The Orevkov invariant of an affine plane curve

We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.

     

Patent-Teil

Ohne Zusammenfassung     

Best affine unbiased representations of the fully restricted general Gauss-Markov model

This article completes and simplifies earlier results on the derivation of best linear, or affine, unbiased estimates in the general Gauss-Markov model with a singular dispersion matrix and additional restrictions under very general conditions. We provide the class of all linear representations of the best affine unbiased estimator with precise statements concerning its indeterminacy.     

Bi5O7Br and its structural relation to α‐Bi5O7I

Pentabismuth heptoxide bromide, Bi₅O₇Br, crystallizes in the space group Cmca. Its structure is compared with the closely related Ibca structure of α‐Bi₅O₇I. The change in the space group is assumedly the result of a compromise between the different spatial needs of Br and I and the rigidity of the {³_∞}[Bi, O] frameworks into which they are embedded. A detailed procedure for the synthesis of Bi₅O₇Br is given.     

Editorial

The principles of quantum-mechanical measurements are a key issue in the foundation of modern physics. A beautiful consequence of these is the concept of Quantum Nondemolition (QND) measurements. Such measurements permit, in principle, to measure particular observables of a quantum system with unlimited precision, leaving their temporal evolution undisturbed. The application of QND measurements may play an important role in future high-sensivity experiments.Experimental QND measurements require appropriate measurements schemes and apparats, whose development took place in the past few years, thanks to strong progress in ultra-low noise mechanical, electronic and optical detection techniques, coherent light sources, and nonlinear optical systems. At present, interest is focused on measurements of mechanical observables, such as displacement of macroscopic masses and of intensity or phases of electomagnetic field modes in the optical spectral range.This special issue contains original papers on theory and experiments of QND measurements. Recent experimental developments are presented, and proposals and analyses of novel QND schemes are made.The issue focuses on contributions presented at the Workshop on QND Measurements, held March 27–29, 1996, on the Island of Reichenau, Lake Constance (Germany). The workshop was made possible through a generous grant from the Directorats General XII for Sciences, Research and Development of the European Commission.We thank Dr. W. Petrich for his help in preparing this special issue.     

Flexural rigidity of a liquid surface

The energy of a mass of liquid is evaluated asymptotically in powers of the range of the intermolecular potential divided by a typical dimension of the liquid. The leading term is the internal energy, proportional to the liquid volume. The second term is the energy of surface tension, proportional to the area of the liquid surface. The third term is proportional to an integral over this surface of the square of the mean curvature of the surface minus one-third of its Gaussian curvature. This new term has exactly the form of the bending energy of a thin elastic plate. Comparing it with the bending energy yields expressions for the flexural rigidity and the Poisson ratio of the liquid surface. This flexural rigidity of the surface leads to new terms in the equation of equilibrium of the liquid surface, in addition to the usual surface tension terms.