Atomic coherence effects in the ion-trap laser

The influence of atomic coherence effects on the statistical and spectral properties of the ion-trap laser is investigated. Various pump configurations are considered for a realistic level scheme using a Ca ion. Compared to previous suggestions, 50% more output is obtained.     

Absorptive corrections to structure functions at small-x

The role of corrections due to the interactions between different branches of parton (gluon) cascades is studied. It is shown that at HERA energies these interactions increase the absorptive (two-Pomeron cut) contributions by about 60 to 80% compared with the Gribov-Levin-Ryskin equation.This work was supported, in part, by a Soros Foundation Grant awarded by the American Physical Society     

The complexity of many cells in arrangements of planes and related problems

We consider several problems involving points and planes in three dimensions. Our main results are: (i) The maximum number of faces boundingm distinct cells in an arrangement ofn planes isO(m ^2/3 n logn +n ²); we can calculatem such cells specified by a point in each, in worst-case timeO(m ^2/3 n log³ n+n ² logn). (ii) The maximum number of incidences betweenn planes andm vertices of their arrangement isO(m ^2/3 n logn+n ²), but this number is onlyO(m ^3/5– n ^4/5+2 +m+n logm), for any>0, for any collection of points no three of which are collinear. (iii) For an arbitrary collection ofm points, we can calculate the number of incidences between them andn planes by a randomized algorithm whose expected time complexity isO((m ^3/4– n ^3/4+3 +m) log² n+n logn logm) for any>0. (iv) Givenm points andn planes, we can find the plane lying immediately below each point in randomized expected timeO([m ^3/4– n ^3/4+3 +m] log² n+n logn logm) for any>0. (v) The maximum number of facets (i.e., (d–1)-dimensional faces) boundingm distinct cells in an arrangement ofn hyperplanes ind dimensions,d>3, isO(m ^2/3 n ^d/3 logn+n ^d–1). This is also an upper bound for the number of incidences betweenn hyperplanes ind dimensions andm vertices of their arrangement. The combinatorial bounds in (i) and (v) and the general bound in (ii) are almost tight.Work on this paper by the first author has been supported by Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and by NSF Grant CCR-8714565. Work by the third author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant DCR-82-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD—the Israeli National Council for Research and Development. An abstract of this paper has appeared in theProceedings of the 13th International Mathematical Programming Symposium, Tokyo, 1988, p. 147.     

Implicitly representing arrangements of lines or segments

Anarrangement ofn lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists ofO(n ²) regions, calledfaces. In this paper we study the problem of calculating and storing arrangementsimplicitly, using subquadratic space and preprocessing, so that, given any query pointp, we can calculate efficiently the face containingp. First, we consider the case of lines and show that with (n) space¹ and (n ^3/2) preprocessing time, we can answer face queries in (n)+O(K) time, whereK is the output size. (The query time is achieved with high probability.) In the process, we solve three interesting subproblems: (1) given a set ofn points, find a straight-edge spanning tree of these points such that any line intersects only a few edges of the tree, (2) given a simple polygonal path , form a data structure from which we can find the convex hull of any subpath of quickly, and (3) given a set of points, organize them so that the convex hull of their subset lying above a query line can be found quickly. Second, using random sampling, we give a tradeoff between increasing space and decreasing query time. Third, we extend our structure to report faces in an arrangement of line segments in (n ^1/3)+O(K) time, given(n ^4/3) space and (n ^5/3) preprocessing time. Lastly, we note that our techniques allow us to computem faces in an arrangement ofn lines in time (m ^2/3 n ^2/3+n), which is nearly optimal.The first author is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and National Science Foundation Grant CCR-8714565. Work on this paper by the fifth author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant NSF-DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD—the Israeli National Council for Research and Development. The sixth author was supported in part by a National Science Foundation Graduate Fellowship. This work was begun while the non-DEC authors were visiting at the DEC Systems Research Center.     

Radiative processes and non-equilibrium thermodynamics

With the assumption of an elementary physical concept meteorologically effective radiative processes (absorption-emission, scattering) can be included consistently in nonequilibrium thermodynamics of irreversible phenomena. Analogously to the usual Gibbs relations a fundamental equation was formulated for monochromatic light rays as the nucleus of the theory.Using the methods of classical irreversible theory, a complete entropy balance equation is derived in which the entropy variations of the mass as well as of the radiation field are explicitly represented. The resulting entropy source strength function through its analytical structure reveals the dynamical character of the irreversible variation terms. The-expression being positive according to the second law of thermodynamics is found to have a bilinear form as a function of the irreversible fluxes representing the entropy generating radiative processes and their conjugated thermodynamic forces. The mathematical structure and the positive sign of, following the usual line of reasoning, motivate the assumption of constitutive relations for the irreversible radiative processes. These equations developed from purely thermodynamical reasoning turn out to be equivalent to the usual radiative transfer equation which is founded on a very different theoretical concept. A very fundamental relationship can be deduced in this context from the entropy production function. It provides a direct thermodynamical proof that in nonscattering media the definition of a local temperature is necessarily accompanied by the validity of the Kirchhoff law.     

Microchemical characterization of paintings — A case study

Summary The fundamental importance of scientific research for the preservation and restoration of works of art is uncontestable. The methods described in this paper, such as light microscopy, microchemical tests, emission spectroscopy, chromatography, scanning electron analysis, electron microprobe analysis and infrared spectroscopy, are of special significance in this filed. Nevertheless a better understanding of the problems that arise out of new special questions of art history can be obtained only by the right interpretation of the data obtained by scientific methods.

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Mikrochemische Charakterisierung von Gemälden

Zusammenfassung Die grundlegende Bedeutung wissenschaftlicher Forschung für die Erhaltung und Restaurierung von Kunstwerken ist unbestritten. Die hier beschriebenen Methoden (Lichtmikroskopie, mikrochemische Reaktionen, Emissionsspektroskopie, Chromatographie, Rasterelektronen-Analyse und Infrarotspektroskopie) sind hierfür von zunehmender Bedeutung. Sie ermöglichen ein besseres Verständnis neuerer kunsthistorischer Probleme nur durch die richtige Interpretation der Ergebnisse wissenschaftlicher Methoden.

     

13C-NMR-spektren stereoisomerer 1,4-dialkylspiro[4.5]decan-derivate

The ¹³C NMR spectra of a series of 7-substituted 1,4-dialkylspiro[4.5]decanes and of suitable reference compounds are assigned and the derived substituent effects upon the chemical shifts are discussed. In particular, consideration of γ and δ-effects allows the differentiation between 1,4-cis- and 1,4-trans-compounds. Furthermore, the (relative) configuration of the chiral spiroatom C-5 is determined.