Speeding-up and scaling of domain-wall relaxation nearT c of a uniaxial ferromagnet

The dynamic susceptibility () measured between 10 Hz and 10 MHz on different GdCl₃-ellipsoids (T _c=2.21 K) reveals a completely reversible motion of the domain walls. Taking into account the contribution of the fast adiabatic intradomain magnetization to the nearly Debye-shaped (), we determine for the first time the kinetic Onsager coefficientL _d of the domain wall relaxation of a ferromagnet. Approaching the CurietemperatureL _d speeds up critically, which by a novel simple relaxational model can be related to the increasing width (=correlation length) of linear Bulaevskii-Ginzburg domain-walls and to the shrinking domain period. The reduction ofL _d by an external field can be represented by a universal scaling function, and within the same dynamical model, this effect is ascribed to the increase of the domain period, predicted for a bubble phase. However, the effect of sample size onL _d is much smaller than expected.     

A random approach to the Lebesgue integral

We construct an integral of a measurable real function using randomly chosen Riemann sums and show that it converges in probability to the Lebesgue integral where this exists. We then prove some conditions for the almost sure convergence of this integral.     

Matching inductive search bias and problem structure in continuous Estimation-of-Distribution Algorithms

Research into the dynamics of Genetic Algorithms (GAs) has led to the field of Estimation-of-Distribution Algorithms (EDAs). For discrete search spaces, EDAs have been developed that have obtained very promising results on a wide variety of problems. In this paper we investigate the conditions under which the adaptation of this technique to continuous search spaces fails to perform optimization efficiently. We show that without careful interpretation and adaptation of lessons learned from discrete EDAs, continuous EDAs will fail to perform efficient optimization on even some of the simplest problems. We reconsider the most important lessons to be learned in the design of EDAs and subsequently show how we can use this knowledge to extend continuous EDAs that were obtained by straightforward adaptation from the discrete domain so as to obtain an improvement in performance. Experimental results are presented to illustrate this improvement and to additionally confirm experimentally that a proper adaptation of discrete EDAs to the continuous case indeed requires careful consideration.     

A normality criterion involving rotations and dilations in the argument

We show that a family F\mathcal{F} of analytic functions in the unit disk \mathbbD{\mathbb{D}} all of whose zeros have multiplicity at least k and which satisfy a condition of the form

Some applications of Cartan's theorem to normality and semiduality of gap power series

In this paper we give partial solutions to some questions concerning analytic functions with AP-Gaps raised by Pinto, Ruscheweyh and Salinas (cf. [9], [12]) using a theorem of H. Cartan which extends Montel's theorem on analytic functions omitting the values 0 and 1. Using the same method, we also prove a generalization of a theorem in [9] on the dual hull of sets containing two elements.     

Zur colorimetrischen Bestimmung von 1,3,5-Thiadiazin-2-thionen

Summary Principles are discussed of the colorimetric determination of 3,5-di-substituted tetrahydro-1,3,5-thiadiazine-2-thiones using the reaction with Cu^II salts. More detailed informations will be given later.     

An extension of one direction in Marty’s normality criterion

We prove the following extension of one direction in Marty’s theorem: If $k$ is a natural number, $\alpha >1$ and $\mathcal{F }$ is a family of functions meromorphic on a domain $D$ all of whose poles have multiplicity at least $\frac{k}{\alpha -1}$ , then the normality of $\mathcal{F }$ implies that the family $$\begin{aligned} \left\{ \frac{|f^{(k)}|}{1+|f|^\alpha }\,:\, f\in \mathcal{F }\right\} \end{aligned}$$ is locally uniformly bounded.