Isometries, Geodesics and Jacobi Fields of Lorentzian Heisenberg Group

The paper is mainly devoted to determine the groups of isometries of the Heisenberg group endowed with each of the three left invariant Lorentzian metrics which are possible on it; also, an explicit computation of all the isometries for the (two) non flat Lorentzian metrics is done. Moreover, explicit formulas for the geodesic curves and the Jacobi vector fields for each of these three Lorentzian metrics are computed.     

Increasing the hydrophilicity of star‐shaped amphiphilic co‐networks by using of PEG and dendritic s‐PCL cross‐linkers

New hyperbranched hydrophobic cross‐linkers with peripheral azide groups were synthesized as follows: First, star‐shaped polycaprolactones (sPCL) were synthesized by ring‐opening polymerization of caprolactone in the presence of pentaerythritol and tin (II) octoate. In the next step, sequential acrylation, Micheal addition, tosylation, and azidation by acryloyl chloride, diethanol amine, tosyl chloride, and sodium azide were respectively exploited to synthesize azide‐functionalized hyperbranched star‐shaped polycaprolactones which were named sPCL‐acrylate‐diethanolamine‐azide (sPCL‐AC‐DEA‐N₃) and sPCL‐acrylate‐diethanolamine‐acrylate‐diethanolamine‐azide (sPCL‐AC‐DEA‐AC‐N₃). All steps were thoroughly characterized by FT‐IR and ¹H NMR spectroscopy. The GPC analysis showed that the molecular weight of sPCL increased after two azide functionalizations. Amphiphilic hydrogels based on sPCL‐AC‐DEA‐N₃ (M_n = 8130 g/mol) and sPCL‐AC‐DEA‐AC‐N₃ (M_n = 10112 g/mol) with linear alkyne‐terminated polyethylene glycols (PEG) (M_n = 2000, 4000, and 6000 g/mol) were synthesized through click coupling between azide and alkyne groups. In both hydrogels, the swelling ratio increased by increasing the molecular weight of PEG. The obtained results showed that the branching of the cross‐linker, significantly affected the swelling ratio of hydrogels. For instance, the swelling ratio of sPCL‐AC‐DEA‐AC‐N₃ and PEG‐6000 (Q = 900) was higher than sPCL‐AC‐DEA‐N₃ and PEG‐6000 (Q = 600). Despite the high cross‐linking density of sPCL‐AC‐DEA‐AC‐DEA‐N₃–based hydrogels, the amount of released theophylline was higher than sPCL‐AC‐DEA‐N₃–based hydrogels, due to the high content of PEG in these hydrogels.     

Mucigerin, a new coumarin from Calophyllum mucigerum (Guttiferae)

Our recent studies on the stem bark of Calophyllum mucigerum (Guttiferae) have yielded a new coumarin mucigerin, a prenylated xanthone cudraxanthone C and the common steroidal triterpenes friedelin and stigmasterol. Structural elucidations of these compounds were achieved using 1H NMR, 13C NMR, DEPT, COSY, HETCOR and HMBC experiments while MS gave the molecular masses. Cytotoxic assays using CEM-SS cell line (T-lymphoblastic leukemia) on the crude extracts of the stem bark indicated some activity. The crude extracts were also found to be moderately toxic against the larvae of Aedes aegypti. This article reports the isolation and identification of mucigerin as well as bioassay data.     

Isocyanide‐Based Multicomponent Reaction: One‐Pot Synthesis of New Derivatives of Iminofuranone

The one‐pot multicomponent reaction of alkyl isocyanide, alkylidene‐substituted Meldrum's acid, and arylcarboxylic acids affords new derivatives of iminofuranone in fair yields. The structure of the products was deduced from their spectroscopic data. Two equivalents of the respective isocyanides participate in this reaction.     

Blends of carbon blacks and multiwall carbon nanotubes as reinforcing fillers for hydrocarbon rubbers

The reinforcement of a styrene‐butadiene rubber (SBR) by single fillers—carbon black (CB) or multiwall carbon nanotubes (MWNTs)—or by mixtures of CB and MWNTs, is investigated. The morphologies, mechanical and electrical properties of the composites, are analyzed. A significant improvement in the tensile properties is observed for samples containing a dual phase. Using atomic force (AFM) and transmission electron (TEM) microscopies, we demonstrate that the double loading improves the dispersion of the nanotubes in SBR. Electrical measurements show lower resistivity and a lower percolation threshhold for composites containing blends of fillers, which provides further evidence of better dispersion. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 46: 1939–1951, 2008     

Comparison of Air-Assisted,Vortex-Assisted and Ultrasound-Assisted Dispersive Liquid–Liquid Microextraction for the Determination of BTEX Compounds in Water Samples Prior to GC-FID Analysis

Three new dispersive liquid–liquid microextraction (DLLME) methods, air-assisted (AA-DLLME), vortex-assisted (VA-DLLME) and ultrasound-assisted (UA-DLLME), were compared from the point of view of their analytical application for preconcentration of trace amounts of benzene, toluene, ethylbenzene and xylene isomers (BTEX) in water samples. In all of these methods, no dispersive solvent is required and dispersion of extractant is carried out by air bubbles, vortex and ultrasound for AA-DLLEM, VA-DLLME, and UA-DLLME, respectively. Advantages and disadvantages of these three liquid phase microextraction methods and their capability in dispersion of a similar extractant phase in sample solutions were comprehensively compared. All other extraction parameters, which have an influence on the microextraction, were also investigated and optimized. Under optimized conditions, analytical figures of merit for the three techniques were determined and compared. It was found that the limit of detection of the three methods is almost the same, while AA-DLLME has a wider linear dynamic range and the shortest analysis time. Enrichment factors of 182, 45 and 245 were achieved for AA-DLLEM, VA-DLLME, and UA-DLLME, respectively.     

Explicit Formulas Associated with Some Families of Generalized Bernoulli and Euler Polynomials

In this paper, we propose and derive several new explicit formulas of the generalized Bernoulli and Euler polynomials in terms of the generalized Stirling numbers of the second kind. A study of some families of the modified generalized Euler polynomials yields an interesting algorithm for calculating the generalized Euler polynomials.     

Two new acridone alkaloids from Glycosmis macrantha

Extraction and chromatographic separation of the extracts of dried stem barks of Glycosmis macrantha lead to isolation of two new acridone alkaloids, macranthanine and 7-hydroxynoracronycine, and a known acridone, atalaphyllidine. The structures of these alkaloids were determined by detailed spectral analysis and also by comparison with reported data.