Browsing Department of Mathematical Sciences by Title

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  • Dallas, A.G. (Department of Mathematical Sciences, 2000)
    The classical solutions of the Heimholtz equation resulting from the separation-of-variables procedure in spherical coördinates are frequently used in one way or another to approximate other solutions. In particular, traces ...
  • Hsiao, George C. (Department of Mathematical Sciences, 2004)
    Variational methods for boundary integral equations deal with the weak formulations of boundary integral equations. Their numerical discretizations are known as the boundary element methods. This paper gives an overview ...
  • Hsiao, George C.; Wendland, W.L. (Department of Mathematical Sciences, 2000)
    This expository paper is concerned with the direct integral formulations for boundary value problems of the Helmholtz equation. We discuss unique solvability for the corresponding boundary integral equations and its ...
  • Debisschop, C.A.; Braun, Richard J.; Snow, S.A. (Department of Mathematical Sciences, 2001-09-12)
    We study the evolution of a Newtonian free surface of a thin film above a solid wall. We consider the case in which the horizontal solid is covered by a non-wetting fluid and an insoluble monolayer of surfactant is present ...
  • Cirillo, Michelle (The Department of Mathematics, National Taiwan Normal University Taipei, Taiwan, 2009)
    As pointed out by Stylianides (2007), a major reason that proof and proving have been given increased attention in recent years is because they are fundamental to doing and knowing mathematics and communicating mathematical ...
  • Rossi, Louis F. (Department of Mathematics, 2003)
    This paper presents results from a head-to-head comparison of two Lagrangian methods for solutions to the two-dimensional, incompressible convection-diffusion equations. The first Lagrangian method is an axisymmetric ...
  • Platte, Rodrigo B.; Driscoll, Tobin A. (Department of Mathematical Sciences, 2003-03-21)
    Radial basis function (RBF) approximations have been successfully used to solve boundary-value problems numerically. We show that RBFs can also be used to compute eigenmodes of elliptic operators. Special attention is ...
  • Cirillo, Michelle; Kosko, Karl W.; Newton, Jill; Staples, Megan; Weber, Keith (East Lansing, MI: Michigan State University, 2015)
    Argumentation, justification, and proof are conceptualized in many ways in extant mathematics education literature. At times, the descriptions of these objects and processes are compatible or complementary; at other ...
  • Chandler, D.B.; Xiang, Qing (Department of Mathematical Sciences, 2002)
    By modifying the constructions in [10] and [15], we construct a family of cyclic ((q 3k − 1)/(q − 1), q − 1, q 3k − 1 , q 3k − 2 ) relative difference sets, where q = 3 e . These relative difference sets are “liftings” ...
  • Cakoni, Fioralba; Colton, David; Monk, Peter B. (Department of Mathematical Sciences, 2002)
    We consider the direct and inverse scattering problems for partially coated obstacles. To this end, we first use the method of integral equations of the first kind to solve a scattering problem for the Helmholtz equation ...
  • Monk, Peter B. (Department of Mathematical Sciences, 2002)
    The time harmonic Maxwell's equations for a lossless medium are neither elliptic or definite. Hence the analysis of numerical schemes for these equations presents some unusual difficulties. In this paper we give a simple ...
  • Hsiao, George C.; Steinbach, O.; Wendland, W.L. (Department of Mathematical Sciences, 2000-12-21)
    Domain decomposition methods are designed to deal with coupled or transmission problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain ...
  • Borwein, J. M.; Luke, D. Russell (Department of Mathematical Sciences, 2004-11-19)
    We study several generalizations of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the continued fraction were ...
  • Borwein, J. M.; Luke, D. Russell (Department of Mathematical Sciences, 2004-11-16)
    We study a generalization of a continued fraction of Ramanujan with random coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the ...
  • Platte, R.B.; Driscoll, Tobin A. (Department of Mathematical Sciences, 2005)
    Differentiation matrices obtained with infinitely smooth radial basis function (RBF) collo- cation methods have, under many conditions, eigenvalues with positive real part, preventing the use of such methods for ...
  • Hsiao, George C.; Monk, Peter B.; Nigam, N. (Department of Mathematical Sciences, 2002)
    In 1996 Hazard and Lenoir suggested a variational formulation of Maxwell's equations using an overlapping integral equation and volume representation of the solution. They suggested a numerical scheme based on this ...
  • Rossi, Louis F. (Mathematical Sciences Department, 2005)
    This paper introduces two techniques for approximating the Biot-Savart integral for deforming elliptical Gaussian functions. The primary motivation is to develop a high spatial accuracy vortex method. The first technique ...
  • Cirillo, Michelle; Todd, Rachael; Obrycki, Joe (2015-05-04)
    We describe an exploratory task intended to support students’ conceptual understandings of triangle congruence with particular emphasis on the Side-Side-Angle (SSA) case. We reveal how SSA, often dismissed, is actually a ...
  • Kirsch, A.; Monk, Peter B. (Department of Mathematical Sciences, 2000)
    We provide an error analysis of a fully discrete finite element – Fourier series method for approximating Maxwell’s equations. The problem is to approximate the electromagnetic field scattered by a bounded, inhomogeneous ...
  • Li, Wenbo (Department of Mathematical Sciences, 2002)
    Consider the first exit time, ˝D of a (d + 1)-dimensional Brownian motion from an unbounded open domain D = (x; y) 2 R d+1 : y > f(x); x 2 R d starting at (x0; f(x0) + 1) 2 R d+1 for some x0 2 R d , where ...

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