Existence and asymptotic behavior for elliptic equations with singular anisotropic potentials

We study the equation Δu+u|u|^p−1+V(x)u+f(x)=0 in Rn, where n?3 and p>n/(n−2). The forcing term f and the potential V can be singular at zero, change sign and decay polynomially at infinity. We can consider anisotropic potentials of form h(x)|x|⁻² where h is not purely angular. We obtain solutions u which blow up at the origin and do not belong to any Lebesgue space Lr. Also, u is positive and radial, in case f and V are. Asymptotic stability properties of solutions, their behavior near the singularity, and decay are addressed.     

Carbon disulfide reagent allows the characterization of nonpolar analytes by atmospheric pressure chemical ionization mass spectrometry

While atmospheric pressure ionization methodologies have revolutionized the mass spectrometric analysis of nonvolatile analytes, limitations native to the chemistry of these methodologies hinder or entirely inhibit the analysis of certain analytes, specifically, many nonpolar compounds. Examination of various analytes, including asphaltene and lignin model compounds as well as saturated hydrocarbons, demonstrates that atmospheric pressure chemical ionization (APCI) using CS₂ as the reagent produces an abundant and stable molecular ion (M^+?) for all model compounds studied, with the exception of completely saturated aliphatic hydrocarbons and the two amino acids tested, arginine and phenylalanine. This reagent substantially broadens the applicability of mass spectrometry to nonvolatile nonpolar analytes and also facilitates the examination of radical cation chemistry by mass spectrometry. Copyright © 2011 John Wiley & Sons, Ltd.     

Green synthesis of novel chalcone and coumarin derivatives via Suzuki coupling reaction

Chalcones and coumarins are important naturally occurring plant constituents and display a wide range of pharmacological and biological activities. In an environmentally benign approach, synthesis of biphenyl chalcone and coumarin derivatives was successfully accomplished via Suzuki coupling by using PEG-400 as a solvent under microwave irradiation. Salient feature of this methodology includes: short reaction time, good to excellent yields, and prominent tolerance of different functional groups.     

Analysis of branched polymers by high resolution multidetector size exclusion chromatography: Separation of the effects of branching and molecular weight distribution

This article presents the SEC analysis of branched polyisobutylene PIB and polystyrene PS with high molecular weight and broad multimodal molecular weight distribution. Both polymers were synthesized using an inimer technique, which results in long‐chain branched polymers with statistical branching and broad multimodal distributions. Using high resolution multidetector Size Exclusion Chromatography SEC the polymers were analyzed based on three branching factors: g = (R_z,br/R_z,lin)_Mw; h = (〈R_h〉_z,br/〈R_h〉_z,lin)_{Mw ;} and ρ = (R ^1/2/〈R_h〉_z). It is generally accepted that for monodisperse branched polymers g and h < 1. In the case of our polydisperse PIB and PS, it was seen that g and h > 1, and ρ increases with molar mass and the number of chain ends as predicted earlier. The multidetector SEC system allowed for the separation of branching and polydispersity, reported here for the first time experimentally. The g parameter as a function of DP_i was compared to the theory developed by Zimm and Stockmayer. The plots followed a similar trend, but were shifted by a factor related to the average chain length between branching points. The ρ parameter decreased with increasing DP_i, as predicted theoretically by Kajiwara. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

A new benzotriazole-mediated stereoflexible gateway to hetero-2,5-diketopiperazines

Open chain Cbz-L-aa(1)-L-Pro-Bt (Bt=benzotriazole) sequences were converted into either the corresponding trans- or cis-fused 2,5-diketopiperazines (DKPs) depending on the reaction conditions. Thermodynamic tandem cyclization/epimerization afforded selectively the corresponding trans-DKPs (69-75%). Complementarily, tandem deprotection/cyclization led to the cis-DKPs (65-72%). A representative set of proline-containing cis- and trans-DKPs has been prepared. A mechanistic investigation, based on chiral HPLC, kinetics, and computational studies enabled a rationalization of the results.     

The smart meter and a smarter consumer: quantifying the benefits of smart meter implementation in the United States

The electric grid in the United States has been suffering from underinvestment for years, and now faces pressing challenges from rising demand and deteriorating infrastructure. High congestion levels in transmission lines are greatly reducing the efficiency of electricity generation and distribution. In this paper, we assess the faults of the current electric grid and quantify the costs of maintaining the current system into the future. While the proposed "smart grid" contains many proposals to upgrade the ailing infrastructure of the electric grid, we argue that smart meter installation in each U.S. household will offer a significant reduction in peak demand on the current system. A smart meter is a device which monitors a household's electricity consumption in real-time, and has the ability to display real-time pricing in each household. We conclude that these devices will provide short-term and long-term benefits to utilities and consumers. The smart meter will enable utilities to closely monitor electricity consumption in real-time, while also allowing households to adjust electricity consumption in response to real-time price adjustments.     

Tuning metal hydride thermodynamics via size and composition: Li-H, Mg-H, Al-H, and Mg-Al-H nanoclusters for hydrogen storage

Nanoscale Li and intermetallic Al-Mg metal hydride clusters are investigated as a possible hydrogen storage material using the high-level quantum Monte Carlo computational method. Lower level methods such as density functional theory are qualitatively, not quantitatively accurate for the calculation of the enthalpy of absorption of H(2). At sizes around 1 nm, it is predicted that Al/Mg alloyed nanoparticles are stable relative to the pure compositions and the metal composition can be tuned in tandem with the size to tune the hydrogen absorption energy, making this a promising route to a rechargeable hydrogen storage material.     

Tail behaviour of credit loss distributions for general latent factor models

Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of credit losses. To capture the co‐movements in defaults over time, we assume that defaults are triggered by a general, possibly non‐linear, factor model involving both systematic and idiosyncratic risk factors. The model encompasses default mechanisms in popular models of portfolio credit risk, such as CreditMetrics and CreditRisk⁺. We show how the tail characteristics of portfolio credit losses depend directly upon the factor model's functional form and the tail properties of the model's risk factors. In many cases the credit loss distribution has a polynomial (rather than exponential) tail. This feature is robust to changes in tail characteristics of the underlying risk factors. Finally, we show that the interaction between portfolio quality and credit loss tail behavior is strikingly different between the CreditMetrics and CreditRisk⁺ approach to modeling portfolio credit risk.     

Size dependence of the mechanical properties of ZnO nanobelts

The Young's modulus of ZnO nanobelts was measured using an atomic force microscope following the modulated nanoindentation method. The nanobelts have a rectangular cross-section, with width-to-thickness ratios ranging 1–10 and lengths up to a few millimetres. The Young's modulus of two nanobelts with width-to-thickness ratio of 2.2 and 1.3 was measured at 55 and 108?GPa, respectively, indicating a size dependence of the elastic properties of the nanobelts.