hsiung Kuo, Suat Namli

Communications on Stochastic Analysis

No abstract provided.

An Extension Of The Itô Integral, Wided Ayed, Hui-Hsiung Kuo

Communications on Stochastic Analysis

No abstract provided.

Locally Integrable Processes With Respect To Locally Additive Summable Processes, Oana Mocioalca

Communications on Stochastic Analysis

No abstract provided.

Interacting Fock Space Versus Full Fock Module, Luigi Accardi, Michael Skeide

Communications on Stochastic Analysis

No abstract provided.

Distribution And Propagation Properties Of Superprocesses With General Branching Mechanisms, Zenghu Li, Xiaowen Zhou

Communications on Stochastic Analysis

No abstract provided.

Optimal Hedging Of Path-Dependent Options In Discrete Time Incomplete Market, Norman Josephy, Lucy Kimball, Victoria Steblovskaya

Communications on Stochastic Analysis

No abstract provided.

A Uniformly Dissipative Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang (Wendy) Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The purpose of this short communication is to announce that a class of numerical schemes, uniformly dissipative approximations, which uniformly preserve the dissipativity of the continuous infinite dimensional dissipative complex (chaotic) systems possess desirable properties in terms of approximating stationary statistics properties. in particular, the stationary statistical properties of these uniformly dissipative schemes converge to those of the continuous system at vanishing mesh size. the idea is illustrated on the infinite Prandtl number model for convection and semi-discretization in time, although the general strategy works for a broad class of dissipative complex systems and fully discretized approximations. as far as …

A Semi-Implicit Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We propose a semisecret in time semi-implicit numerical scheme for the infinite Prandtl model for convection. Besides the usual finite time convergence, this scheme enjoys the additional highly desirable feature that the stationary statistical properties of the scheme converge to those of the infinite Prandtl number model at vanishing time stop. One of the key characteristics of the scheme is that it preserves the dissipativity of the infinite Prandtl number model uniformly in terms of the time stop. So far as wo know, this is the first rigorous result on convergence of stationary statistical properties of numerical schemes for infinite …

On A-Ary Subdivision For Curve Design Ii. 3-Point And 5-Point Interpolatory Schemes, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

The a-ary 3-point and 5-point interpolatery subdivision schemes for curve design are introduced for arbitrary odd integer a greater than or equal to 3. These new schemes further extend the family of the classical 4- and 6-point interpolatory schemes.

The Equivariant Chow Rings Of Quot Schemes, T. Braden, Linda Chen, F. Sottile

Mathematics & Statistics Faculty Works

We give a presentation for the (integral) torus-equivariant Chow ring of the quot scheme, a smooth compactification of the space of rational curves of degree d in the Grassmannian. For this presentation, we refine Evain's extension of the method of Goresky, Kottwitz, and MacPherson to express the torus-equivariant Chow ring in terms of the torus-fixed points and explicit relations coming from the geometry of families of torus-invariant curves. As part of this calculation, we give a complete description of the torus-invariant curves on the quot scheme and show that each family is a product of projective spaces.

High School Mathematics Teachers' Evolving Understanding Of Comparing Distributions, Sandra R. Madden

Dissertations

Statistics has achieved a position of status in the secondary curriculum (College Board, 2006b; Franklin et al., 2007; NCTM, 2000) and understanding of statistics is essential for high school mathematics teachers if they are to engage students in thoughtful pursuit of statistical ideas. High school teachers typically are ill-prepared in the area of statistics (Ben-Zvi & Garfield, 2004a; CBMS, 2001; Shaughnessy, 1992, 2007). Using methods of design research, this study investigated 56 high school mathematics teachers' understanding of the statistical concept ofcomparing distributions and demonstrated that a modest four-day, statistics-oriented, technology-rich, professional development program may significantly improve teachers' understanding. …

Darboux Integrability Of Wave Maps Into 2-Dimensional Riemannian Manifolds, Robert Ream

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The harmonic map equations can be represented geometrically as an exterior differential system (EDS), ε. Using this representation we study the harmonic maps from 2D Minkowski space into 2D Riemannian manifolds. These are also known as wave maps. In this case, E is invariant under conformal transformations of Minkowski space. The quotient of ε by these conformal transformations, E/G, is an s=0 hyperbolic system.

The main result of our study is that the prolonged EDS, ε^(k), is Darboux integrable if and only if the prolonged quotient EDS, ε^(k+1), is Darboux integrable. We also find invariants determining …

A Note On Hamel Bases, Jeremy S. Higdon

Masters Theses

The purpose of this paper is to discuss certain properties of Hamel bases. In particular, we reprove and generalize a theorem of R. Mabry (Aequations Mathematicae 71 (2006) p. 294-299) on the non-existence of nontrivial Hamel bases closed under multiplication.

Optimal Control Of Epidemic Models Involving Rabies And West Nile Viruses, Timothy Joseph Clayton

Doctoral Dissertations

This research considers the application of Optimal Control theory to minimize the spread of viral infections in disease models. The population models under consideration are systems of ordinary differential equations and represent epidemics arising due to either rabies or West Nile virus. Optimal control strategies are analyzed using Pontryagin’s Maximum Principle and illustrated based upon computer simulations.

The first model describes a population of raccoons and its interaction with the rabies virus, thus dividing the animals into four classes: susceptible, exposed, immune, and recovered (SEIR). The model includes a birth pulse during the spring of the year and …

The Process Of Tracking In Mathematics In Box Elder School District, Megan Haramoto Bushnell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Educational policymakers have used tracking to instruct students in a variety of subjects, including mathematics. Tracking, which has also been called ability grouping, is a process by which students in the same grade are placed into different classes based on academic ability. Few educators and sociologists have looked at the process by which students are placed in different mathematics tracks. The research design of this study focused on accumulating, evaluating, and reporting the understanding and observations of 12 teachers and 4 counselors as they discussed their knowledge and involvement in the mathematics placement procedures from the intermediate and middle school …

Biochemical Reactions Instigating Vision – Parameter Sensitivity Analysis, Sophonie Ketcha Tchoua

Masters Theses

The purpose of this work is to investigate the sensitivity of parameters involved in a cascade of biochemical reactions occurring in photoreceptor cells in the retina of the eye. This cascade constitutes the first stage of the elaborate process of vision, by which light captured in a photoreceptor generates an electrical signal. It is this signal that travels to the brain enabling vision.

Sensitivity on parameters was performed on an ODE model of the biochemical cascade using two methods. One method used SimLab, a statistical sensitivity analysis program. We found that there are at most five important parameters out of …

Tree-Like Spaces With The Fixed-Point Property, Realized As Inverse Limits Of Special Finite Trees, Jennifer Katherine Aust

Masters Theses

In this paper, we explore some properties of inverse limit sequences on sub-spaces of Euclidean n-space. We address some well-known examples, in particular the example by David Bellamy of the "tree-like" continuum that does not have the fixed-point property. We highlight some spaces with the fixed-point property that are between snake-like continua and Bellamy's example in their level of complexity. Specifically, we prove the fixed-point property for inverse limits of limit sequences on the unit interval and on the n-ad (in two configurations), and for inverse limits that can be mapped via a continuous function with small point pre-images to …

Do The Coefficients Of A Modular Form Really "Encode Arithmetic Data"?, Ken Mcmurdy, Hari Ravindran

Mathematical Sciences Technical Reports (MSTR)

Language and terminology are so critical to the understanding of modern math- ematics that it is often difficult for even very good mathematicians from different fields to discuss their work in any detail. As a result, common phrases often evolve within each discipline which attempt to capture the avor of some impor- tant idea while avoiding technicality and jargon. For example, when algebraic number theorists are asked why they are so interested in modular forms, it has become common to say with enthusiasm that the coefficients of a modular form "encode arithmetic data". If pressed further, one might go on …

Dynamics Of Quasiconformal Fields, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

A uniqueness theorem is established for autonomous systems of ODEs, x= f(x), where f is a Sobolev vector field with additional geometric structure, such as delta-monoticity or reduced quasiconformality. Specifically, through every non-critical point of f there passes a unique integral curve.

Transformation Groups And Duality In The Analysis Of Musical Structure, Janine Du Plessis

Mathematics Theses

One goal of music theory is to describe the resources of a pitch system. Traditionally, the study of pitch intervals was done using frequency ratios of the powers of small integers. Modern mathematical music theory offers an independent way of understanding the pitch system by considering intervals as transformations. This thesis takes advantage of the historical emergence of algebraic structures in musicology and, in the spirit of transformational theory, treats operations that form mathematical groups. Aspects of Neo-Riemannian theory are explored and developed, in particular the T/I and PLR groups as dual. Pitch class spaces, such as 12, can also …

Factorization Of Quasiseparable Matrices, Paul D. Johnson

Mathematics Theses

This paper investigates some of the ideas and algorithms developed for exploiting the structure of quasiseparable matrices. The case of purely scalar generators is considered initially. The process by which a quasiseparable matrix is represented as the product of matrices comprised of its generators is explained. This is done clearly in the scalar case, but may be extended to block generators. The complete factoring approach is then considered. This consists of two stages: inner-outer factorization followed by inner-coprime factorization. Finally, the stability of the algorithm is investigated. The algorithm is used to factor various quasiseparable matrices R created first using …

Examination Of Initialization Techniques For Nonnegative Matrix Factorization, John Frederic

Mathematics Theses

While much research has been done regarding different Nonnegative Matrix Factorization (NMF) algorithms, less time has been spent looking at initialization techniques. In this thesis, four different initializations are considered. After a brief discussion of NMF, the four initializations are described and each one is independently examined, followed by a comparison of the techniques. Next, each initialization's performance is investigated with respect to the changes in the size of the data set. Finally, a method by which smaller data sets may be used to determine how to treat larger data sets is examined.

An Analysis Of Fourier Transform Infrared Spectroscopy Data To Predict Herpes Simplex Virus 1 Infection, Patrick D. Champion

Mathematics Theses

The purpose of this analysis is to evaluate the usefulness of Fourier Transform Infrared (FTIR) spectroscopy in the detection of Herpes Simplex Virus 1 (hsv1) infection at an early stage. The raw absorption values were standardized to eliminate inter-sampling error. Wilcoxon-Mann-Whitney (WMW) statistic's Z score was calculated to select significant spectral regions. Partial least squares modeling was performed because of multicollinearity. Kolmogorov-Smirnov statistic showed models for healthy tissues from different time groups were not from same distribution. The additional 24 hour dataset was evaluated using the following methods. Variables were selected by WMW Z score. Difference of Composites statistic, DC, …

Semi-Parametric Inference For The Partial Area Under The Roc Curve, Fangfang Sun

Mathematics Theses

Diagnostic tests are central in the field of modern medicine. One of the main factors for interpreting a diagnostic test is the discriminatory accuracy. For a continuous-scale diagnostic test, the area under the receiver operating characteristic (ROC) curve, AUC, is a useful one-number summary index for the diagnostic accuracy of the test. When only a particular region of the ROC curve would be of interest, the partial AUC (pAUC) is a more appropriate index for the diagnostic accuracy. In this thesis, we develop seven confidence intervals for the pAUC under the semi-parametric models for the diseased and non-diseased populations by …