Continuous weak approximation for stochastic differential equations

A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations (SDEs) by general one-step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second order conditions for a class of continuous stochastic Runge–Kutta methods containing the continuous extension of the second order stochastic Runge–Kutta scheme due to Platen are derived. Further, some coefficients for optimal continuous schemes applicable to Itô SDEs with respect to a multi–dimensional Wiener process are presented.     

Novel Bottom‐Up SERS Substrates for Quantitative and Parallelized Analytics

Surface‐enhanced Raman spectroscopy (SERS) is an emerging technology in the field of analytics. Due to the high sensitivity in connection with specific Raman molecular fingerprint information SERS can be used in a variety of analytical, bioanalytical, and biosensing applications. However, for the SERS effect substrates with metal nanostructures are needed. The broad application of this technology is greatly hampered by the lack of reliable and reproducible substrates. Usually the activity of a given substrate has to be determined by time‐consuming experiments such as calibration or ultramicroscopic studies. To use SERS as a standard analytical tool, cheap and reproducible substrates are required, preferably with a characterization technique that does not interfere with the subsequent measurements. Herein we introduce an innovative approach to produce low‐cost and large‐scale reproducible substrates for SERS applications, which allows easy and economical production of micropatterned SERS active surfaces on a large scale. This approach is based on an enzyme‐induced growth of silver nanostructures. The special structural feature of the enzymatically deposited silver nanoparticles prevents the breakdown of SERS activity even at high particle densities (particle density >60 %) that lead to a conductive layer. In contrast to other approaches, this substrate exhibits a relationship between electrical conductivity and the resulting SERS activity of a given spot. This enables the prediction of the SERS activity of the nanostructure ensemble and therewith the controllable and reproducible production of SERS substrates of enzymatic silver nanoparticles on a large scale, utilizing a simple measurement of the electrical conductivity. Furthermore, through a correlation between the conductivity and the SERS activity of the substrates it is possible to quantify SERS measurements with these substrates.     

In vivo biodistribution of <Superscript>131</Superscript>I labeled bleomycin (BLM) and isomers (A2 and B2) on experimental animal models

Bleomycins (BLMs; BLM, A2, and B2) were labeled with ¹³¹I and radiopharmaceutical potentials were investigated using animal models in this study. Quality control procedures were carried out using thin layer radiochromatography (TLRC), high performance liquid chromatography (HPLC), and liquid chromatography (LC/MS/MS). Labeling yields of radiolabeled BLMs were found to be 90, 68, and 71%, respectively. HPLC chromatograms were taken for BLM and cold iodinated BLM (¹²⁷I-BLM). Five peaks were detected for BLM and three peaks for ¹²⁷I-BLM in the HPLC studies. Two peaks belong to isomers of BLM. The isomers of BLM were purified with using HPLC. Biological activity of BLM was determined on male Albino Wistar rats by biodistribution and scintigraphic studies were performed for BLMs by using New Zelland rabbits. The biodistribution results of ¹³¹I-BLM showed high uptake in the stomach, the bladder, the prostate, the testicle, and the spinal cord in rats. Scintigraphic results on rabbits agrees with that of biodistributional studies on rats. The scintigraphy of radiolabeled isomers (¹³¹I-A2 and ¹³¹I-B2) are similiarly found with that of ¹³¹I-BLM.     

Analytic moduli spaces of simple sheaves on families of integral curves

We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo–Mumford regularity of such sheaves, which we provide.     

Laser secondary neutral mass spectrometry for copper detection in micro‐scale biopsies

Disease progression and clinical diagnostics of a number of hereditable metabolic diseases are determined by organ involvement in disturbed deposition of certain molecules. Current clinical imaging is unable to visualize this maldistribution with sufficient specificity and sensitivity, such as in Wilson's disease. The quest for understanding cellular Cu distribution in these patients requires element‐ and molecule‐specific images with nanometer‐scale spatial resolution. We have used a new cryo‐mass spectrometric instrument with an integrated cryosectioning chamber for preparation and analysis of frozen hydrated samples of Wilson's disease tissue. With laser post‐ionization secondary neutral mass spectrometry (laser‐SNMS), we were able to image Cu and other intrinsic elements and molecules in less than 1 mg of frozen hydrated liver tissue from a murine model of Wilson's disease. A 40–50 times higher Cu concentration was measured in the disease tissue as compared to the control mouse. Furthermore, major histomorphological changes were observed using this advanced nano‐science tool. The results showed that the combination of in‐vacuum cryosectioning and cryo‐laser‐SNMS technologies is particularly well suited for identifying specific cell structures and imaging trace element concentrations with subcellular resolution and upper‐parts‐per‐billion sensitivity in biological samples. This technology can provide a novel diagnostic tool for clinical applications in various diseases involving trace elements. Copyright © 2009 John Wiley & Sons, Ltd.