基本弱Hopf代数和弱覆盖箭图

研究了代数闭域K上具有强分次Jacobson根r的有限维基本可裂弱Hopf代数,并刻画了有限维基本可裂半格分次弱Hopf代数H,即存在有限Clifford半群S,使得H/rkS^*.还引入了弱覆盖箭图的概念,其路代数具有半格分次弱Hopf代数的结构,其箭图作为弱覆盖箭图被刻画.进一步地,证明了对上述H存在弱覆盖箭图Г和由长度大于2的路生成的理想I,使得kГ/IH.     

A family of Halley–Chebyshev iterative schemes for non-Fréchet differentiable operators

A modification of some classical third order methods is studied. The main advantage of these methods is that they do not need evaluate any Fréchet derivative. A convergence theorem in Banach spaces, just assuming that the second divided difference is bounded by a nondecreasing function and a punctual condition, is presented. Fréchet differentiability is not required. Finally, a particular example is analyzed where our conditions are fulfilled and the classical ones fail.     

Some results on almost L-weakly and almost M-weakly compact operators

Positivity - We introduce and study a new topology on trees, that we call the countably coarse wedge topology. Such a topology is strictly finer than the coarse wedge topology and it turns every...     

Development of dry derivatization and headspace solid-phase microextraction technique for the GC-ECD determination of haloacetic acids in tap water

A simple, fast and efficient liquid-liquid extraction (LLE) technique using headspace solid-phase microextraction (HS-SPME), in conjunction with gas chromatography-electron capture detection (GC-ECD) has been developed for the determination of haloacetic acids (HAAs) in tap water. The analytical procedure involves LLE, evaporation of extraction solvent to dryness, derivatization of HAAs into their methyl esters with acidic methanol, HS-SPME using 100-μm polydimethylsiloxane (PDMS) fiber, and GC-ECD determination. The derivatization process was optimized in dry conditions to achieve maximum sensitivity using the following conditions: esterification for 10 min at 55°C in 50 μL methanol, 30 μL sulphuric acid and 0.1 g anhydrous sodium sulphate. The HS-SPME conditions were also optimized and good sensitivity was obtained at a sampling temperature of 25°C, an absorption time of 10 min and a desorption time of 2 min. The linear calibration curves were observed for the concentration ranging from 0.1 to 200 μg/L with the correlation coefficients (R ²) greater than 0.993 and the relative standard deviation (RSD) less than 12%. The method detection limits of all analytes ranging from 0.02 to 0.7 μg/L were obtained. The proposed method is compared directly to standard EPA method 552.2 in drinking water, and significant advantage in terms of selectivity was observed. Finally the optimized procedure was applied to the analysis of HAAs in Bizerte drinking water. The studied HAA were detected in all the water samples and the concentration of total HAA5 ranged from 17.8 to 70.3 μg/L.     

Synthesis of β,β‘-Difluorinated and β,β’-F-Dialkylated Acetals

Using the phase transfer catalysis technique, a series of fluorinated acetals has been prepared, in basic medium, by action of dicholromethane on 2-mononfluorinated alcohols or 1-F-alkyl 2-fluoroethanols. The identification of these new acetals has been achived by the study cf their ¹H, 19F NMR and their mass spectra.     

The first chromate containing both Cr<Subscript>2</Subscript>O<Subscript>7</Subscript> and Cr<Subscript>3</Subscript>O<Subscript>10</Subscript> groups,bis(1,3-bis(4-piperidinium)propane) dichromate trichromate monohydrate: Synthesis and crystal structure

A new organic-inorganic hybrid material (C₁₃H₂₈N₂)₂[Cr₂O₇][Cr₃O₁₀]·H₂O (1) was synthesized by slow solvent evaporation at room temperature, and its crystal structure was determined by single crystal X-ray diffraction. This compound crystallizes in the monoclinic space group P2₁/c. The asymmetric unit contains two crystallographically independent 1,3-bis(4-piperidinium)propane, (H₂bppp)²⁺ cations (A and B), one trichromate Cr₃O ₁₀ ^2? anion, one dichromate Cr₂O ₇ ^2? anion, and one water molecule. All these entities are interconnected into a complicated two-dimensional hydrogen bonded network via N–H?O and O–H?O hydrogen bonds. Furthermore, this structure is stabilized by a large number of C–H?O interactions, thus establishing a three-dimensional network structure. This compound appears to be the first example of chromates containing both Cr₂O₇ and Cr₃O₁₀ groups.     

Parabolic equations with measure data in Orlicz spaces

We prove an existence result for solutions of nonlinear parabolic equations with measure data in Orlicz–Sobolev spaces.     

A General Multiresolution Method for Fitting Functions on the Sphere

In [7], Lyche and Schumaker have described a method for fitting functions of class C ¹ on the sphere which is based on tensor products of quadratic polynomial splines and trigonometric splines of order three associated with uniform knots. In this paper, we present a multiresolution method leading to C ²-functions on the sphere, using tensor products of polynomial and trigonometric splines of odd order with arbitrary simple knot sequences. We determine the decomposition and reconstruction matrices corresponding to the polynomial and trigonometric spline spaces. We describe the general tensor product decomposition and reconstruction algorithms in matrix form which are convenient for the compression of surfaces. We give the different steps of the computer implementation of these algorithms and, finally, we present a test example.     

Informational Relationship Measures

This paper gives the definitions of ten normed information ratesas measures of relationship between two random variables. Thebehaviour of these measures have been considered in the caseof a bivariate uniform model. Numerical comparisons betweenthe measures are made, in order to choose a measure which hassome advantages over the other measures.