A mathematical model for unsteady mixed flows in closed water pipes

We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes.In the case of free surface incompressible flows,the FS-model is formally obtained,using formal asymptotic analysis,which is an extension to more classical shallow water models.In the same way,when the pipe is full,we propose the P-model,which describes the evolution of a compressible inviscid flow,close to gas dynamics equations in a nozzle.In order to cope with the transition between a free surface state and a pressured(i.e.,compressible) state,we propose a mixed model,the PFS-model,taking into account changes of section and slope variation.     

Chemical composition and antimicrobial activity of essential oil of Cupressus atlantica

Cupressus atlantica Gaussen, an endemic species from Morocco, is used in traditional medicine. The chemical composition of the essential oil isolated by hydrodistillation from the leaves was investigated by capillary gas chromatography and gas chromatography/mass spectrometry, and also evaluated for in vitro antimicrobial activity. Sixty-one components, representing 98.1% of the total, were detected of which fifty-seven were identified. Germacrene D (34.8%), alpha-pinene (13.6%), delta-cadinene (6.1%), alpha-phellandrene (5.5%), gamma-cadinene (5.0%), beta-caryophyllene (4.8%) and alpha-humulene (4.4%) were the predominant compounds. The oil was characterized by a relatively high amount of oxygenated monoterpenes (66.5%). The oil, screened for antimicrobial activity against both Gram-positive and Gram-negative, showed pronounced activity against all the microbes tested, except Pseudomonas, which showed resistance.     

Fluorodensitometric determination of baclofen

A fluorodensitometric method was developed for the determination of baclofen. The method is based on the reaction of baclofen with 4-chloro-7-nitrobenzofurazan and measurement of the fluorescence intensity at 540 nm after chromatographic separation on a silica-gel plate. A linear relationship was found between relative fluorescence intensity and concentration over the range 4-100 ng of baclofen per spot. The detection and determination limits are 0.4 and 4.0 ng of baclofen per spot, respectively. The method was applied to human plasma. The recovery of baclofen from plasma was 96.67%.     

Hydrolysis Kinetic Studies of Schiff Bases Derived from Pyrrolic Aldehydes in Buffered Aqueous Ethanol and Sulfuric Acid Solutions: Structural Effects of Substitutes

Two series of substituted N‐pyrrolyl‐2‐methylene‐aniline were synthesized and characterized to study their stability in a large domain of pH (0–14) and especially in the H₀ domain (–4 to 0). The hydrolysis kinetics of the azomethine group was established in homogeneous media using a thermostated UV–vis spectrophotometer. The hydrolysis mechanism was investigated, and the experimental kinetic constants were calculated. Then, the pH–rate diagram profile was determined and the structural effect of substitutes on the kinetic constants was clarified and discussed.     

Defect‐induced ferrimagnetism in the half‐metallic Co2CrAl and Co2CrSi compounds

Co₂CrAl and Co₂CrSi are amongst the most studied Heusler alloys due to their half‐metallic character. These compounds are also well‐known to present ferromagnetism with high Curie temperatures. We show using first‐principles calculations that the creation of Cr antisites (Cr atoms at the Co sites) induces ferrimagnetism in these compounds without destroying the half‐metallic character of these alloys. The reduction of the total spin moment causes lower external fields and thus smaller energy losses in realistic magnetoelectronic, also known as spintronic, devices. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a variational problem with lack of compactness: the topological effect of the critical points at infinity

We study the subcritical problemsP :–u=u ^p–,u>0 on;u=0 on , being a smooth and bounded domain in ^N,N–3,p+1=2N/N–2 the critical Sobolev exponent and >0 going to zero — in order to compute the difference of topology that the critical points at infinity induce between the level sets of the functional corresponding to the limit case (P₀).

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Résumé Nous étudions les problèmes sous-critiquesP :–u=u ^p–,u > 0 sur;u=0 sur –où est un domaine borné et régulier de ^N,N–3,p + 1=2N/N –2 est l'exposant critique de Sobolev, et >0 tend vers zéro, afin de calculer la différence de toplogie induite par les points critiques à l'infini entre les ensembles de niveau de la fonctionnelle correspondant au cas limite (P₀).

     

Clifford Algebra-Valued Wavelet Transform on Multivector Fields

This paper presents a construction of the n = 2 (mod 4) Clifford algebra Cl _n,0-valued admissible wavelet transform using the admissible similitude group SIM(n), a subgroup of the affine group of \mathbbRⁿ{\mathbb{R}^{n}} . We express the admissibility condition in terms of the Cl _n,0 Clifford Fourier transform (CFT). We show that its fundamental properties such as inner product, norm relation, and inversion formula can be established whenever the Clifford admissible wavelet satisfies a particular admissibility condition. As an application we derive a Heisenberg type uncertainty principle for the Clifford algebra Cl _n,0-valued admissible wavelet transform. Finally, we provide some basic examples of these extended wavelets such as Clifford Morlet wavelets and Clifford Hermite wavelets.     

Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl 3,0

First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions Third, we show a set of important properties of the Clifford Fourier transform on Cl_3,0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl_3,0 multivector functions.