APPROXIMATING COMMON FIXED POINTS OF NEARLY ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

We use an iteration scheme to approximate common fixed points of nearly asymptotically nonexpansive mappings.We generalize corresponding theorems of [1] to the case of two nearly asymptotically nonexpansive mappings and those of [9] not only to a larger class of mappings but also with better rate of convergence.     

Form of multicomponent Fickian diffusion coefficients matrix

The form of multicomponent Fickian diffusion coefficients matrix in thermodynamically stable mixtures is established based on the form of phenomenological coefficients and thermodynamic factors. While phenomenological coefficients form a symmetric positive definite matrix, the determinant of thermodynamic factors matrix is positive. As a result, the Fickian diffusion coefficients matrix has a positive determinant, but its elements — including diagonal elements — can be negative. Comprehensive survey of reported diffusion coefficients data for ternary and quaternary mixtures, confirms that invariably the determinant of the Fickian diffusion coefficients matrix is positive.     

Static Headspace GC/MS Method for Determination of Methanol and Ethanol Contents,as the Degradation Markers of Solid Insulation Systems of Power Transformers

Methanol in insulating oil has been proposed as a new marker for condition assessment of the solid insulation system of power transformers. In the current work, as a first step of using the new marker, an analytical static headspace gas chromatography/mass spectrometry method has been developed, optimized, and validated to measure methanol and ethanol contents in the insulating mineral oil. The analyzing setup consists of a 6890 N gas chromatograph equipped with a 5973 network mass spectrometer (MS) in the absence of a costly headspace autosampler, and the chromatography separation was performed on a 60 m × 320 µm × 0.5 µm VF-WAXms GC column. Calibration curves have been provided using several concentrations of the alcohols, and also limit of detection (LOD), limit of quantification (LOQ), and relative standard deviation percentage (RSD%) have been determined.     

Facile entries for regioselective synthesis of [1,2,4]triazolo-[4,3-a]pyrimidin-5(1H)-ones from 2-thiouracil

Three new alternative synthetic strategies based on reactions of hydrazonoyl halides 3 with 2-methylthiouracil 2 and treatment of either 2-pyrimidinyl thiohydrazonates 8 or the diazonium coupling products of active (pyrimidin-2-ylthio)methylene compounds 12 with sodium ethoxide in ethanol are described for the title compounds. The mechanisms and regiochemistry of the studied reactions are discussed.     

Sensitive Kinetic-Spectrophotometric Determination of Trace Amounts of Periodate Ion

A simple, precise, sensitive and accurate method was developed for rapid determination of trace quantities of periodate. The method is based on the accelerating effect of periodate on the reaction of bromate and hydrochloric acid in the presence of hydrazine. The decolorization of methyl orange with the reaction products was used to monitor the reaction spectrophotometrically at 525 nm. Periodate could be determined in the concentration ranges of 0.02–1.5 g/mL. The relative standard deviation for ten replicate determinations of 0.3 g/mL of periodate was 1.12%. The method was applied to the determination of periodate in water samples and indirect determination of ethylene glycol in gasoline and glycerol in vegetable oil via Malaprade reaction with satisfactory results.     

The -theory of toric manifolds

Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an -dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the -theory of all toric manifolds and certain singular toric varieties.

     

A Dielectric Chirped Layered Mirror for Optical Telecommunication Wavelengths

We describe in this paper a design procedure for omnidirectional high reflectors with wide bandwidths for optical telecommunication bands. From the numerical results achieved by the transfer matrix method, it is found that a partial omnidirectional high-reflector covering the optical telecommunication wavelengths 1.3 and 1.55 μm is obtained for a partially deformed quarter-wave stack air/H(LH)¹⁵/glass by using the tellurium as a material of high refractive index (n _H = 4.6). The partially deformed stack is a periodic system deformed by a power law y = x ^1+k. Here y is the coordinates of the deformed object, x is the coordinates of the periodic stack and k is the coefficient defining the deformation degree. The study of this system leads to an omnidirectional high reflector band covering the optical telecommunication wavelengths 1.3 and 1.55 μm for k = 0.2.     

Armatans A and B,New Antimicrobial Isoflavans from Colutea armata

Chemistry of Natural Compounds - Armatans A (1) and B (2), new isoflavans, have been isolated from the EtOAc-soluble fraction of the MeOH extract of Colutea armata Hemsl. & Lace, along with...