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.     

Quantum backaction of optical observations on Bose-Einstein condensates

Impressive pictures of moving Bose-Einstein condensates have been taken using phase-contrast imaging [M.R. Andrews et al., Science 273, 84 (1996)]. We calculate the quantum backaction of this measurement technique, assuming the absence of residual absorption. We find that the condensate gets gradually depleted at a universal rate that is proportional to the light intensity and to the inverse cube of the optical wave length. The fewer atoms are condensed the higher is the required intensity to see a picture, and, consequently, the higher is the induced backaction. To describe the quantum physics of phase-contrast imaging we put forward a new approach to quantum-optical propagation. We develop an effective field theory of paraxial optics in a fully quantized atomic medium. Received 25 February 1999     

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.