Calculation of cyclodextrin-mediated enantiomer ratio shifting of racem norgestrel in aqueous solutions

Enantioselective solubility of rac-norgestrel was found in the presence of γ-cyclodextrin or hydroxypropyl-γ-cyclodextrin. In both cases the efficacious enantiomer was dissolved in greater extent. Calculating the molar absorptivity and molar ellipticity spectra of the γ- and hydroxypropyl-γ-cyclodextrin aqueous complexes, a simple and rapid direct circular dichroism (CD) spectrometric method was obtained for the determination of the enantiomer ratio in aqueous solutions.     

Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension, at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross–Pitaevskii scaling included, a less-than-100% condensation into a single-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.     

Voltammetric determination of methyl parathion, ortho, meta and para nitrophenol with a carbon paste electrode modified with C18

Summary The determination of methyl-parathion (MPT), ortho (ONP), meta (MNP) and para nitrophenol (PNP) has been studied by differential pulse voltammetry with a carbon-paste electrode modified with 50% (w/w) of C₁₈. A study of the influence of the pH in the preconcentration cell and the measurement cell was carried out for an electrode with 50% modifier and an accumulation time of 5 min. The voltammograms were recorded with a sweep rate of 40 mV s^–1 and a pulse amplitude of 50 mV. With the optimum conditions of pH for both of the steps, various other variables were studied. The variables for each compound were optimized and the possibility of application to the determination of a mixture of the four compounds was investigated. The determination limits found for all the compounds are: 2 ng ml^–1 for ONP, 5 ng ml^–1 for MNP, 4.3 ng ml^–1 for PNP and 7.9 ng ml^–1 for MPT. The method was applied to samples of a small lake which gathers rain water and water filtered from land on which cereals are grown.     

Weak singularities may help periodic solutions to exist

In a periodically forced semilinear differential equation with a singular nonlinearity, a weak force condition enables the achievement of new existence criteria through a basic application of Schauder's fixed point theorem. The originality of the arguments relies in that, contrary to the customary situation in the available references, a weak singularity facilitates the arguments of the proofs.     

Synthesis of poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) by the competitive single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization in water

The synthesis of a block copolymer poly(vinyl chloride)‐b‐poly(n‐butyl acrylate)‐b‐poly(vinyl chloride) is reported. This new material was synthesized by single‐electron‐transfer/degenerative‐chain‐transfer‐mediated living radical polymerization (SET‐DTLRP) in two steps. First, a bifunctional macroinitiator of α,ω‐di(iodo)poly (butyl acrylate) [α,ω‐di(iodo)PBA] was synthesized by SET‐DTLRP in water at 25 °C. The macroinitiator was further reinitiated by SET‐DTLRP, leading to the formation of the desired product. This ABA block copolymer was synthesized with high initiator efficiency. The kinetics of the copolymerization reaction was studied for two PBA macroinitiators with number–average molecular weight of 10 k and 20 k. The relationship between the conversion and the number–average molecular weight was found to be linear. The dynamic mechanical thermal analysis suggests just one phase, indicating that copolymer behaves as a single material with no phase separation. This methodology provides the access to several block copolymers and other complex architectures that result from combinations of thermoplastics (PVC) and elastomers (PBA). From industrial standpoint, this process is attractive, because of easy experimental setup and the environmental friendly reaction medium. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3001–3008, 2006     

Single electron transfer–degenerative chain transfer living radical polymerization of N‐butyl acrylate catalyzed by Na2S2O4 in water media

Living radical polymerization of n‐butyl acrylate was achieved by single electron transfer/degenerative‐chain transfer mediated living radical polymerization in water catalyzed by sodium dithionate. The plots of number–average molecular weight versus conversion and ln[M]₀/[M] versus time are linear, indicating a controlled polymerization. This methodology leads to the preparation of α,ω‐di(iodo) poly (butyl acrylate) (α,ω‐di(iodo)PBA) macroinitiators. The influence of polymerization degree ([monomer]/[initiator]), amount of catalyst, concentration of suspending agents and temperature were studied. The molecular weight distributions were determined using a combination of three detectors (TriSEC): right‐angle light scattering (RALLS), a differential viscometer (DV), and refractive index (RI). The methodology studied in this work represents a possible route to prepare well‐tailored macromolecules made of butyl acrylate in an environmental friendly reaction medium. Moreover, such materials can be subsequently functionalized leading to the formation of different block copolymers of composition ABA. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2809–2825, 2006     

On the second smallest distance between finitely many points on the sphere

In the following note we investigate the second smallest distance between finitely many points on the sphere. Actually we look for the smallest upper bound for the second smallest distance between n points on the unit sphere. We solve this problem for n=9 and also we give a general, non-trivial upper bound for the second smallest distance of n points with n9.Supported by the Hungarian National Foundation for Scientific Research, Number 1238.     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

A confidence interval for the slope of a truncated regression

Summary Bhattacharya, Chernoff and Yang (1983) proposed a nonparametric estimate for the slope of a regression lineY = _o X + V subjected to the truncationYy ₀. The estimate corresponds to the zero-crossing of a random functionS _n (). In this paper an estimate for the asymptotic variance of the estimate of the slope is proposed and the rate of convergence is given. The proofs rest heavily on the local behavior ofS _n () in the neighborhood of the true value _o.