On the uniqueness of sign changing bound state solutions of a semilinear equation

We establish the uniqueness of the higher radial bound state solutions of \Delta u +f(u)=0,\quad x\in \RR^n. \leqno(P) We assume that the nonlinearity $f\in C(-\infty,\infty)$ is an odd function satisfying some convexity and growth conditions, and either has one zero at $b>0$, is non positive and not identically 0 in $(0,b)$, and is differentiable and positive $[b,\infty)$, or is positive and differentiable in $[0,\infty)$

A study of seedling reproduction in Eber White Woods

Master of ScienceForestryUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/101296/2/39015003286641.pd

Unified Solution of the Expected Maximum of a Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived explicitly. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.Comment: Two figs. Accepted for publication, Journal of Statistical Physic

Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models

We study the probability density function $P(h_m,L)$ of the maximum relative height $h_m$ in a wide class of one-dimensional solid-on-solid models of finite size $L$. For all these lattice models, in the large $L$ limit, a central limit argument shows that, for periodic boundary conditions, $P(h_m,L)$ takes a universal scaling form $P(h_m,L) \sim (\sqrt{12}w_L)^{-1}f(h_m/(\sqrt{12} w_L))$, with $w_L$ the width of the fluctuating interface and $f(x)$ the Airy distribution function. For one instance of these models, corresponding to the extremely anisotropic Ising model in two dimensions, this result is obtained by an exact computation using transfer matrix technique, valid for any $L>0$. These arguments and exact analytical calculations are supported by numerical simulations, which show in addition that the subleading scaling function is also universal, up to a non universal amplitude, and simply given by the derivative of the Airy distribution function $f'(x)$.Comment: 13 pages, 4 figure

Full separability criterion for tripartite quantum systems

In this paper, an intuitive approach is employed to generalize the full separability criterion of tripartite quantum states of qubits to the higher-dimensional systems (Phys. Rev. A \textbf{72}, 022333 (2005)). A distinct characteristic of the present generalization is that less restrictive conditions are needed to characterize the properties of full separability. Furthermore, the formulation for pure states can be conveniently extended to the case of mixed states by utilizing the kronecker product approximate technique. As applications, we give the analytic approximation of the criterion for weakly mixed tripartite quantum states and investigate the full separability of some weakly mixed states.Comment: 5 pages. To be published in Europ. J.

Local symmetry properties of pure 3-qubit states

Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilisers.Comment: 32 pages, 5 encapsulated PostScript files for 3 figures. Published version, with minor correction

COMM 1311: Fundamentals of Speech Communication

This OER packet contains the course materials for COMM 1311: Fundamentals of Speech Communication that introduce you to why do we/I need to take a public speaking course. The answer is also always the same. “Because it is required.” However, you the reader, and us as the authors/editors, know that this doesn’t answer the question. The real answer can be complicated, but this author/editor believes that the skills gained by public speaking will help you in any field, despite whether or not you end up working in a field that requires public speaking.https://digitalcommons.pvamu.edu/pv-open-education-resources/1009/thumbnail.jp

Gaussian limits for multidimensional random sequential packing at saturation (extended version)

Consider the random sequential packing model with infinite input and in any dimension. When the input consists of non-zero volume convex solids we show that the total number of solids accepted over cubes of volume $\lambda$ is asymptotically normal as $\lambda \to \infty$. We provide a rate of approximation to the normal and show that the finite dimensional distributions of the packing measures converge to those of a mean zero generalized Gaussian field. The method of proof involves showing that the collection of accepted solids satisfies the weak spatial dependence condition known as stabilization.Comment: 31 page

Aerogel Blanket Insulation Materials for Cryogenic Applications

Aerogel blanket materials for use in thermal insulation systems are now commercially available and implemented by industry. Prototype aerogel blanket materials were presented at the Cryogenic Engineering Conference in 1997 and by 2004 had progressed to full commercial production by Aspen Aerogels. Today, this new technology material is providing superior energy efficiencies and enabling new design approaches for more cost effective cryogenic systems. Aerogel processing technology and methods are continuing to improve, offering a tailor-able array of product formulations for many different thermal and environmental requirements. Many different varieties and combinations of aerogel blankets have been characterized using insulation test cryostats at the Cryogenics Test Laboratory of NASA Kennedy Space Center. Detailed thermal conductivity data for a select group of materials are presented for engineering use. Heat transfer evaluations for the entire vacuum pressure range, including ambient conditions, are given. Examples of current cryogenic applications of aerogel blanket insulation are also given. KEYWORDS: Cryogenic tanks, thermal insulation, composite materials, aerogel, thermal conductivity, liquid nitrogen boil-of