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 (?).     

Synthesis of a new pyrrolo[1,3]diazepine: 4H-pyrrolo[1,2-a]thieno[2,3-e][1,3]diazepine

The 4H-pyrrolo[1,2-a]thieno[2,3-e][1,3]diazepine (20) was synthesized by the one-pot intramolecular cyclization of the appropriate nitroaldehyde 13 . This key intermediate 13 was obtained by two pathways from methyl 3-bromomethylthiophene-2-carboxylate (6).     

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.

     

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.      

Non-observable chaos in piecewise smooth systems

In the present paper, we discuss bifurcations of chaotic attractors in piecewise smooth one-dimensional maps with a high number of switching manifolds. As an example, we consider models of DC/AC power electronic converters (inverters). We demonstrate that chaotic attractors in the considered class of models may contain parts of a very low density, which are unlikely to be observed, neither in physical experiments nor in numerical simulations. We explain how the usual bifurcations of chaotic attractors (merging, expansion and final bifurcations) in piecewise smooth maps with a high number of switching manifolds occur in a specific way, involving low-density parts of attractors, and how this leads to an unusual shape of the bifurcation diagrams.     

Réarrangement de thiénobenzothiépinones en thiénoisothiazolinone et benzoisothiazolinone

Under the conditions of the Schmidt reaction the thienobenzothiepinones 1 , 2 and 13 involve a rearrangement respectively in N-benzythieno[2,3-d]isothiazolin-3-one ( 5 ) and benzoisthiazolin-3-one ( 6 ). A mechanism for this rearrangement is proposed.     

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 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.      

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 .