Well-posedness of the free-surface incompressible Euler equations with or without surface tension

We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid. This is a free boundary problem for the motion of an incompressible perfect liquid in vacuum, wherein the motion of the fluid interacts with the motion of the free-surface at highest-order.

     

Learning Theory Estimates via Integral Operators and Their Approximations

The regression problem in learning theory is investigated with least square Tikhonov regularization schemes in reproducing kernel Hilbert spaces (RKHS). We follow our previous work and apply the sampling operator to the error analysis in both the RKHS norm and the L² norm. The tool for estimating the sample error is a Bennet inequality for random variables with values in Hilbert spaces. By taking the Hilbert space to be the one consisting of Hilbert-Schmidt operators in the RKHS, we improve the error bounds in the L² metric, motivated by an idea of Caponnetto and de Vito. The error bounds we derive in the RKHS norm, together with a Tsybakov function we discuss here, yield interesting applications to the error analysis of the (binary) classification problem, since the RKHS metric controls the one for the uniform convergence.     

A Study of Highly Qualified Science Teachers' Career Trajectory in the Deep,Rural South: Examining a Link Between Deprofessionalization and Teacher Dissatisfaction

Science teacher retention, attrition, and migration continue to perplex educational scholars, political entities, as well as the general public. This study utilized an interpretive methodological design to generate assertions regarding career choice made by highly qualified science teachers in the deep, rural South through analysis of documents, interviews, focus groups, and observation. Generally considered “difficult to staff” because of location, socioeconomics, and demographics, Wilson County High School is an exemplar in science teacher retention and student achievement. Findings presented include how the science department at Wilson County improved student learning outcomes as well as the reasons why two of the highly qualified science teachers at this school were considering leaving the profession they love.     

Option pricing when asset returns jump interruptedly

This paper proposes an extension of Merton's jump‐diffusion model to reflect the time inhomogeneity caused by changes of market states. The benefit is that it simultaneously captures two salient features in asset returns: heavy tailness and volatility clustering. On the basis of an empirical analysis where jumps are found to happen much more frequently in risky periods than in normal periods, we assume that the Poisson process for driving jumps is governed by a two‐state on‐off Markov chain. This makes jumps happen interruptedly and helps to generate different dynamics under these two states. We provide a full analysis for the proposed model and derive the recursive formulas for the conditional state probabilities of the underlying Markov chain. These analytical results lead to an algorithm that can be implemented to determine the prices of European options under normal and risky states. Numerical examples are given to demonstrate how time inhomogeneity influences return distributions, option prices, and volatility smiles. The contrasting patterns seen in different states indicate the insufficiency of using time‐homogeneous models and justify the use of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

Threshold-based interventions to optimize performance in preemptive priority queues

This paper studies a single-server priority queueing model in which preemptions are allowed during the early stages of service. Once enough service effort has been rendered, however, further preemptions are blocked. The threshold where the change occurs is either a proportion of the service requirement, or time-based. The Laplace–Stieltjes transform and mean of each class sojourn time are derived for a model which employs this hybrid preemption policy. Both preemptive resume and preemptive repeat service disciplines are considered. Numerical examples show that it is frequently the case that a good combination of preemptible and nonpreemptible service performs better than both the standard preemptive and nonpreemptive queues. In a number of these cases, the thresholds that optimize performance measures such as overall average sojourn time are determined. This revised version was published online in June 2006 with corrections to the Cover Date.     

Irreducible Apollonian Configurations and Packings

An Apollonian configuration of circles is a collection of circles in the plane with disjoint interiors such that the complement of the interiors of the circles consists of curvilinear triangles. One well-studied method of forming an Apollonian configuration is to start with three mutually tangent circles and fill a curvilinear triangle with a new circle, then repeat with each newly created curvilinear triangle. More generally, we can start with three mutually tangent circles and a rule (or rules) for how to fill a curvilinear triangle with circles.     

Permutations Generated by Stacks and Deques

Lower and upper bounds are given for the the number of permutations of length n generated by two stacks in series, two stacks in parallel, and a general deque.