On the Whitham system for the (2+1)-dimensional nonlinear Schrödinger equation

Whitham modulation equations are derived for the nonlinear Schrödinger equation in the plane ((2+1)-dimensional nonlinear Schrödinger [2d NLS]) with small dispersion. The modulation equations are obtained in terms of both physical and Riemann-type variables; the latter yields equations of hydrodynamic type. The complete 2d NLS Whitham system consists of six dynamical equations in evolutionary form and two constraints. As an application, we determine the linear stability of one-dimensional traveling waves. In both the elliptic and hyperbolic cases, the traveling waves are found to be unstable. This result is consistent with previous investigations of stability by other methods and is supported by direct numerical calculations.     

A method for predicting the stability characteristics of three-term homogeneous recurrence relations

A simple method is presented which determines the numerical stability or instability in the computation of any solution of a three-term homogeneous linear difference equation of order m in terms of the size of a single parameter. The method is illustrated by application to a second order and to a third order difference equation. Excellent agreement with predictions is reported.     

The universality of equivariant complex bordism

We show that if A is an abelian compact Lie group, all A-equivariant complex vector bundles are orientable over a complex orientable equivariant cohomology theory. In the process, we calculate the complex orientable homology and cohomology of all complex Grassmannians. Received: 14 February 2000; in final form: 4 August 2000 / Published online: 19 October 2001     

On the multi-attribute stopping problem with general value functions

We examine a sequential selection problem in which a single option must be selected. Each option's value is a function of its attributes, whose precise values can be ascertained at a given cost. We prove the optimality of a threshold stopping rule for a general class of objective functions.     

Fully asynchronous stochastic coordinate descent: a tight lower bound on the parallelism achieving linear speedup

Mathematical Programming - We seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent that achieves linear speedup. We focus on asynchronous coordinate...     

Synthesis and axial chirality of an enantiopure aminodibenzazepinone

A route for the synthesis of (S,S)-7-amino-5-methyl-5H-dibenzo[b,d]azepin-6(7H)-one hydrochloride is disclosed. The synthesis includes a Friedel–Crafts alkylation to form the seven-membered ring and a highly efficient classical resolution. Additional studies on the enantiopure material showed the amine to be highly resistant to racemization, which led us to investigate the unexpected stability. We propose that the inherent axial chirality contained in the dibenzazepinone works to produce an interesting chirality transfer mechanism, which accounts for the observed robustness of the stereocenter. This previously unrecognized stereochemical element exists within this specific class of molecules, and they should be drawn in a manner which displays the axial chirality.     

An improved linearization strategy for zero-one quadratic programming problems

We present a new linearized model for the zero-one quadratic programming problem, whose size is linear in terms of the number of variables in the original nonlinear problem. Our derivation yields three alternative reformulations, each varying in model size and tightness. We show that our models are at least as tight as the one recently proposed in [7], and examine the theoretical relationship of our models to a standard linearization of the zero-one quadratic programming problem. Finally, we demonstrate the efficacy of solving each of these models on a set of randomly generated test instances.     

Transonic Hodograph Design Problems

The hodograph method is used to formulate several design problems in transonic flow using small-disturbance theory. Analytical and numerical methods give solutions to several optimum critical airfoil designs with different constraints on the tail angle. Special airfoil shapes flying at free-stream Mach number one are designed. The problem of constructing a shock-free body of revolution at subsonic speed but having a supersonic zone is formulated in the hodograph and solved numerically. Received 10 January 1997 and accepted 14 April 1997