Problèmes mathématiques de l'équation de Boltzmann relativiste

This work deals with relativistic Boltzmann equation and more particulary with integral operator of complete equation and integral operator of linearized equation. These operators depend on the differential cross sectionh(〈p, q〉, cos θ) which is a fonction of energy 〈p, q〉 and of the deviation angle θ. The only hypothesis is thath is a symetric function of cosθ. The second part deals essentially with linearized equation in Special Relativity. We take for the distribution function: $$F\left( {x,p} \right) = a e^{ - \frac{{\lambda p}}{2}} \left( {e^{ - \frac{{\lambda p}}{2}} + \varepsilon f\left( {x,p} \right)} \right)$$ wherea is a constant, λ a constant vector and ? a small constant so that ?² can be neglected. We obtain the equation: $$\frac{{p^\alpha }}{{p^0 }}\frac{{\partial f}}{{\partial x^\alpha }} = - K\left( p \right) \cdot f + G\left( f \right)$$ whereK(p) is a positive function andG an Hilbert-Schmidt operator. Then we resolve the Cauchy's problem by taking the Fourier's transformation off, and in the last part by investigating properties of the resolvent of ?K+G we establish that asx ⁰→+∞ the solution of this problem has for limit the equilibrium distributiona e ^?λp .     

The highest D value for a Mn(II) ion: investigation of a manganese(II) polyoxometalate complex by high-field electron paramagnetic resonance

Using magnetization measurements and multifrequency high-field electron paramagnetic resonance, the largest zero-field splitting for any individual isolated Mn(II) ion has been found in a polyoxometalate complex, suggesting that the inorganic ligand induces large Ising-type magnetic anisotropy.     

Use of porous graphitic carbon for the analysis of nitrate ester, nitramine and nitroaromatic explosives and by-products by liquid chromatography-atmospheric pressure chemical ionisation-mass spectrometry

A new LC/MS method was developed for the analysis of sixteen different analytes including the most common organic explosives encountered in forensic investigations. The separation was achieved using a porous graphitic carbon (PGC) column with a binary gradient elution. Molecular modeling suggested a possible interpretation for the elution order of explosive compounds on PGC. The introduction of ammonium formate in the mobile phase resulted in the formation of characteristic adduct ions thus enhancing the mass spectrometric detection of nitrate ester and nitramine compounds. Atmospheric pressure chemical ionization (APCI) and electrospray ionization (ESI) were compared in terms of sensitivity. The final LC/APCI-MS method allowed easy identification of investigated compounds with limits of detection ranging from 0.04 to 1.06 ng/microl. The analysis of simulated forensic samples confirmed the performance of the method.     

β‐Elimination of an aziridine to an allylic amine: a mechanistic study

The base‐induced rearrangement of aziridines has been examined using a combination of calculations and experiment. The calculations show that the substituent on nitrogen is a critical feature that greatly affects the favorability of both α‐deprotonation, and β‐elimination to form an allylic amine. Experiments were carried out to determine whether E2‐like rearrangement to the allylic amine with lithium diisopropyl amide (LDA) is possible. N‐tosyl aziridines were found to deprotonate on the tosyl group, preventing further reaction. A variety of N‐benzenesulfonyl aziridines having both α‐ and β‐protons decomposed when treated with LDA in either tetrahydrofuran or hexamethylphosphoramide. However, when α‐protons were not present, allylic amine was formed, presumably via β‐elimination. Copyright © 2011 John Wiley & Sons, Ltd.     

Solid-Phase Extraction,Clean-pp and Liquid Chromatography for Routine Multiresidue Analysis of Neutral and Acidic pesticides In Natural Waters in One Run

Abstract

Solid-phase extraction using C₁₈ silica cartridges, liquid chromatography analysis and UV diode array detection were investigated for the routine trace-level determination of neutral pesticides over a wide range of polarity. Detection limits below the 0.1 μg/1 range were easily obtained in drinking water. If neutral and acidic pesticides over a wide range of polarity have to be determined in the same run, samples have to be acidified to obtain good recoveries of extraction. The effect of the sample matrix was studied and detection limits in the 0.1 μg/1 range were obtained in drinking water except for the more polar ones which are in the interfering peak of humic and fulvic acids. For surface water, a clean-up step using a Florisil cartridge has to be included in the procedure that allows detection limits in the range 0.05–0.3 μg/1.     

Raman spectrum of Si nanowires: temperature and phonon confinement effects

The Raman spectrum of Si nanowires (NWs) is a matter of controversy. Usually, the one-phonon band appears broadened and shifted. This behaviour is interpreted in terms of phonon confinement; however, similar effects are observed for NWs with dimensions for which phonon confinement does not play any relevant role. In this context, the temperature increase induced by the laser beam is recognized to play a capital role in the shape of the spectrum. The analysis of the Raman spectrum, under the influence of the heating induced by the laser beam, is strongly dependent on the excitation conditions and the properties of the NWs. We present herein an analysis of the Raman spectrum of Si NWs based on a study of the interaction between the laser beam and the NWs, for both ensembles of NWs and individual NWs, taking account of the temperature increase in the NWs under the focused laser beam and the dimensions of the NWs.     

Octa- and nonanuclear nickel(II) polyoxometalate clusters: synthesis and electrochemical and magnetic characterizations

Three high-nuclearity NiII-substituted polyoxometalate compounds functionalized by exogenous ligands have been synthesized and characterized. The octanuclear complexes in Na15[Na{(A-R-SiW9O34)Ni4(CH3COO)3(OH)3}2] . 4NaCl . 36H2O (1) and Na15[Na{(A-R-SiW9O34)Ni4(CH3COO)3(OH)2(N3)}2] . 32H2O (2) can be described as two {Ni4} subunits connected via a {Na(CH3COO)6} group, with the acetato ligands also ensuring in each subunit the connection between the paramagnetic centers. In 2, two azido groups replace two of the six mu-hydroxo ligands present in 1. The nonanuclear complex K7Na7[(A-R-SiW9O34)2Ni9(OH)6(H2O)6(CO3)3] . 42H2O (3) exhibits a double cubanestructure with two [(A-R-SiW9O34)Ni4(OH)3]5- subunits linked by three carbonato ligands. A ninth NiII center connected to one subunit via a carbonato ligand and a O=W group completes this asymmetric polyoxometalate.Electronic spectroscopy and electrochemical studies indicate that, while compounds 1-3 decompose in a pure aqueous medium, these complexes are very stable in a pH 6 acetate medium. The cyclic voltammetry pattern of each complex is constituted by a first eight-electron reduction wave followed by a second large-current intensity wave. The characteristics of the first waves of the complexes are clearly distinct from those obtained for their lacunary precursor [A-R-SiW9O34]10-, a feature that is due to the Ni centers in the complexes. Such observations of electroactive, stable, and highly nickel-rich polyoxometalates are not common. Measurements of the magnetic susceptibility revealed the occurrence of concomitant ferromagnetic and antiferromagnetic interactions in 1 and 3.For both of these compounds, the extension of the magnetic exchange has been determined by means of a spin Hamiltonian with three and four J constants, respectively.     

Novel neutral imidazole-lipophosphoramides for transfection assays

New helper lipids, possessing an imidazole polar head, have been synthesized and included in formulations for transfection assays; these new helper lipids can improve the transfection by a factor of up to 100 compared to the use of DOPE as co-lipid.     

Cyanido-bridged one-dimensional systems assembled from [ReIVCl4(CN)2]2? and [MII(cyclam)]2+ (M = Ni, Cu) precursors

Three new cyanido-bridged heterometallic Re^IVNi^II and Re^IVCu^II one-dimensional systems were synthesized and extensively characterized both structurally and magnetically. Single-crystal X-ray diffraction analysis revealed that these compounds display a common topology, with chains composed of alternating [Re^IVCl₄(CN)₂]^2? and [M^II(cyclam)]²⁺ (M = Ni in 1, Cu in 2) or [Cu^II(N,N??-dimethylcyclam)]²⁺ (in 3) building units. Two different chain orientations with a tilt angle of ca. 51° to 55° are present in the crystal packing of these compounds. The magnetic susceptibility measurements suggest the presence of intrachain ferromagnetic interactions between the S = 3/2 Re^IV centers and the 3d metal ions: S = 1 Ni^II or S = 1/2 Cu^II. At low temperature, a three-dimensional ordered magnetic phase induced by interchain antiferromagnetic interactions (antiferromagnetic for 1 and 2; canted antiferromagnetic for 3) is detected for the three compounds.     

Cyanido-bridged Fe(III)-Mn(III) heterobimetallic materials built from Mn(III) Schiff base complexes and di- or tri-cyanido Fe(III) precursors

The reaction of [Fe(III)L(CN)(3)](-) (L being bpca = bis(2-pyridylcarbonyl)amidate, pcq = 8-(pyridine-2-carboxamido)quinoline) or [Fe(III)(bpb)(CN)(2)](-) (bpb = 1,2-bis(pyridine-2-carboxamido)benzenate) ferric complexes with Mn(III) salen type complexes afforded seven new bimetallic cyanido-bridged Mn(III)-Fe(III) systems: [Fe(pcq)(CN)(3)Mn(saltmen)(CH(3)OH)]·CH(3)OH (1), [Fe(bpca)(CN)(3)Mn(3-MeO-salen)(OH(2))]·CH(3)OH·H(2)O (2), [Fe(bpca)(CN)(3)Mn(salpen)] (3), [Fe(bpca)(CN)(3)Mn(saltmen)] (4), [Fe(bpca)(CN)(3)Mn(5-Me-saltmen)]·2CHCl(3) (5), [Fe(pcq)(CN)(3)Mn(5-Me-saltmen)]·2CH(3)OH·0.75H(2)O (6), and [Fe(bpb)(CN)(2)Mn(saltmen)]·2CH(3)OH (7) (with saltmen(2-) = N,N'-(1,1,2,2-tetramethylethylene)bis(salicylideneiminato) dianion, salpen(2-) = N,N'-propylenebis(salicylideneiminato) dianion, salen(2-) = N,N'-ethylenebis(salicylideneiminato) dianion). Single crystal X-ray diffraction studies were carried out for all these compounds indicating that compounds 1 and 2 are discrete dinuclear [Fe(III)-CN-Mn(III)] complexes while systems 3-7 are heterometallic chains with {-NC-Fe(III)-CN-Mn(III)} repeating units. These chains are connected through π-π and short contact interactions to form extended supramolecular networks. Investigation of the magnetic properties revealed the occurrence of antiferromagnetic Mn(III)···Fe(III) interactions in 1-4 while ferromagnetic Mn(III)···Fe(III) interactions were detected in 5-7. The nature of these Mn(III)···Fe(III) magnetic interactions mediated by a CN bridge appeared to be dependent on the Schiff base substituent. The packing is also strongly affected by the nature of the substituent and the presence of solvent molecules, resulting in additional antiferromagnetic interdinuclear/interchain interactions. Thus the crystal packing and the supramolecular interactions induce different magnetic properties for these systems. The dinuclear complexes 1 and 2, which possess a paramagnetic S(T) = 3/2 ground state, interact antiferromagnetically in their crystal packing. At high temperature, the complexes 3-7 exhibit a one-dimensional magnetic behavior, but at low temperature their magnetic properties are modulated by the supramolecular arrangement: a three-dimensional antiferromagnetic order with a metamagnetic behavior is observed for 3, 4, and 7, and Single-Chain Magnet properties are detected for 5 and 6.