Abstract. In the early 90's J. Birman and W. Menasco worked out a nice technique for studying links presented in the form of a closed braid. The technique is based on certain foliated surfaces and uses tricks similar to those that were introduced earlier by D. Bennequin. A few years later P. Cromwell adapted Birman-Menasco's method for studying so-called arc-presentations of links and established some of their basic properties. Here we further develop that technique and the theory of arc-presentations, and prove that any arc-presentation of the unknot admits a (non-strictly) monotonic simplification by elementary moves; this yields a simple algorithm for recognizing the unknot. We also show that the problem of recognizing split links and that of factorizing a composite link can be solved in a similar manner. We also define two easily checked sufficient conditions for knottedness. Contents

The present volume follows a book, "Why are braids orderable?", written by the same authors and published in 2002 by the Société Mathématique de France in the series Panoramas et Synthèses. We emphasize that this is not a new edition of that book. Although this book contains most of the material in the previous book, it also contains a considerable amount of new material. In addition, much of the original text has been completely rewritten, with a view to making it more readable and up-to-date. We have been able not only to include ideas that were unknown in 2002, but we have also benefitted from helpful comments by colleagues and students regarding the contents of the SMF book, and we have taken their advice to heart in writing this book. The reader is assumed to have some basic background in group theory and topology. However, we have attempted to make the ideas in this volume accessible and interesting to students and seasoned professionals alike. Really, the question "Why are braids orderable?" has not been answered to our satisfaction, either in the book with that title, or the present volume. That is, we do not understand precisely what makes the braid groups particularly special, so that they enjoy an ordering which is so easy to describe, so challenging to establish and with such subtle properties as are described in these pages. The best we can offer is some insight into the easier question, "How are braids orderable?"

No abstract

Silicon photodiodes of different types were tested for the possibility of measurement of high-intensity x-ray pulses from the plasmas produced by the 1 kJ PALS laser system in Prague. The x-ray energy range of the operation of the detectors was 1-20 keV. The tests were done with the use of different targets at the laser energy up to 740 J in the case of fundamental frequency (1ω, 1315 nm) and up to 230 J in the case of the 3rd harmonics (3ω). The detectors that were assigned for the measurement of the harder part of the spectrum (5-20 keV) can operate without overloading at all laser energies used, but the detectors for soft radiation can be easily overloaded above 200 J (at the fundamental frequency). Some problems with noise compatibility were encountered, as well. The possible improvements of detection systems for the future experiments are proposed. The detectors investigated in the experiment can be applied for finding the optimal condition for producing the hottest plasmas and for a precise calibration of the target positioning system.

A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors in 1997. At the same time we started studying first order difference "black and white triangle operators (equations)" on triangulated surfaces with a black and white coloring of triangles. In this work, we develop the theory of these operators and equations, showing their similarity with the complex derivatives ∂ and ∂.