Über die polarographische Bestimmung von Parathion und seinem Metabolit p-Nitrophenol in Blutextrakten

Microchimica Acta - Zur Bestimmung von Parathion und seinem Metabolit p-Nitrophenol im Blut wurde eine vereinfachte polarographische Methode vorgeschlagen. Die Trennung beider...     

An overview on available models and techniques for the multicriteria reliability problem with emphasis on a potential use in a DSS for this problem type

The paper reviews available models and techniques covering three classes of the multi-criteria reliability problem. These classes include allocation of reliabilities in presence of multiple goals, reliability optimization with several kinds of failures and allocation of resources to optimize multiattribute systems. Optimization techniques are also suggested. The models and techniques are also evaluated with respect to their potential use in a DSS for reliability optimization.     

Zur Quantentheorie der Néel-Wände in dünnen ferromagnetischen Schichten

Using a general quantum mechanical method earlier developed by the author it is shown, that the periodic domain structure of thin ferromagnetic single-crystal films (thickness below 500 Å) as well as the rotation of the magnetization vector in theNéel wall can be obtained by a simple minimalisation procedure based on a variational principle. As an example some calculations and results for a unixial film are presented.     

On the generalized Fréchet functional equation with constant coefficients and its stability

We study a generalization of the Fréchet functional equation, stemming from a characterization of inner product spaces. We show, in particular, that under some weak additional assumptions each solution of such an equation is additive. We also obtain a theorem on the Ulam type stability of the equation. In its proof we use a fixed point result to show the existence of an exact solution of the equation that is close to a given approximate solution.     

Remarks on solutions to a generalization of the radical functional equations

During the \(16{\text {th}}\) International Conference on Functional Equations and Inequalities a talk was given concerning the stability of the so-called radical functional equation \(f(\sqrt{x^2+y^2\,}\,)=f(x)+f(y)\). The second author’s question about the general solution of the equation itself was answered later by the first one. Contrary to some assertions in the literature the general solution is not an arbitrary quadratic function, but of the form \(x\mapsto a(x^2)\) with additive a. Here we present far reaching generalizations of this result.     

Heat conduction in transversally graded laminates with non-uniform microstructure

Two-component laminates made of conductors distributed non-periodically as laminas along one direction are considered in this note. The macroscopic properties of these laminates are described by continuous slowly-varying functions across laminas. In order to analyse heat conduction, the approach, called the tolerance modelling, is used. The aim of this note is to use averaged equations of the tolerance model for transversally graded laminates to analyse stationary heat conduction across laminas. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A sharp maximal inequality for continuous martingales and their differential subordinates

Assume that X, Y are continuous-path martingales taking values in ? ^ν , ν ? 1, such that Y is differentially subordinate to X. The paper contains the proof of the maximal inequality $$\left\| {\mathop {\sup }\limits_{t \geqslant 0} \left| {Y_t } \right|} \right\|_1 \leqslant 2\left\| {\mathop {\sup }\limits_{t \geqslant 0} \left| {X_t } \right|} \right\|_1 .$$ The constant 2 is shown to be the best possible, even in the one-dimensional setting of stochastic integrals with respect to a standard Brownian motion. The proof uses Burkholder’s method and rests on the construction of an appropriate special function.     

Bohr–Sommerfeld–Heisenberg theory in geometric quantization

In the framework of geometric quantization we extend the Bohr–Sommerfeld rules to a full quantum theory which resembles the Heisenberg matrix theory. This extension is possible because Bohr–Sommerfeld rules not only provide an orthogonal basis in the space of quantum states, but also give a lattice structure to this basis. This permits the definition of appropriate shifting operators. As examples, we discuss the 1–dimensional harmonic oscillator and the coadjoint orbits of the rotation group.     

A characterization of p-bases of rings of constants

We obtain two equivalent conditions for m polynomials in n variables to form a p-basis of a ring of constants of some polynomial K-derivation, where K is a unique factorization domain of characteristic p > 0. One of these conditions involves Jacobians while the other some properties of factors. In the case m = n this extends the known theorem of Nousiainen, and we obtain a new formulation of the Jacobian conjecture in positive characteristic.