K-contact Lie groups of dimension five or greater

We prove that a K-contact Lie group of dimension five or greater is the central extension of a symplectic Lie group by complexifying the Lie algebra and applying a result from complex contact geometry, namely, that, if the adjoint action of the complex Reeb vector field on a complex contact Lie algebra is diagonalizable, then it is trivial

Mathematical algorithms to maximize performance in numerical weather prediction

Numerical weather prediction models, which involve the solution of non-linear partial differential equations at points on an extensive three dimensional grid, are ideally suited for processing on vector machines. It was logical therefore that the new global forecast model to be implemented at the Meteorological Office should be written in vector code for the CYBER 205. In order to achieve full efficiency and to reduce storage requirements the model used 32-bit arithmetic which was found to provide high enough precision. Unfortunately, however, the trigonometrical and logarithmic functions provided by CDC could only handle 64-bit vectors and, although written in efficient scalar code, did not take advantage of the special facilities of a vector processor. It was therefore necessary to rewrite the functions in vector code to handle both 32 and 64-bit vectors. There was also no half-precision compiler available for the Cyber 205 at that time and so the functions, like the model, had to make extensive use of the special call syntax. This made the code more difficult to write but it allowed much greater flexibility in that it became possible to access the exponent of a floating-point number independently of its coefficient. A description is given of the technique and the results which were achieved are summarized

A Model of Later Nineteenth Century European Economic Development

Editada en la Fundación Empresa PúblicaEn este trabajo se desarrolla y estima un modelo para explicar los motivos por los cuales algunos países europeos prosperaron más rápidamente que otros en el período 1860- 1910. El modelo cuantifica por dos vías distintas los factores que contribuyeron a las diferencias de ingreso entre España y Gran Bretaña. Los determinantes que se consideran más significativos son los recursos naturales, la política económica y la herencia cultural reflejada en los niveles educativos.A model is developed and estimated to explain why some European countries were richer than others between 1860 and 1910 and why some increased their prosperity faster in the period. The model quantifies by two methods some of the contributors to the income gap between the economies of Spain and Britain in 1880 and 1910. Determinants of European nations' output per head included natural endowments (climate and coal deposits), economic policy (tariff protection and very marginally the gold standard), and cultural heritage as reflected in literacy. Measurement errors, country specific factors and perhaps variables not considered in this analysis account for less than half Spanish-UK income differences at the dates estimated.Publicad

Measure Preserving Diffeomorphisms of the Torus are Unclassifiable

The isomorphism problem in ergodic theory was formulated by von Neumann in 1932 in his pioneering paper Zur Operatorenmethode in der klassischen Mechanik (Ann. of Math. (2), 33(3):587--642, 1932). The problem has been solved for some classes of transformations that have special properties, such as the collection of transformations with discrete spectrum or Bernoulli shifts. This paper shows that a general classification is impossible (even in concrete settings) by showing that the collection $E$ of pairs of ergodic, Lebesgue measure preserving diffeomorphisms $(S,T)$ of the 2-torus that are isomorphic is a complete analytic set in the $C^\infty$- topology (and hence not Borel).Comment: 97 pages, 4 figure