Physical Sciences and Mathematics Commons^™

The Second Hull Of A Knotted Curve, Jason Cantarella, Greg Kuperberg, Robert B. Kusner, John M. Sullivan

Robert Kusner

The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This provides a new proof of the Fary/Milnor theorem that every knotted curve has total curvature at least 4pi.

Exact Multiplicity For Periodic Solutions Of Duffing Type, Hongbin Chen, Yi Li, Xiaojie Hou

Yi Li

In this paper, we study the following Duffing-type equation: x″+cx′+g(t,x)=h(t),

where g(t,x) is a 2π-periodic continuous function in t and concave–convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability of periodic solutions are obtained.

The Global Dynamics Of Isothermal Chemical Systems With Critical Nonlinearity, Yi Li, Yuanwei Qi

Yi Li

In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u_1,t = u_1,xx − u^α₁ u^β₂, u_2,t = du_2,xx+ u^α₁ u^β₂ with non-negative initial data, where the exponents α,β satisfy 1<α,β<2, α+β = 3 and the constant d>0 is the Lewis number. Our purpose is to study the global dynamics of solutions under mild decay of initial data as |x|→∞. We show the exact large time behaviour of solutions which is universal.

Investigations Of Nonstandard, Mickens-Type, Finite-Difference Schemes For Singular Boundary Value Problems In Cylindrical Or Spherical Coordinates, Ron Buckmire

Ron Buckmire

No abstract provided.

Balanced Configurations Of Lattice Vectors And Gkz-Rational Toric Fourfolds In P^6, Eduardo Cattani, Alicia Dickenstein

Eduardo Cattani

We introduce a notion of balanced configurations of vectors. This is motivated by the study of rational A-hypergeometric functions in the sense of Gelfand, Kapranov and Zelevinsky. We classify balanced configurations of seven plane vectors up to GL(2,R)-equivalence and deduce that the only gkz-rational toric four-folds in P6 are those varieties associated with an essential Cayley configuration. We show that in this case, all rational A-hypergeometric functions may be described in terms of toric residues. This follows from studying a suitable hyperplane arrangement.

Benefits Of A Comprehensive Undergraduate Teaching Assistant Program, Christopher Goff, Brigitte Lahme

Christopher Goff

Plane-Wave Impulse Approximation Extraction Of The Neutron Magnetic Form Factor From Quasielastic 3He → (E,E') At Q2=0.3 To 0.6(Gev/C)2, W. Xu, B. Anderson, L. Auberbach, T. Averett, W. Bertozzi, T. Black, J. Calarco, L. Cardman, G. D. Cates, Z. W. Chai, J. P. Chen, S. Choi, E. Chudakov, S. Churchwell, G. S. Corrado, C. Crawford, D. Dale, A. Deur, P. Djawotho, T. W. Donnelly, D. Dutta, J. M. Finn, H. Gao, R. Gilman, A. V. Glamazdin, C. Glashausser, W. Glockle, J. Golak, J. Gomez, V. G. Gorbenko, J. O. Hansen, F. W. Hersman, D. W. Higinbotham, R. Holmes, C. R. Howell, E. Hughes, B. Humensky, S. Incerti, C. W. De Jager, J. S. Jensen, X. Jiang, C. E. Jones, M. Jones, R. Kahl, H. Kamada, A. Kievsky, I. Kominis, W. Korsch, K. Kramer, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, M. Liang, N. Liyanage, J. Lerose, S. Malov, D. J. Margaziotis, J. W. Martin, K. Mccormick, R. D. Mckeown, K. Mcilhany, Z. E. Meziani, R. Michaels, G. W. Miller, J. Mitchell, S. Nanda, E. Pace, T. Pavlin, G. G. Petratos, R. I. Pomatsalyuk, D. Pripstein, D. Prout, R. D. Ransome, Y. Roblin, M. Rvachev, A. Saha, G. Salme, M. Schnee, T. Shin, K. Slifer, P. A. Souder, S. Strauch, R Suleiman, M. Sutter, B. Tipton, L. Todor, M. Viviani, B. Vlahovic, J. Watson, C. F. Williamson, H. Witala, B. Wojtsekhowski, F. Xiong, J. Yeh, P. Zolnierczuk

Enkeleida K. Lakuriqi

A high precision measurement of the transverse spin-dependent asymmetry AT' in 3He→(e,e') quasielastic scattering was performed in Hall A at Jefferson Lab at values of the squared four-momentum transfer, Q2, between 0.1 and 0.6 (GeV/c)2.AT' is sensitive to the neutron magnetic form factor, GnM. Values of GnM at Q2=0.1 and 0.2(GeV/c)2, extracted using Faddeev calculations, were reported previously. Here, we report the extraction of GnM for the remaining Q2 values in the range from 0.3 to 0.6(GeV/c)2 using a …

Nonlinear Equations And Wavelets, Andrei Ludu

Andrei Ludu

No abstract provided.

Radial Basis Function Interpolation: Numerical And Analytical Developments, Grady Wright

Grady Wright

The Radial Basis Function (RBF) method is one of the primary tools for interpolating multidimensional scattered data. The methods' ability to handle arbitrarily scattered data, to easily generalize to several space dimensions, and to provide spectral accuracy have made it particularly popular in several different types of applications. Some of the more recent of these applications include cartography, neural networks, medical imaging, and the numerical solution of partial differential equations (PDEs). In this thesis we study three issues with the RBF method that have received very little attention in the literature.

First, we focus on the behavior of RBF interpolants …

Relations Between $\Lambda{\Rm Bv}$ And ${\Rm Bv}(P(N)\Uparrow\Infty)$ Classes Of Functions, Ushangi Goginava

Ushangi Goginava

No abstract provided.

On The Uniform Convergence And $L$-Convergence Of Double Fourier Series With Respect To The Walsh-Kaczmarz System, Ushangi Goginava

Ushangi Goginava

No abstract provided.

Assessing The Impacts Of Global Climate Changeon Forest Pests, J. A. Logan, J. Reniere, James A. Powell

James A. Powell

No abstract provided.

Evaluation Of Dedekind Sums, Eisenstein Cocycles, And Special Values Of L-Functions, Pe Gunnells, R Sczech

Paul Gunnells

We define higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums as well as Zagier's sums, and we show how to compute them effectively using a generalization of the continued-fraction algorithm. We present two applications. First, we show how to express special values of partial zeta functions associated to totally real number fields in terms of these sums via the Eisenstein cocycle introduced by R. Sczech. Hence we obtain a polynomial time algorithm for computing these special values. Second, we show how to use our techniques to compute certain special values of the Witten zeta function, and we compute some …

Sensorimotor Coordination And The Structure Of Space, Gin Mccollum

Gin McCollum

Embedded in neural and behavioral organization is a structure of sensorimotor space. Both this embedded spatial structure and the structure of physical space inform sensorimotor control. This paper reviews studies in which the gravitational vertical and horizontal are crucial. The mathematical expressions of spatial geometry in these studies indicate methods for investigating sensorimotor control in freefall.

In freefall, the spatial structure introduced by gravitation – the distinction between vertical and horizontal – does not exist. However, an astronaut arriving in space carries the physiologically-embedded distinction between horizontal and vertical learned on earth. The physiological organization based on this distinction collapses …

Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang

Yi Li

We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.

Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao

Yi Li

No abstract provided.

Working Across Cultures, John Hooker

John Hooker

No abstract provided.

Graphs Of Essentially Equivalent Lattice Paths, Lara Pudwell, Marjorie Brewer, Adam Hughes

Lara K. Pudwell

No abstract provided.

On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Tian-Xiao He

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples.

Boundary-Type Quadrature And Boundary Element Method, Tian-Xiao He

Tian-Xiao He

In this paper, we apply a boundary-type quadrature technique to derive a type of boundary element scheme, which is used to solve the boundary-value problems of partial differential equations.Numerical examples for solving the exterior boundary-value problem of Helmholtz equation by using the spline approximation and the spline wavelet approximation are given.

Analytical Upstream Collocation Solution Of A Forced Steady-State Convection-Diffusion Equation, Stephen Brill

Stephen H. Brill

We give herein formulas for the solution of the Hermite collocation discretization of a nonhomogeneous steady-state convection-diffusion equation in one spatial dimension and with constant coefficients, defined on a uniform mesh, with Dirichlet boundary conditions. The accuracy of the method is enhanced by employing "upsteam weighting" of the convective term in an optimal way. We discuss also the issue of where to optimally sample the forcing function. Computational examples illustrate the efficacy of the optimal upstream weighting technique combined with optimal sampling of the forcing function.

Length-Preserving Transformations On Polygons, Brad Ballinger

Brad Ballinger

Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench

William F. Trench

No abstract provided.

A Note On Asymptotic Zero Distribution Of Orthogonal Polynomials, William F. Trench

William F. Trench

No abstract provided.

A Family Of Isomorphic Fusion Algebras Of Twisted Quantum Doubles Of Finite Groups, Christopher Goff

Christopher Goff

Absolute Equal Distribution Of The Spectra Of Hermitian Matrices, William F. Trench

William F. Trench

No abstract provided.

Absolute Equal Distribution Of Families Of Finite Sets, William F. Trench

William F. Trench

No abstract provided.

Open Problems From The Linz2000 Closing Session, Lawrence N. Stout

Lawrence N. Stout

No abstract provided.

Strukturationen Der Interaktivität, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Linear Perturbations Of A Nonoscillatory Second Order Differential Equation Ii, William F. Trench

William F. Trench

No abstract provided.