Une classe d'algèbres de Fréchet à caractères continus

We prove in a simpler and direct manner using the spectral theory that every Fréchet algebra which is rationnally generated by a real or orthogonal subset is functionally continuous. These results include as a special case the results of R. Arens, H. Goldmann, E. A. Michael and W. Zelazko.

     

On Φ-Derivation in Banach Algebras

Using Bre?ar and ?emrl approach, we give a proof of the extended Jacobson density theorem for Φ-derivations. Further, some applications on Banach algebras will be given. Precisely, for d being a continuous Φ-derivation on a given Banach algebra ?, we show that: d(?) ? rad (?) ? [b,[a, d(a)]] ∈ rad (?) for all a, b ∈ ? and d leaves invariant all maximal ideals of codimension one?for every a ∈ ? there exists a positive integer n such that (d(a)) ⁿ is quasi-nilpotent ? [d, Φ](?) ? rad (?) and d ²(a) ∈ rad (?) for all a ∈ ?. Finally, we characterize all pairs d, δ of continuous Φ-derivations such that dδ(a) is quasi-nilpotent for all a ∈ ? and [d, δ](?), [d, Φ](?), [δ,Φ](?) are subsets of rad (?).     

3-Methyl-3a,4-Dihydro-3H-Thiochromeno[4,3-c]isoxazol

Abstract  The crystal structure of the title compound, C₁₁H₁₁NOS, was determined by an X-ray diffraction analysis. The compound crystallizes in the monoclinic space group P2₁/c with cell parameters a = 10.533(2) ?, b = 12.7826(19) ?, c = 7.6491(17) ?, β = 107.997(17)^°, V = 979.5(3) ?³ and Z = 4. The S containing heterocycle adopts a sofa conformation, whereas the 5-membered ring adopts an envelope conformation. The crystal packing is characterized by weak C–H···N contacts and π-stacking interactions. Graphical Abstract  The title compound, 3-methyl-3a,4-dihydro-3H-thiochromeno[4,3-c]isoxazol was synthesized by an 1,3 dipolar cycloaddition reaction and its crystal structure determined. Single crystal X-ray diffraction analysis reveals that the aromatic 6-membered ring is planar, whereas the ring containing the S atom adopts a sofa conformation and the 5-membered ring an envelope conformation. The methyl group is in an equatorial position.      

Research on nitrogen and sulfur heterocyclic compounds: Synthesis of 10H-pyrrolo[1,2-a]thieno[3,4-e][1,4]-diazepin-5(4H)-one and some derivatives

The synthesis of 10H-pyrrolo[1,2-a]thieno[3,4-e][1,4]diazepin-5(4H)-one ( 16 ) and some derivatives are described from methyl 3-bromomethylthiophene-4-carboxylate ( 5 ). The key step of these sequences is the intramolecular cyclization of the carbonylazides 12 and 13 .     

Simple and efficient synthesis of racemic 2-(tert-butoxycarbon-ylamino)-2-methyl-3-(1H-1,2,4-triazol-1-yl)propanoic acid, a new derivative of β-(1,2,4-triazol-1-yl)alanine

A simple synthetic approach to racemic N-tert-butyloxycarbonyl-2-methyl-3-(1H-1,2,4-triazol-1-yl)alanine (5) in four steps and 68% overall yield starting from oxazoline derivative 1 is reported. This synthesis involves the alkylation of 1H-1,2,4-triazole with an O-tosyloxazoline derivative, followed by an oxazoline ring-opening reaction and oxidation of the N-protected β?aminoalcohol by potassium permanganate.     

Assessing impact force localization by using a particle swarm optimization algorithm

This paper focuses on the inverse problem regarding force localization in the case of impacts not concentrated at a point but which occur on elastic beams. Following the identification approach proposed to solve this problem and which is based on the reciprocity theorem, the impact location characteristics were determined by using particle swarm optimization algorithm. To eliminate numerical trouble due to the trivial solutions appearing in this formulation, the fitness function was customized by introducing a set of weighting coefficients. Four different formulations of the fitness function were considered and their performances with regards to the number of sensors used and their positions were analyzed. They enabled a selection of the best combination of weighting coefficients to be used in the context of an impact force localization process based on the particle swarm optimization technique. Three sensors were found to be required and comparison with a genetic algorithm has revealed the effectiveness of the proposed method in terms of accuracy and computational time.     

Structure and stability of (CuNO) isomers

Quantum-mechanical calculations have been performed on various isomers of the (CuNO)⁺ system. A ²Π ground state is found for the linear CuNO⁺ and CuON⁺ isomers and a ²A′ state for the bent CuNO⁺ and CuON⁺ isomers. Energy calculations indicate that the linear CuNO⁺ structure is the most stable, the bent CuNO⁺ and CuON⁺ and the linear CuON⁺ structures are at 0.86 eV, 0.99 eV and 1.04 eV above this respectively. In the CuNO⁺ → CuON⁺ interconversion between the linear isomers, three transition states are involved, whereas the bent CuNO⁺ isomer is found to be an intermediate species. The isomerization barriers, dissociation energies, equilibrium geometries and vibration frequencies are given for all isomers in their ground and first excited states.     

Heterodyne mixing experiments with NbN-based SIS junctions

Tests of niobium-nitride-based SIS junctions in our experimental receiver at ENS¹ have shown the remarkable stability in time and through thermal cycling of these high T_C material junctions; they were used to evaluate the real junction temperature in our vacuum cryogenerator. Results of heterodyne mixing experiments are presented at 100 GHz, showing that further progress in fabrication would be necessary. Detection experiments were performed at 460 GHz with encouraging results.     

A novel practical synthesis of pyrrolo[1,2-a]thieno[2,3-e][1,4]diazepines

In an investigation of new heterocyclic systems, a novel way to obtain pyrrolo[1,2-a]thieno[2,3-e][1,4]diazepine 8 was effected by ring closure to the appropriate nitroaldehyde compound which was synthesized in five steps from 3-bromomethyl-2-nitrothiophene 1 .     

A G2(MP2) theoretical study of substituent effects on H3BNHnCl3−n (n= 3-0) donor-acceptor complexes

The complexation energies of H₃BNH_nCl_3−n (n= 3-0) complexes and the proton affinities of NH_nCl_3−n compounds have been computed at the G2(MP2) level of theory. G2(MP2) results show that the successive chlorine substitution on the ammonia decreases both the basicity of the NH_nCl_3−n ligands and the stability of H₃BNH_nCl_3−n complexes. The findings are interpreted in terms of the rehybridisation of the nitrogen lone-pair orbital. The NBO partitioning scheme shows that the variation of the N-H and N-Cl bond lengths, upon complexation, is due to variation of “s” character in these bonds.