Reverse inequalities for zonoids and their application

We prove inequalities for mixed volumes of zonoids with isotropic generating measures. A special case is an inequality for zonoids that is reverse to the generalized Urysohn inequality, between mean width and another intrinsic volume; here the equality case characterizes parallelepipeds. We apply this to a question from stochastic geometry. It is known that among the stationary Poisson hyperplane processes of given positive intensity in n-dimensional Euclidean space, the ones with rotation invariant distribution are characterized by the fact that they yield, for k∈{2,…,n}, the maximal intensity of the intersection process of order k. We show that, if the kth intersection density is measured in an affine-invariant way, the processes of hyperplanes with only n fixed directions are characterized by a corresponding minimum property.     

Graph problems arising from parameter identification of discrete dynamical systems

This paper focuses on combinatorial feasibility and optimization problems that arise in the context of parameter identification of discrete dynamical systems. Given a candidate parametric model for a physical system and a set of experimental observations, the objective of parameter identification is to provide estimates of the parameter values for which the model can reproduce the experiments. To this end, we define a finite graph corresponding to the model, to each arc of which a set of parameters is associated. Paths in this graph are regarded as feasible only if the sets of parameters corresponding to the arcs of the path have nonempty intersection. We study feasibility and optimization problems on such feasible paths, focusing on computational complexity. We show that, under certain restrictions on the sets of parameters, some of the problems become tractable, whereas others are NP-hard. In a similar vein, we define and study some graph problems for experimental design, whose goal is to support the scientist in optimally designing new experiments.     

Small faces in stationary Poisson hyperplane tessellations

We consider the tessellation induced by a stationary Poisson hyperplane process in d‐dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the k‐faces of the tessellation by a suitable size functional, we determine a limit distribution for the shape of the typical k‐face, under the condition of given size and this tending to zero. The limit distribution is concentrated on simplices. This extends a result of Gilles Bonnet.     

Spin-orbit interaction in molecular photoelectron spectra An intermediate coupling approach

A new and general semiempirical method for calculating ionization energies of molecules containing heavy atoms is presented. The extended Hückel hamiltonian is amended with a phenomenological one-electron spin-orbit interaction operator, and ionization energies are equated to orbital energies according to Koopmans' theorem. Calculations are presented for molecules with Br and I as heavy atoms. The systems considered are the hydrogen halides, diatomic halogens and interhalogens, haloacetylenes, halomethanes, and boron trihalides. Good agreement with the observed spin-orbit splitting is obtained. New assignments are proposed for the trihalides considered.     

BEEM-π calculations for a series of pyridines and their 14N N.Q.R.

The ⁵⁷Fe Mössbauer spectrum of a powdered sample of phthalocyanine-iron(II) in an applied magnetic field of 3·0 teslas has been measured as a function of temperature in the range 4·2 K to 100 K. Measurements have also been made at 4·2 K with 6·0 teslas applied, and on a single crystal specimen at 4·2 K with 3·0 teslas applied. Independent computer fits to the three measurements taken at 4·2 K were found to be consistent with one another, and showed that detailed information concerning magnetic anisotropy can be obtained even from powdered samples of paramagnets by Mössbauer spectroscopy. Although the asymmetry parameter in the electric field gradient tensor was found to be small, there was a significant departure from tetragonal symmetry in the magnetic properties of the molecule. The magnetic hyperfine field at the ⁵⁷Fe nucleus was found to be positive in all directions, indicating that all three electronic g values are significantly greater than 2·0.     

Vibrational Spectra of Ethylenediamine Salts. I. Tentative Assignments of Infrared and Far Infrared Spectra

Abstract

We wish to report on some hitherto partly unnoticed and unexplained features in the infrared spectra of hydrogen halides of ethylenediamine. We have prepared normal, C-, N-, and perdeuterated ethylenediammonium chlorides and bromides and measured their infrared spectra in the range 4000–10 cm^?1.     

A novel monochromator for experiments with ultrashort X‐ray pulses

Aiming at advancing storage‐ring‐based ultrafast X‐ray science, over the past few years many upgrades have been undertaken to continue improving beamline performance and photon flux at the Femtoslicing facility at BESSY II. In this article the particular design upgrade of one of the key optical components, the zone‐plate monochromator (ZPM) beamline, is reported. The beamline is devoted to optical pump/soft X‐ray probe applications with 100 fs (FWHM) X‐ray pulses in the soft X‐ray range at variable polarization. A novel approach consisting of an array of nine off‐axis reflection zone plates is used for a gapless coverage of the spectral range between 410 and 1333 eV at a designed resolution of E/ΔE = 500 and a pulse elongation of only 30 fs. With the upgrade of the ZPM the following was achieved: a smaller focus, an improved spectral resolution and bandwidth as well as excellent long‐term stability. The beamline will enable a new class of ultrafast applications with variable optical excitation wavelength and variable polarization.     

Die selektive invers-voltammetrische Bestimmung des Antimons in salzsauren L?sungen nach L?sungswechsel in einer einfachen Durchflu?zelle

Summary The selective invers-voltammetric determination of antimony in a simple flow-through cell in hydrochloric acid solutions is described. After double medium exchange for post-electrolysis and inverse-voltammetric determination, the determination of antimony is possible in the presence of a large excess of copper, bismuth and other elements. The limit of determination is 0.2–0.3 ppb Sb, the reproducibility 1.5% (10 ppb Sb).     

Typical Cells in Poisson Hyperplane Tessellations

It is proved that the shape of the typical cell of a stationary and isotropic Poisson random hyperplane tessellation is, with high probability, close to the shape of a ball if the kth intrinsic volume (k ≥ 2) of the typical cell is large. The shape of typical cells of large diameter is close to the shape of a segment.