Probenchemische Methode zur Bestimmung von 15N an in Gesteinen fixiertem Stickstoff

Zur Klärung geologischer Prozesse werden in zunchmendem Maße die Isotopenvariationen des Stickstoffs herangezogen. Da der größte Teil des Stickstoffs der Gesteine in gebundener Form als Ammoniumstickstoff [1–6] vorliegt, kommt der Untersuchung der Isotopenvariationen desselben eine große Bedeutung zu.     

Untersuchungen zur Empfindlichkeit der β-Rückstreumethode bei der Messung dünner Auftragsschichten mit einem 11C-Spezialpräparat

Die Bestimmung dünner Auftragsschichten auf bewegten Trāgermaterialien mit der β-Rūckstreumethode hängt wesentlich von der Empfindlichkeit der Messung und der Dynamik des Prozesses ab.

In diesem Beitrag wird für spezielle Stoffe der Einfluβ der Trāgermaterialien bei Mehrschichtproblemen auf die Empfindlichkeit untersucht.     

Efficient synthesis of the C/D rings of atisine-type C20-diterpenoid alkaloids

A bicyclo[2.2.2]octane C/D ring system,with a lactonic ring at C-8 and C-9,of the atisine-type C₂₀-diterpenoid alkaloids,was successfully synthesized,using an oxidative dearomatization/intramolecular Diels-Alder reaction.     

TrigonometricR matrices related to ‘dilute’ Birman-Wenzl-Murakami algebra

Explicit expressions for three series ofR matrices which are related to a dilute generalisation of the Birman-Wenzl-Murakami algebra are presented. Of those, one series is equivalent to the quantumR matrices of theD _n+1 ⁽²⁾ generalised Toda systems, whereas the remaining two series appear to be new.     

论中国海洋砂矿床类型

本文总结了作者二十多年砂矿工作的经验,搜集了国内近三百处海洋砂矿床(点)五十余种矿床类型划分的资料,比照国外同类型矿床,结合我国矿床特征,提出了新的海洋砂矿分类原则,矿床工业类型、成因-形态类型、成矿时代类型和保存类型等的划分系统,以及今后的找矿方向。     

The asymptotic numbers of regular tournaments,Eulerian digraphs and Eulerian oriented graphs

LetRT(n), ED(n) andEOG(n) be the number of labelled regular tournaments, labelled loop-free simple Eulerian digraphs, and labelled Eulerian oriented simple graphs, respectively, onn vertices. Then, asn,, for any>0. The last two families of graphs are also enumerated by their numbers of edges. The proofs use the saddle point method applied to appropriaten-dimensional integrals.     

A shape-optimization technique for the capillary surface problem

Summary The problem of the construction of an equilibrium surface taking the surface tension into account leads to Laplace-Young equation which is a nonlinear elliptic free-boundary problem. In contrast to Orr et al. where an iterative technique is used for direct solution of the equation for problems with simple geometry, we propose here an alternative approach based on shape optimization techniques. The shape of the domain of the liquid is varied to attain the optimality condition. Using optimal control theory to derive expressions for the gradient, a numerical scheme is proposed and simple model problems are solved to validate the scheme.     

The continuous solution of a functional equation of Abel

Summary The functional equation(x) + (y) = (xf(y) + yf(x)) (1) for the unknown functionsf, and mapping reals into reals appears in the title of N. H. Abel's paper [1] from 1827 and its differentiable solutions are given there. In 1900 D. Hilbert pointed to (1), and to other functional equations considered by Abel, in the second part of his fifth problem. He asked if these equations could be solved without, for instance, assumption of differentiability of given and unknown functions. Hilbert's question was recalled by J. Aczél in 1987, during the 25th International Symposium on Functional Equations in Hamburg-Rissen. In particular Aczél asked for all continuous solutions of (1). An answer to his question is contained in our paper. We determine all continuous functionsf: I ,: A _f (I × I) and: I that satisfy (1). HereI denotes a real interval containing 0 andA _f (x,y) := xf(y) + yf(x), x, y I. The list contains not only the differentiable solutions, implicitly described by Abel, but also some nondifferentiable ones.Applying some results of C. T. Ng and A. Járai we are able to obtain even a more general result. For instance, the assertion (i.e. the list of solutions) remains unchanged if we replace continuity of and by local boundedness of orf(0)I from above or below. Strengthening a bit the assumptions onf we can preserve a large part of the assertion requiring only the measurability of either orf(0)I.     

Tracking poles and representing Hankel operators directly from data

Summary We propose and analyse a method of estimating the poles near the unit circleT of a functionG whose values are given at a grid of points onT: we give an algorithm for performing this estimation and prove a convergence theorem. The method is to identify the phase for an estimate by considering the peaks of the absolute value ofG onT, and then to estimate the modulus by seeking a bestL ² fit toG over a small arc by a first order rational function. These pole estimates lead to the construction of a basis ofL ² which is well suited to the numerical representation of the Hankel operator with symbolG and thereby to the numerical solution of the Nehari problem (computing the bestH , analytic, approximation toG relative to theL norm), as analysed in [HY]. We present the results of numerical tests of these algorithms.Partially supported by grants from the AFOSR and NSF