Mathematics Scholarly Works: Recent submissions
Now showing items 181-200 of 283
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Symmetric powers of complete modules over a two-dimensional regular local ring
(American Mathematical Society, 1997-02-02) -
On the existence of maximal Cohen-Macaulay modules over pth root extensions
(American Mathematical Society, 1999-04-15) -
A linear function associated to asymptotic prime divisors
(American Mathematical Society, 2003-10-21) -
On the degree of Hilbert polynomials associated with the torsion functor
(American Mathematical Society, 2009-05-14) -
Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Korteweg–de Vries Equation9
(Society for Industrial and Applied Mathematics, 2009-11-18)In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg–de Vries equation $u_t=u_{xxx}+f(u)_x$. In particular, we derive sufficient ... -
Transverse Instability of Periodic Traveling Waves in the Generalized Kadomtsev–Petviashvili Equation
(Society for Industrial and Applied Mathematics, 2010-10-21)In this paper, we investigate the spectral instability of periodic traveling wave solutions of the generalized Korteweg–de Vries equation to long wavelength transverse perturbations in the generalized Kadomtsev–Petviashvili ... -
Nonlinear Stability of Viscous Roll Waves
(Society for Industrial and Applied Mathematics, 2011-03-01)Extending results of Oh and Zumbrun and of Johnson and Zumbrun for parabolic conservation laws, we show that spectral stability implies nonlinear stability for spatially periodic viscous roll wave solutions of the ... -
Nonlinear Stability of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Dimensions One and Two
(Society for Industrial and Applied Mathematics, 2011-01-01)Extending results of Oh and Zumbrun in dimensions $d\geq3$, we establish nonlinear stability and asymptotic behavior of spatially periodic traveling-wave solutions of viscous systems of conservation laws in critical ... -
Convergence of Hill's Method for Nonselfadjoint Operators
(Society for Industrial and Applied Mathematics, 2012-01-01)By the introduction of a generalized Evans function defined by an appropriate 2-modified Fredholm determinant, we give a simple proof of convergence in location and multiplicity of Hill's method for numerical approximation ... -
A note on finite abelian gerbes over toric Deligne-Mumford stacks
(American Mathematical Society, 2008-07-01) -
The pseudospectral method for third-order differential equations
(Society for Industrial and Applied Mathematics, 1992-12-01)Generalized quadrature rules are derived which assist in the selection of collocation points for the pseudospectral solution of differential equations. In particular, it is shown that for an nth-order differential equation ... -
A simple adaptive grid method in two dimensions
(Society for Industrial and Applied Mathematics, 1994-07-01)This paper gives an interpretation of the concept of equidistribution in the context of adaptive grid generation for multidimensional problems. It is shown that the equidistribution principle cannot be satisfied throughout ... -
Moving mesh partial differential equations (MMPDEs) based upon the equidistribution principle
(Society for Industrial and Applied Mathematics, 1994-06-01)This paper considers several moving mesh partial differential equations that are related to the equidistribution principle. Several of these are new, and some correspond to discrete moving mesh equations that have been ... -
Moving Mesh Methods for Problems with Blow-Up
(Society for Industrial and Applied Mathematics, 1996-03-01)In this paper we consider the numerical solution of PDEs with blow-up for which scaling invariance plays a natural role in describing the underlying solution structures. It is a challenging numerical problem to capture the ... -
Finite difference preconditioning for solving orthogonal collocation equations of boundary value problems
(Society for Industrial and Applied Mathematics, 1996-12-01)A technique to construct a low-order finite difference preconditioner for solving orthogonal collocation equations for boundary value problems is presented. It is shown numerically and theoretically that the spectral ... -
The adaptive Verlet method
(Society for Industrial and Applied Mathematics, 1997-01-01)We discuss the integration of autonomous Hamiltonian systems via dynamical rescaling of the vector field (reparameterization of time). Appropriate rescalings (e.g., based on normalization of the vector field or on minimum ... -
Analysis of moving mesh partial differential equations with spatial smoothing
(Society for Industrial and Applied Mathematics, 1997-06-01)Two moving mesh partial differential equations (MMPDEs) with spatial smoothing are derived based upon the equidistribution principle. This smoothing technique is motivated by the robust moving mesh method of Dorfi and Drury ... -
Pseudospectral solution of near-singular problems using numerical coordinate transformations based on adaptivity
(Society for Industrial and Applied Mathematics, 1998-07-01)The work presented here describes a method of coordinate transformation that enables spectral methods to be applied efficiently to differential problems with steep solutions. The approach makes use of the adaptive finite ... -
Moving mesh strategy based upon a gradient flow equation for two dimensional problems
(Society for Industrial and Applied Mathematics, 1999-07-01)In this paper we introduce a moving mesh method for solving PDEs in two dimensions. It can be viewed as a higher-dimensional generalization of the moving mesh PDE (MMPDE) strategy developed in our previous work for ... -
A study of monitor functions for two dimensional adaptive mesh generation
(Society for Industrial and Applied Mathematics, 1999-11-01)In this paper we study the problem of two-dimensional adaptive mesh generation using a variational approach and, specifically, the effect that the monitor function has on the resulting mesh behavior. The basic theoretical ...