We are concerned here with well-posed problems for the partial differential equation uₜ(x, t) + yMuₜ(x, t) + Lu(x, t) = f(x, t) containing the elliptic differential operator M of order 2m and the differential operator L of order ≤2m. Hilbert space methods are used to formulate and solve an...
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]
We provide several examples of the use of geometric reasoning with three-dimensional spacetime diagrams, rather than algebraic manipulations using three-dimensional Lorentz transformations, to analyze problems in special relativity.
Gene regulatory networks are commonly used for modeling biological processes and revealing underlying molecular mechanisms. The reconstruction of gene regulatory networks from observational data is a challenging task, especially considering the large number of players (e.g. genes) involved and the small number of biological replicates available for analysis. Herein, we...
The distributed-microstructure model for the flow of single phase
fluid in a partially fissured composite medium due to Douglas-Peszyńska-Showalter [12] is extended to a quasi-linear version. This model contains the
geometry of the local cells distributed throughout the medium, the flux exchange
across their intricate interface with the imbedded fissure...
The spectrum of the interior transmission problem is related to the unique determination of the acoustic properties of a body in thermoacoustic imaging. Under a non-trapping hypothesis, we show that sparsity of the interior transmission spectrum implies a range separation condition for the thermoacoustic operator. In odd dimensions greater than...
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...
Anderson and DeWitt considered the quantization of a massless scalar field in a spacetime whose spacelike hypersurfaces change topology and concluded that the topology change gives rise to infinite particle and energy production. We show here that their calculations are insufficient and that their propagation rule is unphysical. However, our...
We compare two independent generalizations of the usual spherical harmonics, namely monopole harmonics and spin‐weighted spherical harmonics, and make precise the sense in which they can be considered to be the same. By analogy with the spin‐gauge language, raising and lowering operators for the monopole index of the monopole harmonics...
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant...
We derive the fundamental solution of the linearized problem of the motion of a viscous uid around a rotating body when the axis of rotation of the body is not parallel to the velocity of the uid at infinity.
We examine some of the subtleties inherent in formulating a theory of spinors on a manifold with a smooth degenerate metric. We concentrate on the case where the metric is singular on a hypersurface that partitions the manifold into Lorentzian and Euclidean domains. We introduce the notion of a complex...
A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proven, which gives the second derivative of the tensor in terms of the curvature tensor, generalizing a...
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...
Abstract: We prove that for all ergodic extensions S-1 of a transformation by a locally compact second countable group G, and for all G-extensions S₂ of an aperiodic transformation, there is a relative speedup of S₁ that is relatively isomorphic to S₂. We apply this result to give necessary and...
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...
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...
Results are provided that highlight the effect of interfacial discontinuities in the
diffusion coefficient on the behavior of certain basic functionals of the diffusion, such
as local times and occupation times, extending previous results in [2, 3] on the behavior
of first passage times. The main goal is to obtain...
We consider the (massless) scalar field on a two-dimensional manifold with metric that changes signature from Lorentzian to Euclidean. Requiring a conserved momentum in the spatially homogeneous case leads to a particular choice of propagation rule. The resulting mix of positive and negative frequencies depends only on the total (conformal)...