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2008

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Articles 1 - 30 of 351

Full-Text Articles in Mathematics

Best Proximity Pairs Theorems For Continuous Set-Valued Maps, Alireza Amini-Harandi, Ali P. Farajzadeh, Donal O'Regan, Ravi P. Agarwal Dec 2008

Best Proximity Pairs Theorems For Continuous Set-Valued Maps, 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 set-valued map G : A -○ A is defined, and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive retract metric spaces. As an application, we derive a coincidence point theorem. Copyright © 2008 A. Amini-Harandi et al.

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Topological Structures In The Equities Market Network, Gregory Leibon, Scott Pauls, Daniel Rockmore, Robert Savell Dec 2008

Topological Structures In The Equities Market Network, Gregory Leibon, Scott Pauls, Daniel Rockmore, Robert Savell

Dartmouth Scholarship

We present a new method for articulating scale-dependent topological descriptions of the network structure inherent in many complex systems. The technique is based on “partition decoupled null models,” a new class of null models that incorporate the interaction of clustered partitions into a random model and generalize the Gaussian ensemble. As an application, we analyze a correlation matrix derived from 4 years of close prices of equities in the New York Stock Exchange (NYSE) and National Association of Securities Dealers Automated Quotation (NASDAQ). In this example, we expose (i) a natural structure composed of 2 interacting partitions of …

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Coincidence Point, Best Approximation, And Best Proximity Theorems For Condensing Set-Valued Maps In Hyperconvex Metric Spaces, Alireza Amini-Harandi, Ali P. Farajzadeh, Ravi P. Agarwal, Donal O'Regan Dec 2008

Coincidence Point, Best Approximation, And Best Proximity Theorems For Condensing Set-Valued Maps In Hyperconvex Metric Spaces, Alireza Amini-Harandi, Ali P. Farajzadeh, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

In hyperconvex metric spaces, we first present a coincidence point theorem for condensing set-valued self-maps. Then we consider the best approximation problem and the best proximity problem for set-valued mappings that are condensing. As an application, we derive a coincidence point theorem for nonself-condensing set-valued maps.

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A Trust-Based Secure Service Discovery (Tssd) Model For Pervasive Computing, Sheikh Iqbal Ahamed, Moushumi Sharmin Dec 2008

A Trust-Based Secure Service Discovery (Tssd) Model For Pervasive Computing, Sheikh Iqbal Ahamed, Moushumi Sharmin

Mathematics, Statistics and Computer Science Faculty Research and Publications

To cope with the challenges posed by device capacity and capability, and also the nature of ad hoc networks, a Service discovery model is needed that can resolve security and privacy issues with simple solutions. The use of complex algorithms and powerful fixed infrastructure is infeasible due to the volatile nature of pervasive environment and tiny pervasive devices. In this paper, we present a trust-based secure Service discovery model, TSSD (trust-based secure service discovery) for a truly pervasive environment. Our model is a hybrid one that allows both secure and non-secure discovery of services. This model allows Service discovery and …

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Delay-Induced Destabilization Of Entrainment Of Nerve Impulses On Ephaptically Coupled Nerve Fibers, Evangelos A. Coutsias, Mohit H. Adhikari, John K. Mciver Dec 2008

Delay-Induced Destabilization Of Entrainment Of Nerve Impulses On Ephaptically Coupled Nerve Fibers, Evangelos A. Coutsias, Mohit H. Adhikari, John K. Mciver

Branch Mathematics and Statistics Faculty and Staff Publications

We study the effect of delay on the synchronization of two nerve impulses traveling along two ephaptically coupled, unmyelinated nerve fibers. The system is modeled as a pair of delay-coupled Fitzhugh-Nagumo equations. A multiple-scale perturbation approach is used for the analysis of these equations in the limit of weak coupling. In the absence of delay, two pulses with identical speeds are shown to be entrained precisely. However, as the delay is increased beyond a critical value, we show that this precise entrainment becomes unstable. We make quantitative estimates for the actual values of delay at which this can occur in …

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Unfolding Convex Polyhedra Via Quasigeodesic Star Unfoldings, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu Dec 2008

Unfolding Convex Polyhedra Via Quasigeodesic Star Unfoldings, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu

Computer Science: Faculty Publications

We extend the notion of a star unfolding to be based on a simple quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron P to a simple, planar polygon: shortest paths from all vertices of P to Q are cut, and all but one segment of Q is cut.

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Singularities Of Hinge Structures, Ciprian Borcea, Ileana Streinu Dec 2008

Singularities Of Hinge Structures, Ciprian Borcea, Ileana Streinu

Computer Science: Faculty Publications

Motivated by the hinge structure present in protein chains and other molecular conformations, we study the singularities of certain maps associated to body-and-hinge and panel-and-hinge chains. These are sequentially articulated systems where two consecutive rigid pieces are connected by a hinge, that is, a codimension two axis. The singularities, or critical points, correspond to a dimensional drop in the linear span of the axes, regarded as points on a Grassmann variety in its Pl¨ucker embedding. These results are valid in arbitrary dimension. The three dimensional case is also relevant in robotics.

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Recursive Dispersion Relations In One-Dimensional Periodic Elastic Media, Ani P. Velo, George A. Gazonas, Erwin Bruder, Nancy Rodriguez Dec 2008

Recursive Dispersion Relations In One-Dimensional Periodic Elastic Media, Ani P. Velo, George A. Gazonas, Erwin Bruder, Nancy Rodriguez

Mathematics: Faculty Scholarship

A frequency bandgap is a range of wave frequencies that are prohibited from passing through a medium. The dispersion relation, which links the frequency to the wave number, enables us to illustrate the bandgaps. In [E. H. Lee, “A survey of variational methods for elastic wave propagation analysis in composites with periodic structures,” in Dynamics of Composite Materials, E. H. Lee, ed., ASME, New York, 1972, pp. 122–138] and [E. H. Lee and W. H. Yang, SIAM J. Appl. Math., 25 (1973), pp. 492–499] the dispersion relation was studied theoretically for the one-dimensional periodic structure made of two materials …

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Locality And Stability Of The Cascades Of Two-Dimensional Turbulence, Eleftherios Gkioulekas Dec 2008

Locality And Stability Of The Cascades Of Two-Dimensional Turbulence, Eleftherios Gkioulekas

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L’vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of nonperturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that …

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Robust Stability And Optimality Conditions For Parametric Infinite And Semi-Infinite Programs, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra Dec 2008

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 …

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Sublimital Analysis, Thomas Q. Sibley Dec 2008

Sublimital Analysis, Thomas Q. Sibley

Mathematics Faculty Publications

The Bolzano-Weierstrass theorem asserts, under appropriate circumstances, the convergence of some subsequence of a sequence. While this famous theorem ignores the actual limit of the subsequence, it is natural to investigate such limits. This note characterizes the set of possible limits of subsequences of a given sequence.

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Partial Automorphism Semigroups, Jennifer Chubb, Valentina Harizanov, Andrei Morozov, Sarah Pingrey, Eric Ufferman Dec 2008

Partial Automorphism Semigroups, Jennifer Chubb, Valentina Harizanov, Andrei Morozov, Sarah Pingrey, Eric Ufferman

Mathematics

We study the relationship between algebraic structures and their inverse semigroups of partial automorphisms. We consider a variety of classes of natural structures including equivalence structures, orderings, Boolean algebras, and relatively complemented distributive lattices. For certain subsemigroups of these inverse semigroups, isomorphism (elementary equivalence) of the subsemigroups yields isomorphism (elementary equivalence) of the underlying structures. We also prove that for some classes of computable structures, we can reconstruct a computable structure, up to computable isomorphism, from the isomorphism type of its inverse semigroup of computable partial automorphisms.

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A Uniformly Dissipative Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang (Wendy) Cheng, Xiaoming Wang Dec 2008

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 …

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A Semi-Implicit Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang Cheng, Xiaoming Wang Dec 2008

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 …

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The Equivariant Chow Rings Of Quot Schemes, T. Braden, Linda Chen, F. Sottile Dec 2008

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.

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Do The Coefficients Of A Modular Form Really "Encode Arithmetic Data"?, Ken Mcmurdy, Hari Ravindran Nov 2008

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 …

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Dynamics Of Quasiconformal Fields, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen Nov 2008

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.

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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 Nov 2008

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.

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Metric Regularity Of Mappings And Generalized Normals To Set Images, Boris S. Mordukhovich, Nguyen Mau Nam, Bingwu Wang Nov 2008

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 …

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Selective Screenability In Topological Groups, Liljana Babinkostova Nov 2008

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 Sc(Onbd,O) and Smirnov-Sc(Onbd,O) in terms of the Haver property and finitary Haver property respectively relative to left-invariant metrics. We prove theorems stating conditions under which Sc(Onbd,O) is preserved by products. Among metrizable groups we characterize the countable dimensional ones by a natural game.

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Prey Behavior, Age-Dependent Vulnerability, And Predation Rates, Susan Lingle, Alex Feldman, Mark S. Boyce, W. Finbarr Wilson Nov 2008

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 …

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Ubi-App: A Ubiquitous Application For Universal Access From Handheld Devices, Shameem Ahmed, Moushumi Sharmin, Sheikh Iqbal Ahamed Nov 2008

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). …

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A Window On The Fifth Dimension, Frank A. Farris Nov 2008

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.

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Asymptotic Behavior Of Linearized Viscoelastic Flow Problem, Yinnian He, Yi Li Nov 2008

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.

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Mathematics In The Mountains: The Park City Mathematics Institute, Andrew J. Bernoff Nov 2008

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.

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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 Nov 2008

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 …

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Queen's Domination Using Border Squares And (A,B)-Restricted Domination, Anne Sinko, Peter J. Slater Oct 2008

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 …

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On Injectivity Of Quasiregular Mappings, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen Oct 2008

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.

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On The Colored Jones Polynomial, Sutured Floer Homology, And Knot Floer Homology, J. Elisenda Grigsby, Stephan Wehrli Oct 2008

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 Einfinity 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 …

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Siegel’S Lemma Outside Of A Union Of Varieties, Lenny Fukshansky Oct 2008

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.

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