Representations of bornological algebras

Bounded representations of bornological algebras are considered. The left and right bornological radicals in bornological algebras are introduced. It is shown that the left (right) bornological radical of a bornological algebra A is equal to the intersection of all bornologically closed maximal regular left (respectively, right) ideals of A, and both these radicals of A and the Jacobson radical of A coincide if A is an advertive and simplicial bornological algebra (in particular, a bornological Q-algebra). Bibliography: 16 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 9–22.     

Dense Monolayers of Monodisperse Opaque Spheres: Transmission and diffraction in the fraunhofer domain

The transmission and diffraction of radiation through dense monolayers of monodisperse opaque spheres were studied for the Fraunhofer domain. Theoretical considerations, numerical calculations and experiments on ultrasonic transmission and on laser light transmission and diffraction yielded corresponding results. Complementary studies included the cases of sterically non-interacting particles (by numerical simulation) and of small particle size parameters (by ultrasonic extinction). Transmission was found to be, in general, a non-linear function of the monolayer density. Secondary effects on the transmission can be attributed to the effect of the monolayer structure (characterized by the pair correlation function) on the angular distribution of diffracted intensity. The results were found to be in accordance with experimental results on extinction in three-dimensional systems.     

A concept of fuzzy transition probabilities

Starting from fuzzy real numbers with an arbitrary lattice of belief and following the extension principle, we develop concepts of fuzzy probabilities, transition probabilities and random variables and of their combinations, and show that these concepts are consistent. We derive some results on fuzzy real numbers, on the expectation of fuzzy random variables and on fuzzy stochastic processes. To sketch the range of applications of fuzzy stochastics, we give two examples that show how real-world problems may be modeled by means of fuzzy probabilities and that give small numerical examples. Moreover, we give a brief outlook for a possible expansion of our theory to fuzzy Markovian decision processes by means of a partial order on the set of all fuzzy real numbers.     

The Mössbauer effect and collective motions in glass-forming liquids and polymeric networks

Glass-forming liquids, synthetic polymers and biopolymers share essential properties. Dynamic processes in these complex systems are characterized by cooperative motions with wide distributions of time scales, which manifest themselves in broad quasielastic lines in the Mössbauer spectrum. In this article, the application of the Mössbauer effect to the study of structural dynamics in complex systems is discussed.     

Stressed states in domain switching of ferroelectric liquid crystal devices

In this paper we show that the director profile of a low pre-tilt surface stabilized ferroelectric liquid crystal passes through quasi-static stressed states during domain switching under direct drive conditions. Using polarized stroboscopic microscopy, we have observed two quasi-static transmission levels during a domain switching transition from dark to light. This is a result of the directors reorienting into stressed profiles both before and after the chevron interface has switched. By modelling the interaction between the elastic forces and the torque from the applied field, we have determined these voltage dependent director profiles and, by calculating their corresponding transmissivities, have shown very good agreement with the experimentally observed values.