The use of magnetic fields in vertical Bridgman/Gradient Freeze-type crystal growth

This paper outlines advanced vertical Bridgman/Gradient Freeze techniques with flow control using magnetic fields developed for the growth of semiconductor crystals. Low-temperature flow modelling, as well as laboratory-scaled crystal growth under the influence of rotating, travelling, and static magnetic fields are presented. Experimental and numerical flow modelling demonstrate the potential of the magnetic fields to establish a well-defined flow for tailoring heat and mass transfer in the melt during growth. The results of the growth experiments are discussed with a focus on the influence of a rotating field on the segregation of dopants, the influence of a travelling field on the temperature field and thermal stresses, and the potential of rotating and static fields for a stabilization of the melt flow.     

Inequalities for some blocks of finite groups

We analyze some inequalities for numbers of characters in p-blocks of finite groups and prove them in the case of blocks with a normal defect group, as well as in the case of certain blocks in non-abelian simple groups. Received: 27 October 2005     

Topological Fixed Point Theorems Do Not Hold for Random Dynamical Systems

The aim of this paper is to demonstrate that topological fixed point theorems have no canonical generalization to the case of random dynamical systems. This is done by using tools from algebraic ergodic theory. We give a criterion for the existence of invariant probability measures for group valued cocycles. With that, examples of continuous random dynamical systems on a compact interval without random invariant points, which are an appropriate generalization of fixed points, are constructed.     

An electronic to ultrasonic image converter tube

This article describes in detail the elucidation of an equivalent RF-circuit diagram for an electronic ultrasonic image converter tube, and discusses practical aspects of the construction of the tube itself.     

A rapid and sensitive assay for determining human brain levels of farnesyl-(FPP) and geranylgeranylpyrophosphate (GGPP) and transferase activities using UHPLC–MS/MS

The isoprenoids farnesyl-(FPP) and geranylgeranylpyrophosphate (FPP and GGPP) are two major lipid intermediates in the mevalonate pathway. They participate in post-translational modification of members of the superfamily of small guanosine triphosphatases (GTPases; Ras, Rab, Rac, etc.) via prenylation reactions. Due to the important role of these proteins in a number of cell processes, in particular cell growth, division, and differentiation, investigation of the involvement of isoprenoids in these processes is of great interest. In a previously published report, we described a fully validated assay for the quantitation of the two isoprenoids using a high-performance liquid chromatography (HPLC)–fluorescence detection (FLD) method. The current work expands on the previous method and enhances it greatly by using a much faster state-of-the-art ultrahigh-performance liquid chromatography (UHPLC) technique coupled to tandem mass spectrometry (MS/MS). The method exhibited a linear concentration range of 5–250 ng/mL for FPP and GGPP in human brain tissue; it was shown to be unaffected by ion suppression and provided results almost six times faster than the HPLC–FLD assay. Comparison of UHPLC–MS/MS and HPLC–FLD yielded excellent comparability of the two assays for both isoprenoids. Based on the UHPLC–MS/MS assay, a novel in vitro test system was implemented to study enzyme specificity for distinct amino acid CAAX motifs, which is potentially useful for investigating target interactions of new therapeutics for diseases involving pathological regulation of isoprenoids and/or small GTPases.     

Decay Bounds on Eigenfunctions and the Singular Spectrum of Unbounded Jacobi Matrices

Bounds on the exponential decay of generalized eigenfunctionsof bounded and unbounded selfadjoint Jacobi matrices in are established. Two cases are considered separatelyand lead to different results: (i) the case in which the spectralparameter lies in a general gap of the spectrum of the Jacobimatrix and (ii) the case of a lower semibounded Jacobi matrixwith values of the spectral parameter below the spectrum. Itis demonstrated by examples that both results are sharp. Weapply these results to obtain a "many barriers-type" criterionfor the existence of square-summable generalized eigenfunctionsof an unbounded Jacobi matrix at almost every value of the spectralparameter in suitable open sets. In particular, this leads toexamples of unbounded Jacobi matrices with a spectral mobilityedge, i.e., a transition from purely absolutely continuous spectrumto dense pure point spectrum.