We study the stability properties of, and the phase error present in, a finite element scheme for Maxwell’s
equations coupled with a Debye or Lorentz polarization model. In one dimension we consider a second order
formulation for the electric field with an ordinary differential equation for the electric polarization added...
Advective skew dispersion is a natural Markov process defined ned
by a di ffusion with drift across an interface of jump discontinuity in
a piecewise constant diff usion coeffcient. In the absence of drift this
process may be represented as a function of -skew Brownian motion
for a uniquely determined...
The authors of this paper met at a summer institute sponsored by the Oregon Collaborative for Excellence in the Preparation of Teachers (OCEPT). Edwards is a researcher in undergraduate mathematics education. Ward, a pure mathematician teaching at an undergraduate institution, had had little exposure to mathematics education research prior to...
Given two rational maps φ and ψ on Ρ¹ of degree at least two, we study a symmetric, nonnegative real-valued pairing〈φ, ψ〉which is closely related to the canonical height functions hφ and hψ associated to these maps. Our main results show a strong connection between the value of〈φ, ψ〉and the...
We extend the idea of bilateral determinism of a free Z-action by D. Ornstein and B. Weiss to a free Z²-action. We show that we have a 'stronger' spatial determinism for Z²-actions: to determine the complete Z²-name of a point, it is enough to know the name of a fraction...
The degenerate nature of the metric on null hypersurfaces makes it difficult to define a covariant derivative on null submanifolds. Recent approaches using decomposition to define a covariant derivative on null hypersurfaces are investigated, with examples demonstrating the limitations of the methods. Motivated by Geroch’s work on asymptotically flat spacetimes,...
In [BH], a chain complex was constructed in a combinatorial way
which conjecturally is a resolution of the (dual of the) integral Specht
module for the symmetric group in terms of permutation modules.
In this paper we extend the definition of the chain complex to the
integral Iwahori Hecke algebra...
Let K be a cyclic number field of prime degree ℓ. Heilbronn showed that for a given ℓ there are only finitely many such fields that are norm-Euclidean. In the case of ℓ = 2 all such norm-Euclidean fields have been identified, but for ℓ ≠ 2, little else is...
Double-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and perform a comparison between the micro- and macro-model....
We consider a renewal jump diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin...
We explore two characteristic features of x-ray computed tomography inversion formulas in two and
three dimensions that are dependent on π-lines. In such formulas the data from a given source
position contribute only to the reconstruction of ƒ(x) for x in a certain region, called the region
of backprojection. The...
A mathematical evidence-in a statistically significant sense-of a geometric scenario leading to criticality of the Navier-Stokes problem is presented. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4752170]
The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from the eigenvalues and eigenfunctions of the Laplace-Beltrami operator determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete heat kernel and the...
In this paper dynamic von Karman equations with localized interior damping supported in a boundary collar are considered. Hadamard well-posedness for von Karman plates with various types of nonlinear damping are well known, and the long-time behavior of nonlinear plates has been a topic of recent interest. Since the von...
We consider the well-posedness of a model for a flow-structure interaction. This model describes the dynamics of an elastic flexible plate with clamped boundary conditions immersed in a supersonic flow. A perturbed wave equation describes the flow potential. The plateʼs out-of-plane displacement can be modeled by various nonlinear plate equations...
Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich’s theorem...
We give continued fraction algorithms for each conjugacy class of triangle Fuchsian group of signature
(3, n, ∞), with n ≥ 4. In particular, we give an explicit form of the group that is a subgroup of the Hilbert
modular group of its trace field and provide an interval map...
The P1 discretization of the Laplace operator on a triangulated
polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the P1 discretization of the
Laplace operator. Among all triangles, an equilateral triangle has the maximal first positive eigenvalue. Among all cyclic...
We investigate a number of simple toy models to explore interesting relationships between dynamics and typicality. We start with an infinite model that has been proposed as an illustration of how nonergodic dynamics can produce interesting features that are suggestive for cosmological applications. We consider various attempts to define the...