Initial-boundary value problems for non-linear equations of generalized thermoelasticity and elasticity

We formulate a local existence theorem for the initial-boundary value problems of generalized thermoelasticity and classical elasticity. We present a unified approach to such boundary conditions as, for example, the boundary condition of traction, pressure or place combined with the boundary condition of heat flux or temperature.     

A novel liquid crystal light modulator

We present a conception of two optical modulators. One of these, which we have called the scattering liquid crystal cell seems to be promising with a view to possible applications. We assumed that the modulator could be used in optical logic as a gate element, but other applications in optoelectronics would appear also to be possible. Some preliminary results of an experimental examination of the modulators are also presented.     

Equivariant entire cyclic cohomology: I. Finite groups

We extend the framework of entire cyclic cohomology to the equivariant context.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065.     

In situ characterization of an iron catalyst by potassium ion desorption and electron emission measurements

The surface conditions of an industrial iron catalyst were monitoredin situ by work function measurements and measurements of thermal desorption of potassium ions. Changes in activation energy for potassium ion desorption and in work function values during catalyst activation and deactivation are discussed in terms of the potassium coverage and chemical composition of the catalyst surface.     

Chern character in equivariant entire cyclic cohomology

We construct the Chern character in the equivariant entire cyclic cohomology. We prove a general index theorem for theG-invariant Dirac operator.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065.     

Constraint aggregation principle in convex optimization

A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single surrogate inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new aggregation coefficients are calculated and the iteration continues. This general aggregation principle is incorporated into a number of specific algorithms. Convergence of the new methods is proved and speed of convergence analyzed. Next, dual interpretation of the method is provided and application to decomposable problems is discussed. Finally, a numerical illustration is given.     

A Note on Graph Pebbling

 We say that a graph G is Class 0 if its pebbling number is exactly equal to its number of vertices. For a positive integer d, let k(d) denote the least positive integer so that every graph G with diameter at most d and connectivity at least k(d) is Class 0. The existence of the function k was conjectured by Clarke, Hochberg and Hurlbert, who showed that if the function k exists, then it must satisfy k(d)=Ω(2 ^d /d). In this note, we show that k exists and satisfies k(d)=O(2 ^2d ). We also apply this result to improve the upper bound on the random graph threshold of the Class 0 property. Received: April 19, 1999 Final version received: February 15, 2000