we have calculated the phonon frequencies of kc1 along symmetry directions using an approach which is a combination of the frozen phonon and force constants methods. we also calculated griineisen parameters for all modes at x and l points in the brillouin zone. finally, the slope of acoustic dispersion curves around zone center were used to calculate the three independent elastic coefficients c...

1. INTRODUCTION. Negative theorems have a rich tradition in mathematics. In fact mathematics seems to be unique among the sciences in that negative results are very much a part of the mathematical edifice. Most mathematical theories try to explain what is possible and also what is not. To understand the structure of a mathematical theory is also to understand its limitations. There are many dif...

Learning theory studies data structures from samples and aims at understanding unknown function relations behind them. This leads to interesting theoretical problems which can be often attacked with methods from Approximation Theory. This workshop the second one of this type at the MFO has concentrated on the following recent topics: Learning of manifolds and the geometry of data; sparsity and ...

In many practical situations, one needs to construct a model for an input/output process. For example, one is interested in the price of a stock five years from now. The rating industry description for the stock typically lists such indicators as the increase in the price over the last year, the last 5 years, 10 years, life of the stock, P/E ratio, and alpha and beta risk factors. The buyer is ...

This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis; their properties depend on combinatorics, topology, and geometry of a simplicial or polyhedral subdivision of a region in Rk, and are often quite subtle. We describe four algebraic technique...

This monograph presents ideas and techniques from approximation theory for approximating functions such as xs, x−1 and e−x, and demonstrates how these results play a crucial role in the design of fast algorithms for problems which are increasingly relevant. The key lies in the fact that such results imply faster ways to compute primitives such as Asv, A−1v, exp(−A)v, eigenvalues, and eigenvecto...

This paper is an attempt to both expound and expand upon, from an approximation theorist’s point of view, some of the theoretical results that have been obtained in the sparse representation (compressed sensing) literature. In particular, we consider in detail l1 -approximation, which is fundamental in the theory of sparse representations, and the connection between the theory of sparse represe...