Numerical implementation of the QMR algorithm by using discrete stochastic arithmetic

In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced byA, it is necessary to decide whether to construct the Lanczos vectorsv _n +1 andw _n +1 as regular or inner vectors. For a regular step it is necessary thatD _k =W _k ^T V _k is nonsingular. Therefore, in the floating-point arithmetic, the smallest singular value of matrix D_k,σ _min (D _k ), is computed and an inner step is performed ifσ _min (D _k )<∈, where ∈ is a suitably chosen tolerance. In practice it is absolutely impossible to choose correctly the value of the tolerance ∈. The subject of this paper is to show how discrete stochastic arithmetic remedies the problem of this tolerance, as well as the problem of the other tolerances which are needed in the other checks of the QMR method with the estimation of the accuracy of some intermediate results. Numerical examples are used to show the good numerical properties.     

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.     

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.     

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.     

Synthesis of a graphene‐based nanocomposite for the dispersive solid‐phase extraction of vancomycin from biological samples

The approach of this work was to study the capability of graphene‐based materials in the field of biological sample preparation. A polypyrrole/graphene composite was synthesized and characterized. The potential of the nanocomposite was investigated as a sorbent in dispersive solid‐phase extraction followed by high‐performance liquid chromatography with UV detection for vancomycin as a model drug. The effect of different parameters influencing extraction efficiency such as sample pH and sample volume, ionic strength, extraction time, type, and volume of desorption solvent and desorption time were investigated. A comparison study was also conducted between polypyrrole/graphene and some different novel and classic sorbents. Under optimized conditions, the calibration curve for vancomycin showed linearity in the range of 0.05–10 μg/mL. In addition, limits of detection, and quantification were 0.003 and 0.01 μg/mL, respectively. The intraday and interday relative standard deviations at a concentration of 0.05 μg/mL (n = 3) were 1.6 and 2.1%, respectively. Furthermore, the proposed method was successfully applied for the determination of vancomycin in plasma and urine samples. The relative recoveries indicated the feasibility of graphene‐based sorbents in biological sample analysis.     

Highly efficient synthesis of dicoumarols and xanthene derivatives in presence of Brønsted–Lewis acidic ionic liquids catalyst

A series of metal chloride-based acidic ionic liquids have been prepared and used as an efficient catalyst in one-pot multicomponent synthesis of biscoumarins and substituted xanthenes derivatives under solvent-free conditions. Among the acidic ionic liquids, N-methylpyrrolidonium zinc chloride (Hnmp/ZnCl₃)-based Brønsted–Lewis acidic ionic liquids were found to be an effective and recyclable catalyst for a one-pot synthesis of biscoumarins through the domino Knoevenagel–Michael reaction of a variety of aldehydes with 4-hydroxycoumarin in short reaction times. The reactions which occur under relatively mild conditions afforded the biscoumarin derivatives employing a very low loading of catalyst in satisfactory isolated yields and high purity after simple work-up. The Brønsted–Lewis acidic ionic liquid catalyst was reused four times without any variation in yield.     

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.