An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems

In this paper we develop a numerical method for two-dimensionaltime-dependent reaction-diffusion problems. This method, whichcan immediately be generalized to higher dimensions, is shownto be uniformly convergent with respect to the diffusion problems.This method, which can immediately be generalized to higherdimensions, is shown to be uniformly convergent with respectto the diffusion parameter.     

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.