Mathematics Commons^™

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.

Robust Stability And Optimality Conditions For Parametric Infinite And Semi-Infinite Programs, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

This paper primarily concerns the study of parametric problems of infinite and semi-infinite programming, where functional constraints are given by systems of infinitely many linear inequalities indexed by an arbitrary set T, where decision variables run over Banach (infinite programming) or finite-dimensional (semi-infinite case) spaces, and where objectives are generally described by nonsmooth and nonconvex cost functions. The parameter space of admissible perturbations in such problems is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set T is finite, this space is intrinsically infinite-dimensional (nonreflexive and nonseparable) of the l(infinity)-type. By using …

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

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.

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.

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 …

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 …

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. …

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.

Best Proximity Pairs For Upper Semicontinuous Set-Valued Maps In Hyperconvex Metric Spaces, Alireza Amini-Harandi, Ali P. Farajzadeh, Donal O'Regan, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

A best proximity pair for a set-valued map F : A → B with respect to a map g : A → A is defined, and new existence theorems of best proximity pairs for upper semicontinuous set-valued maps with respect to a homeomorphism are proved in hyperconvex metric spaces.

Prey Behavior, Age-Dependent Vulnerability, And Predation Rates, Susan Lingle, Alex Feldman, Mark S. Boyce, W. Finbarr Wilson

Mathematics Faculty Publications and Presentations

Variation in the temporal pattern of vulnerability can provide important insights into predator-prey relationships and the evolution of antipredator behavior. We illustrate these points with a system that has coyotes (Canis latrans) as a predator and two species of congeneric deer (Odocoileus spp.) as prey. The deer employ different antipredator tactics (aggressive defense vs. flight) that result in contrasting patterns of age-dependent vulnerability in their probability of being captured when encountered by coyotes.We use longterm survival data and a simple mathematical model to show that (1) species differences in age-dependent vulnerability are reflected in seasonal predation rates …

A Window On The Fifth Dimension, Frank A. Farris

Mathematics and Computer Science

Is there enough mathematics in your home? What visual aids do you keep on hand for that inevitable moment when guests want to know why you spend your life on mathematics? Feeling a lack in this area, I commissioned glass artist Hans Schepker to produce a window - from the fifth dimension? - based on an image that came up in my research. It turned out splendidly, and you can see it on the cover of this issue of MAA FOCUS.

Mathematics In The Mountains: The Park City Mathematics Institute, Andrew J. Bernoff

All HMC Faculty Publications and Research

It's noon. A Fields medalist, master high school teachers from the US and abroad, aspiring undergraduate and graduate students, gifted expositors of mathematics, and mathematical artists gather at tables under a tent. Lunch and so much more is served at these meetings of the minds.

Selective Screenability In Topological Groups, Liljana Babinkostova

Mathematics Faculty Publications and Presentations

We examine the selective screenability property in topological groups. In the metrizable case we also give characterizations of S_c(O_nbd,O) and Smirnov-S_c(O_nbd,O) in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We prove theorems stating conditions under which S_c(O_nbd,O) is preserved by products. Among metrizable groups we characterize the countable dimensional ones by a natural game.

Genetic Markers Of Igg Influence The Outcome Of Infection With Hepatitis C Virus, Janardan P. Pandey, Aryan M. Namboodiri, Yuqun Luo, Yuping Wu, Robert C. Elston, David L. Thomas, Hugo R. Rosen, James J. Goedert

Mathematics and Statistics Faculty Publications

We examined the role that immunoglobulin GM and KM allotypes—genetic markers of γ and κ chains, respectively—play in the outcome of hepatitis C virus (HCV) infection in white Americans. A total of 119 persons who had cleared HCV and 111 with persistent HCV infection were genotyped for the presence of several GM and KM determinants. Persistent HCV infection was more than three times as likely (odds ratio, 3.50; P = .01) in subjects who were carriers of the GM3 allele than in those who were noncarriers. These results show that particular GM alleles may be important determinants of the outcome …

Metric Regularity Of Mappings And Generalized Normals To Set Images, Boris S. Mordukhovich, Nguyen Mau Nam, Bingwu Wang

Mathematics Research Reports

The primary goal of this paper is to study some notions of normals to nonconvex sets in finite-dimensional and infinite-dimensional spaces and their images under single-valued and set-valued mappings. The main motivation for our study comes from variational analysis and optimization, where the problems under consideration play a crucial role in many important aspects of generalized differential calculus and applications. Our major results provide precise equality formulas (sometimes just efficient upper estimates) allowing us to compute generalized normals in various senses to direct and inverse images of nonconvex sets under single-valued and set-valued mappings between Banach spaces. The main tools …

Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li

Mathematics and Statistics Faculty Publications

In this article, we provide some asymptotic behaviors of linearized viscoelastic flows in a general two-dimensional domain with certain parameters small and the time variable large.

Ubi-App: A Ubiquitous Application For Universal Access From Handheld Devices, Shameem Ahmed, Moushumi Sharmin, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Universal access from a handheld device (such as a PDA, cell phone) at any time or anywhere is now a reality. Ubicomp Assistant (UA) (Sharmin et al. in Proceedings of the 21st annual ACM symposium on applied computing (ACM SAC 2006), Dijon, France, pp 1013–1017, 2006) is an integral service of MARKS (Sharmin et al. in Proceedings of the third international conference on information technology: new generations (ITNG 2006), Las Vegas, Nevada, USA, pp 306–313, 2006). It is a middleware developed for handheld devices, and has been designed to accommodate different types of users (e.g., education, healthcare, marketing, or business). …

Queen's Domination Using Border Squares And (A,B)-Restricted Domination, Anne Sinko, Peter J. Slater

Mathematics Faculty Publications

In this paper we introduce a variant on the long studied, highly entertaining, and very difficult problem of determining the domination number of the queen's chessboard graph, that is, determining how few queens are needed to protect all of the squares of a k by k chessboard. Motivated by the problem of minimum redundance domination, we consider the problem of determining how few queens restricted to squares on the border can be used to protect the entire chessboard. We give exact values of "border-queens" required for the k by k chessboard when 1≤k≤13. For the general case, we …

Contributions To Random Energy Models., Nabin Kumar Jana Dr.

Doctoral Theses

In this introductory chapter, we begin with a brief description of spin glasses in section 1. We are not physicists. The purpose of this section is to trace the history of the models. Section 2 gives a brief summary of the thesis and section 3 recalls certain known facts which will be used later in the thesis.Origin of the problem The models considered in this thesis have their origin in spin glass theory. Roughly, spin glass is a glassy state in a spin system or a disordered material exhibiting high magnetic frustration. The origin of this behavior can be either …

On Injectivity Of Quasiregular Mappings, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

We give sufficient conditions for a planar quasiregular mapping to be injective in terms of the range of the differential matrix.

On The Colored Jones Polynomial, Sutured Floer Homology, And Knot Floer Homology, J. Elisenda Grigsby, Stephan Wehrli

Mathematics - All Scholarship

Let K in S³ be a knot, and let K denote the preimage of K inside its double branched cover, Sigma(S³, K). We prove, for each integer n > 1, the existence of a spectral sequence from Khovanov's categorification of the reduced n-colored Jones polynomial of K (mirror of K) and whose E^infinity term is the knot Floer homology of (Sigma(S³,K),K) (when n odd) and to (S³, K # K) (when n even). A corollary of our result is that Khovanov's categorification of the reduced n-colored Jones polynomial detects the unknot whenever n …

Siegel’S Lemma Outside Of A Union Of Varieties, Lenny Fukshansky

CMC Faculty Publications and Research

Lecture given at the AMS Special Session on Number Theory, October 2008.

Unavoidable Subgraphs Of Colored Graphs, Jonathan Cutler, Balázs Montágh

Department of Mathematics Faculty Scholarship and Creative Works

A natural generalization of graph Ramsey theory is the study of unavoidable sub-graphs in large colored graphs. In this paper, we find a minimal family of unavoidable graphs in two-edge-colored graphs. Namely, for a positive even integer k, let Sk be the family of two-edge-colored graphs on k vertices such that one of the colors forms either two disjoint Kk / 2's or simply one Kk / 2. Bollobás conjectured that for all k and ε{lunate} > 0, there exists an n (k, ε{lunate}) such that if n ≥ n (k, ε{lunate}) then every two-edge-coloring of Kn, in which the density …

Contributions To Khovanov Homology, Stephan M. Wehrli

Mathematics - All Scholarship

Khovanov homology ist a new link invariant, discovered by M. Khovanov, and used by J. Rasmussen to give a combinatorial proof of the Milnor conjecture. In this thesis, we give examples of mutant links with different Khovanov homology. We prove that Khovanov's chain complex retracts to a subcomplex, whose generators are related to spanning trees of the Tait graph, and we exploit this result to investigate the structure of Khovanov homology for alternating knots. Further, we extend Rasmussen's invariant to links. Finally, we generalize Khovanov's categorifications of the colored Jones polynomial, and study conditions under which our categorifications are functorial …

Optimization Of Delay-Differential Inclusions Of Infinite Dimensions, Boris S. Mordukhovich, Dong Wang, Lianwen Wang

Mathematics Research Reports

No abstract provided.

Math/Compsci Newsletter, Fall 2008, Department Of Mathematics And Computer Science, Bridgewater State College

Department of Mathematics Newsletter

No abstract provided.

Tiling Proofs Of Recent Sum Identities Involving Pell Numbers, Arthur T. Benjamin, Sean S. Plott '08, James A. Sellers

All HMC Faculty Publications and Research

In a recent note, Santana and Diaz-Barrero proved a number of sum identities involving the well-known Pell numbers. Their proofs relied heavily on the Binet formula for the Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the results by interpreting the Pell numbers as enumerators of certain types of tilings. In turn, our proofs provide helpful insight for straightforward generalizations of a number of the identities.

Using Spreadsheets To Discover Meaning For Parameters In Nonlinear Models, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

Using spreadsheets one can develop an exploratory environment where mathematics students can develop their own understanding of the relationship between the parameters of commonly encountered families of functions (linear, logarithmic, exponential and power) and a natural interpretation of “rate of change” for those functions. The key to this understanding involves expanding the concept of rate of change to include percent changes. Through the use of the spreadsheet model, students can explore and easily determine which type of change is most natural for a given family of functions. This, in turn, provides a mechanism for interpreting the parameters of the function …