Nonlinear estimates for hypersurfaces in terms of their fundamental forms

A sufficiently regular hypersurface immersed in the $(n+1)$-dimensional Euclidean space is determined up to a proper isometry of ${\mathbb{R}}^{n+1}$ by its first and second fundamental forms. As a consequence, a sufficiently regular hypersurface with boundary, whose position and positively-oriented unit normal vectors are given on a non-empty portion of its boundary, is uniquely determined by its first and second fundamental forms. We establish here stronger versions of these uniqueness results by means of inequalities showing that an appropriate distance between two immersions from a domain ω of ${\mathbb{R}}^n$ into ${\mathbb{R}}^{n+1}$ is bounded by the $L^p$-norm of the difference between matrix fields defined in terms of the first and second fundamental forms associated with each immersion.     

The Spectrum and Convergence Rates of Exclusion and Interchange Processes on the Complete Graph

We give a short and completely elementary method to find the full spectrum of the exclusion process and a nicely limited superset of the spectrum of the interchange process (a.k.a. random transpositions) on the complete graph. In the case of the exclusion process, this gives a simple closed-form expression for all the eigenvalues and their multiplicities. This result is then used to give an exact expression for the distance in \( L^2 \) from stationarity at any time and upper and lower bounds on the convergence rate for the exclusion process. In the case of the interchange process, upper and lower bounds are similarly found. Our results strengthen or reprove many known results about the mixing time for the two processes in a very simple way.     

Unexpected C-H activation of Ru(II)-dithiomaltol complexes upon oxidation

Thione-substituted derivatives of maltol are of interest in several applications of metal-based drugs. In order to investigate the effect of the oxygenation on such thione chelates, Ru complexes of 3-hydroxy-2-methyl-4-thiopyrone (thiomaltol or Htma) and 3-hydroxy-2-methyl-4H-thiopyran-4-thione (dithiomaltol or Httma), [Ru(bpy)2(tma)](+), 1, and [Ru(bpy) 2(ttma)] (+), 2, were synthesized as diamagnetic PF6(-) salts. Peroxidation of 2 unexpectedly generated products of C-H activation at its pendant methyl group; an air-stable aldehyde [Ru(bpy)2(ttma-aldehyde)](+), 4, was the major product. In addition, an intermediate oxidation product [Ru(bpy) 2(ttma-alcohol)](PF6), 3, was characterized. Both 3 and 4 are also formed by reaction of 2 with outersphere oxidants (e.g., Na2IrCl6) and by bulk electrolysis under anaerobic conditions. Similar oxidations of the analogous [Ru(bpy)2(ettma)](+), 2' , complex (3-hydroxy-2-ethyl-4H-thiopyran-4-thione; ethyl dithiomaltol or Hettma) formed the corresponding ketone, [Ru(bpy)2(ettma-ketone)](PF6), 4', by oxidation at the same position adjacent to the conjugated ring. The structures of the aldehyde 4 and starting materials 1 and 2 have been confirmed by X-ray crystallography, and all complexes have been characterized by UV-vis, (1)H NMR, and IR spectroscopies. Initial mechanistic investigations are discussed.     

Interaction of nitrate, barium, strontium and cadmium ions with fused quartz/water interfaces studied by second harmonic generation

Inorganic anions and cations are ubiquitous in environmental chemistry. Here, we use second harmonic generation to track the interaction of the environmentally important metal cations barium, strontium, and cadmium and the nitrate anion with fused quartz/water interfaces at pH 7. Using a dynamic flow system, we assess the extent of reversibility in the binding process and report the absolute number density of adsorbed cations, their charge densities, and their free energies of adsorption. We also present resonantly enhanced second harmonic generation experiments that show that nitrate is surface active and report the free energies and binding constants for the adsorption process. The second harmonic generation spectrum of surface-bound nitrate shows a new adsorption band that cuts further into the solar spectrum than nitrate in the aqueous or solid state. The results that we obtain for all four inorganic ions and the implications for tropospheric and aquatic chemistry as well as geochemistry are discussed in the context of fundamental science as well as pollutant transport models.     

Rapid affinity purification of erythropoietin from biological samples using disposable monoliths

Identification of post-translational modifications of proteins in biological samples often requires access to preanalytical purification and concentration methods. In the purification step high or low molecular weight substances can be removed by size exclusion filters, and high abundant proteins can be removed, or low abundant proteins can be enriched, by specific capturing tools. In this paper is described the experience and results obtained with a recently emerged and easy-to-use affinity purification kit for enrichment of the low amounts of EPO found in urine and plasma specimens. The kit can be used as a pre-step in the EPO doping control procedure, as an alternative to the commonly used ultrafiltration, for detecting aberrantly glycosylated isoforms. The commercially available affinity purification kit contains small disposable anti-EPO monolith columns (6 μL volume, Ø7 mm, length 0.15 mm) together with all required buffers. A 24-channel vacuum manifold was used for simultaneous processing of samples. The column concentrated EPO from 20 mL urine down to 55 μL eluate with a concentration factor of 240 times, while roughly 99.7% of non-relevant urine proteins were removed. The recoveries of Neorecormon (epoetin beta), and the EPO analogues Aranesp and Mircera applied to buffer were high, 76%, 67% and 57%, respectively. The recovery of endogenous EPO from human urine was 65%. High recoveries were also obtained when purifying human, mouse and equine EPO from serum, and human EPO from cerebrospinal fluid. Evaluation with the accredited EPO doping control method based on isoelectric focusing (IEF) showed that the affinity purification procedure did not change the isoform distribution for rhEPO, Aranesp, Mircera or endogenous EPO. The kit should be particularly useful for applications in which it is essential to avoid carry-over effects, a problem commonly encountered with conventional particle-based affinity columns. The encouraging results with EPO propose that similar affinity monoliths, with the appropriate antibodies, should constitute useful tools for general applications in sample preparation, not only for doping control of EPO and other hormones such as growth hormone and insulin but also for the study of post-translational modifications of other low abundance proteins in biological and clinical research, and for sample preparation prior to in vitro diagnostics.     

Effective mode area and its optimization in silicon-nanocrystal waveguides

We revisit the problem of the optimization of a silicon-nanocrystal (Si-NC) waveguide, aiming to attain the maximum field confinement inside its nonlinear core and to ensure optimal waveguide performance for a given mode power. Using a Si-NC/SiO2 slot waveguide as an example, we show that the common definition of the effective mode area may lead to significant errors in estimation of optical intensity governing the nonlinear optical response and, as a result, to poor strength evaluation of the associated nonlinear effects. A simple and physically meaningful definition of the effective mode area is given to relate the total mode power to the average field intensity inside the nonlinear region and is employed to study the optimal parameters of Si-NC slot waveguides.     

Synthesis of Thymidine Derivatives as Potential Pharmaceuticals against HIV/AIDS Infection

Data on preparation methods for 3'-modified oxythymidines are summarized and systematized. A synthesis tree is presented permitting a selection of rational schemes for thymidine derivatives preparation, in particular those that can be potential anti-HIV/AIDS drugs.     

Electrodynamics in terms of functions over the groupSU(2): II. Quantization

In a previous article by two of the present authors Carmeli's group-theoretic method for the formulation of wave equations was applied to the case of the electromagnetic field, and the equations for the vector potential were derived. In the present paper a quantization procedure for these equations is carried out in the Lorentz gauge. It involves two independent variables, corresponding to the number of degrees of freedom of the electromagnetic field in a Hilbert space with a positive-definite metric. Conserved quantities are derived.