Spline collocation for strongly elliptic equations on the torus

Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].     

The universal nilpotent group compactification of a semigroup

The purpose of this paper is to introduce an algebra of functions on a semitopological semigroup and to study these functions from the point of view of universal semigroup compactification. We show that the corresponding semigroup compactification of this algebra is universal with respect to the property of being a nilpotent group.

     

Chalcogenide based all-solid-state thin electroplated ion-selective membrane for Hg(II) flow-injection determinations

The response to Hg(II) of a thin all-solid-state Te-doped silver chalcogenide membrane, described by the general formula Ag₂ + δSe_{1 − x}Te_x, which has been electrochemically prepared following a previously proposed approach, has been investigated. The kinetics of formation of the membrane's secondary dynamic response to Hg(II) has been successfully combined with the precise timing and transient signal, typical for flow-injection (FI) measurements, in developing a sensitive and reliable mercury FI detector. Under optimized stream conditions it exhibits a linear Nernstian response, with a double slope of the calibration graph of 59 mV dec⁻¹, over the mercury(II) concentration range 10⁻⁶ − 10⁻³ M, the typical sample throughput amounting to about 70 samples per hour. The observed chemical amplification of the signal is due to the specificity of the processes dominating the initial step in formation of the steady-state signal of the membrane to mercury. The analytical performance of the Hg(II) FI detector, as regards sensitivity, reproducibility, selectivity and long-term stability has been thoroughly investigated. The exact procedure for membrane electrodeposition is given and the potential of the proposed approach as a cost-effective way for preparing chalcogenides of unique structure and properties has been outlined in the above context.     

Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.     

Differential Proteomic Analysis of Neonatal Cardiomyocytes in Response to β-Adrenergic Receptor Stimulation

Introduction Adrenoceptors(ARs),membersofthesuperfami lyofG proteincoupledreceptors,arethemostimpor tantreceptorsinvolvedincardiacregulation[1].ARsin cardiacmuscleincludebothαARsandβARssub types,whileinmostmammalianheart,βARsarethe predominantsubtypes.…     

Analysis method of the effect of fabrication errors on a planar waveguide demultiplexer

The impact of fabrication errors on a planar waveguide demultiplexer is analyzed based on an analytical method. The explicit expression of the transfer function taking into account phase and amplitude errors is presented in order to analyze the loss and crosstalk of the demultiplexer caused by fabrication errors. A basic requirement for the demultiplexer with a certain crosstalk criterion can be easily obtained. Using an etched diffraction grating demultiplexer as an example, it is shown that the analytical results have a good agreement with results from a numerical method.     

Synthesis,dynamic light scattering,and luminescence properties of copolymers containing iridium(III) bisterpyridine in the side chain

Supramolecular block‐random copolymers containing [Ir(terpy)₂]³⁺ in the side chain were synthesized via postfunctionalization of a P(S‐b‐AC_terpy) block copolymer. Absorbance and emission spectra compared to a model compound show that the polymer backbone has a minor effect on the polymer absorbance but produces a larger shift for the phosphorescence signals to higher wavelength. Dynamic light scattering of the metal complex containing copolymer studied in various solvents showed monomodal aggregation with decreasing aggregate size as the solvent dielectric constant increased. The copolymer precursor P(S‐b‐AC_terpy) shows multimodal aggregation in different solvents with the major population consisting of single chains. This difference in behavior between the two polymers is attributed to the electrolytic nature of the complex and the amphiphilicity induced by the charged metal complex. Supramolecular copolymers like these will continue to have interesting self‐organizational properties and may find applications in multicomponent systems for photoinduced charge separation processes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1109–1121, 2007     

Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.      

Long-wavelength GaInAsSb/AlGaAsSb DFB lasers emitting near 2.6 μm

We have successfully fabricated and characterized room temperature continuous wave (cw) GaInAsSb/AlGaAsSb distributed feedback lasers emitting in the wavelength region between 2.499 and 2.573 μm. To the best of our knowledge, this is the longest emission wavelength realized with a GaSb-based DFB laser diode. The laser structure used for DFB processing was grown by solid source molecular beam epitaxy. A DFB concept requiring no subsequent overgrowth step was used by defining first-order Cr-Bragg gratings laterally patterned to a ridge waveguide. Threshold currents smaller than 60 mA and room temperature cw output powers up to 6.5 mW were obtained. The laser diodes show single mode emission with side mode suppression ratios (SMSR) of up to 32 dB.     

Degradative chain transfer in vinyl acetate polymerizations using toluene as solvent

In this work, we propose that retardation in vinyl acetate polymerization rate in the presence of toluene is due to degradative chain transfer. The transfer constant to toluene (C_trs) determined using the Mayo method is equal to 3.8 × 10^?3, which is remarkably similar to the value calculated from the rate data, assuming degradative chain transfer (2.7 × 10^?3). Simulations, including chain‐length‐dependent termination, were carried out to compare our degradative chain transfer model with experimental results. The conversion–time profiles showed excellent agreement between experiment and simulation. Good agreement was found for the M_n data as a function of conversion. The experimental and simulation data strongly support the postulate that degradative chain transfer is the dominant kinetic mechanism. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3620–3625, 2007