A divalent germanium complex of calix[5]arene

The reaction of the germylene Ge[N(SiMe(3))(2)](2) with calix[5]arene yields the first example of a group 14 calix[5]arene complex. The crystal structure of this material has been obtained and contains two calix[5]arene macrocycles held together by a Ge(2)O(2) rhombus.     

Trapping a labile adduct formed between an ortho-quinone methide and 2'-deoxycytidine

Selective oxidation by bis[(trifluoroacetoxy)iodo]benzene (BTI) provides an effective trap for quenching adducts formed reversibly between dC and an ortho-quinone methide (QM) under physiological conditions. A model adduct generated by 4-methyl-o-QM and 2'-deoxycytidine is rapidly converted by intramolecular cyclization and loss of aromaticity to a characteristic product for quantifying QM alkylation. However, BTI induces a surprising rearrangement driven by overoxidation of a derivative lacking an alkyl substituent at the 4-position of the QM.     

Linearly implicit time discretization of non-linear parabolic equations

We give a stability and error analysis of linearly implicitone-step methods for time discretization of non-linear parabolicequations. We derive precise error bounds for Rosenbrock andW-methods, and we explain the error reduction by Richardsonextrapolation of the linearly implicit Euler method which occursin spite of the breakdown of asymptotic expansions. The parabolicequations are studied in a Hilbert space framework that includessemilinear and quasilinear parabolic equations, and also stiffreaction-diffusion equations with reactions at different timescales.     

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Vector-valued Lg-splines II. Smoothing splines

In the first paper of this series, Lg-spline theory was extended to the vector-valued interpolating case. Here this work is complemented by giving the extension for smoothing splines. The problem is formulated as a constrained minimum norm problem in a reproducing kernel Hilbert space, and solved recursively using a congruent stochastic estimation model.     

Zur konstruktion bewerteter dicksonscher fastkörper

Zusammenfassung  After a short introduction to the valuation theory of nearfields, we give criteria for when a valuation of a skewfield F is also a valuation of the Dickson nearfield F^K which is derived from F by the coupling K on F. For the construction of examples, a rational function field F =K(t) is given. The set of all prolongations of a valuation v on K to F is well known. Sufficient conditions are given which guarantee that couplings K on F and elements are in this sense compatible so that w is a valuation of the Dickson nearfield F^K. Examples demonstrate the results.

     

Halbruppen ohne Frattinische Unterhalbgruppe

Ohne ZusammenfassungVorgelegt vonL. Rédei     

A stochastic framework for recursive computation of spline functions: Part II,smoothing splines

Many of the optimal curve-fitting problems arising in approximation theory have the same structure as certain estimation problems involving random processes. We develop this structural correspondence for the problem of smoothing inaccurate data with splines and show that the smoothing spline is a sample function of a certain linear least-squares estimate. Estimation techniques are then used to derive a recursive algorithm for spline smoothing.     

Box-modeling of bone and tooth phosphate oxygen isotope compositions as a function of environmental and physiological parameters*

A time-dependent box model is developed to calculate oxygen isotope compositions of bone phosphate as a function of environmental and physiological parameters. Input and output oxygen fluxes related to body water and bone reservoirs are scaled to the body mass. The oxygen fluxes are evaluated by stoichiometric scaling to the calcium accretion and resorption rates, assuming a pure hydroxylapatite composition for the bone and tooth mineral. The model shows how the diet composition, body mass, ambient relative humidity and temperature may control the oxygen isotope composition of bone phosphate. The model also computes how bones and teeth record short-term variations in relative humidity, air temperature and δ¹⁸O of drinking water, depending on body mass. The documented diversity of oxygen isotope fractionation equations for vertebrates is accounted for by our model when for each specimen the physiological and diet parameters are adjusted in the living range of environmental conditions.     

On the Behavior of the Solutions for Certain Linear Autonomous Difference Equations

Certain linear autonomous delay as well as neutral delay difference equations are considered. A class of linear autonomous delay difference equations with continuous variable is also considered. Some results on the behavior of the solutions are established via two distinct positive roots of the corresponding characteristic equation.