Different moment-angle manifolds arising from two polytopes having the same bigraded Betti numbers

Two simple polytopes of dimension 3 having the identical bigraded Betti numbers but non-isomorphic Tor-algebras are presented. These polytopes provide two homotopically different moment-angle manifolds having the same bigraded Betti numbers. These two simple polytopes are the first examples of polytopes that are (toric) cohomologically rigid but not combinatorially rigid.Comment: 9 page, 2 figures, 2 table

Laser Induced Gas Vortices

Properly polarized and correctly timed femtosecond laser pulses have been demonstrated to create rotational states with a preferred sense of rotation. We show that due to conservation of angular momentum, collisional relaxation of these unidirectionally rotating molecules leads to the generation of macroscopic vortex flows in the gas. The emerging velocity field converges to a self-similar Taylor vortex, and repeated laser excitations cause a continuous stirring of the gas.Comment: 4 pages, 5 figure

Volume estimates for equiangular hyperbolic Coxeter polyhedra

An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to \pi/n for some fixed integer n at least 2. It is a consequence of Andreev's theorem that either n=3 and the polyhedron has all ideal vertices or that n=2. Volume estimates are given for all equiangular hyperbolic Coxeter polyhedra.Comment: 27 pages, 11 figures; corrected typo in Theorem 2.

Automation - Development of the Material-Technological Basis - Changed Conditions of Efficiency

This paper was presented at a joint seminar on flexible automation held in Berlin (East) from June 8-11, 1982. The seminar was a collaborative project between IIASA and the Academy of Sciences of the German Democratic Republic. The report and the working material presented to the conference deal, among other things, with the influence of the flexible automation on the further development of the material-technological basis and on the whole system of the productive forces. Hence the following questions arise: Does the qualitatively new level of automation mean in connection with the development and application of micro-electronics and what is flexible automation? What are the constituent elements of the new level of automation and which are the consequences for the development of the material-technological basis? and Which changes within the conditions of efficiency take place due to the new level of automation on the basis of micro-electronics? The presented paper offers some aspects regarding these questions