Space-Time Directional Lyapunov Exponents for Cellular Automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved.     

Spectral decomposition of an elementary 3-fermion 2-body operator

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P²_g∧I¹A³∑_{1≤i≤j≤3}P²_g(i, j)A³ acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here P_g² denotes the projection operator onto a 2-particle antisymmetric function g², while A³ denotes the 3-particle antisymmetrizing operator.     

Scheduling data transfers in a network and the set scheduling problem

In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as max-stretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum max-stretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the max-stretch and total flow time for the case where online and offline algorithms are using same-capacity edges. Moreover, we also give polylogarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and max-stretch within a constant factor of optimum.     

Mechanisms of n‐butanol formation in butyl acrylate latexes

The mechanisms involved in the formation of n‐butanol during the synthesis of butyl acrylate containing latices were investigated. The experimental results showed that neither the hydrolysis of butyl acrylate nor of the ester bond in the butyl acrylate segments of the polymer played a major role in the formation of n‐butanol, which was mainly generated from the polymer backbone, by transfer reactions to polymer chain followed by cyclization. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5838–5846, 2007     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Time structure of iodine laser pulse in the free running mode of operation

Time structure of iodine laser pulse in the free running mode of operation was studied using the power amplifier of laser system PERUN as the laser oscillator. Two characteristic shapes of laser pulse correspond to different regimes of laser operation, the existence of which is ascribed to the critical concentration of I₂ molecules. Simultaneously an additional chemical pumping was proved at least in the initial phase of photodissociation and in a late-time lasing after the end of flashlamps pumping light.     

Analysis of Glycosides and Aglycones of Flavonoid Compounds by Double-Development Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - Flavonoid glycosides are much more polar than their aglycones and the two groups of compounds are difficult to separate by planar...     

The Effects of a Study‐Group Process on the Implementation of Reform in Mathematics Education

In each of three consecutive years, 16 teachers were admitted to a program in which they participated in a study group to reform their teaching practices in mathematics. The 48 (total) elementary school teachers in this program were selected to ensure diversity of setting— urban and suburban, as well as public and parochial. Teachers routinely met with the study group for 1 year, engaging in follow‐up activities after that year. Surveys, interviews, and site visits showed that teachers underwent significant changes in their knowledge, beliefs, and teaching practices and were attempting to implement reform consistent with current standards. Teachers with 11 to 25 years of experience demonstrated the greatest changes. Long‐term effects of the program and its impact on colleagues within the building and district have yet to be studied.     

The capacity of parabolic julia sets

Supported by SFB 170 “Geometrie und Analysis” at the University of G?ttingen     

The complete grapht-packings andt-coverings

The aim of this paper is to introduce the notions of floor and ceiling functions related to graph edge-decompositions intot mutually isomorphic parts. It is shown that, given any natural numbert, uniform and extremal t-packing andt-covering exist for each complete graph and each complete bipartite graph. Extremal in this context means that both a remainder and a surplus are absolutely minimum. In proofs, decompositions of multigraphs into matchings are involved. Open problems and conjectures are stated.