Algebraic properties of discrete box splines

The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as a device for the fast computation of multivariate splines. The results obtained here allow us to draw conclusions about the structure of such discrete splines which have, in particular, applications to counting the number of nonnegative integer solutions of linear diophantine equations.     

A characterization of the \Sigma_1-definable functions of KP\omega + (uniform\; AC)

The subject of this paper is a characterization of the -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a given choice functional and . This goal is achieved by a G?del Dialectica-style functional interpretation of and a computability proof for the involved functionals. Received October 9, 1996     

QCD corrections to the forward-backward asymmetries of c and b quarks at the Z pole

Measurements of the forward-backward production asymmetry of heavy quarks in Z decays provide a precise determination of . The asymmetries are sensitive to QCD effects, in particular hard gluon radiation. In this paper QCD corrections for and are discussed. The interplay between the experimental techniques used to measure the asymmetries and the QCD effects is investigated using simulated events. A procedure to estimate the correction needed for experimental measurements is proposed, and some specific examples are given. Received: 26 February 1998 / Published online: 2 June 1998     

Frequency-dependent spin-lattice relaxation study of transport processes in superionic conductors

The sensitivity of the¹⁹F spin-lattice relaxation dispersion, T₁,(ω), to motional disorder in crystalline superionic conductors of the type La_1?xSr_xF_3?x (x = 0; 0.03) is shown. T₁ times are measured in the frequency range from 90 kHz to 370 MHz using standard techniques in combination with field-cycling. The relaxation dispersion shows qualitative differences from the standard Bloembergen-Purcell-Pound behavior. At low frequencies a relaxation model using a distribution of correlation times for diffusing ions is found to be consistent with the experimental results. At frequencies higher than 50 MHz another process of the Debye type which is not induced by ionic hopping dominates the relaxation.     

Two Ergodic Sample-Path Properties of the Poisson Process

For increasing sequences of real numbers we consider two types of asymptotic behavior that remind of the defining property of a (homogeneous) Poisson process according to which the numbers of points in disjoint intervals are independent and follow Poisson distributions with specified parameters. We prove that almost all paths of a Poisson process show this asymptotic behavior, and characterize the Poisson process by these properties. Further we discuss the connection to equidistribution notions.     

Conversion estimates for gas-solid reactions: Improved estimates for irreversible systems

Solid conversion has been of much interest to research workers and the Cumulative Gas Concentration Method (CGCM) has been developed to provide bounds for the reactant solid in irreversible systems having power-law type kinetics. This CGCM is used in conjunction with the Pseudo-Steady-State (PSS) assumption and these bounds appear to be good under certain conditions and for long times.

In this work, the PSS condition is not assumed when deriving the bounds on the cumulative gas concentration and the effect of the inclusion of the transient part is analysed. A technique, based on an iterative scheme incorporating the CGCM, is developed to provide improved estimates for the reactant solid.     

A bandstructure approach to the calculation of density correlation functions with application to Vanadium

We discuss how to use KKR bandstructure to evaluate the density-density correlation function in DFA (density functional) — RPA approximation without introducing adjustable parameters. We stress the importance to determine the dielectric function to a high degree of accuracy in the high frequency range to guarantee the fulfillment of the f-sum rule. Results for Vanadium as a typical example of a transition metal are presented and compared to experiment.