Variations on the Theorem of Birkhoff – von Neumann and Extensions

 The theorem of Birkhoff – von Neumann concerns bistochastic matrices (i.e., matrices with nonnegative real entries such that all row sums and all column sums are equal to one). We consider here real matrices with entries unrestricted in sign and we extend the notion of permutation matrices (integral bistochastic matrices); some generalizations of the theorem are derived by using elementary properties of graph theory. Received: October 10, 2000 Final version received: April 11, 2002     

Second-harmonic generation from monolayer Langmuir–Blodgett films of various push–pull pyridine and terpyridine metal complexes

The new ligands (E)-4-[2-(4-(N-methyl-N-hexadecylaminophenyl)ethenyl]pyridine (L¹) and 4′-(C₆H₄-p-N(Me)(hexadecyl))-2,2′:6′,2″-terpyridine (L²) were prepared along with their complexes [cis-Ir(CO)₂ClL¹], [fac-Os(CO)₃Cl₂L¹], [ZnCl₂L²] and [IrCl₃L²]. Whereas these complexes show a large second-order nonlinear optical (NLO) response at the molecular level, similar to that of related organic alkylated salts as evidenced by the Electric Field Induced Second-Harmonic (EFISH) generation technique, their Langmuir–Blodgett (LB) film susceptibility is lower than that of the salts.     

A Matrix-analog for Viennot's construction of the Robinson correspondence

The notion of Viennot matrix which is here introduced provides a convenient combinatorial set-up to describe the Robinson correspondence between permutations and pairs of Young tableaux. By means of that set-up a Simon-Newcomb property is reproved in a simple manner.     

A note on taxation,incentives and risk sharing

The necessary and sufficient conditions for a tax system to guarantee the consistency of private and public evaluation of risky projects are derived. A stochastic dominance approach is used.     

Obtention d'hétérocycles par action de binucléophiles diazotés sur des chalcones: Influence du substituant en position 2

Reactivity of 2-susbituted chalcones against diaza binucleophiles (hydrazines, thiourea, guanidine) has been studied. Various heterocycles (pyrazoles, pyrazolines, pyrimidines) or substituted hydrazines were obtained. A general interpretation is given according to the substituent of the enone system, R, the nature of binucleophile and the medium.     

Studies on pyrrolidinones. Synthesis of 2-(5-oxo-2-pyrrolidinyl)-1,3,4-oxadiazoles and 2-(5-oxo-2-pyrrolidinyl)benzimidazoles

The condensation of pyroglutamic acids with 1,2-phenylenediamine leads to 2-(5-oxo-2-pyrrolidinyl)benzimidazoles and the cyclization of disilylated diacylhydrazines derived from the same acids gives 2-(5-oxo-2-pyrrolidinyl)-1,3,4-oxadiazoles. These compounds show weak antifungal activity.     

Electrochemistry of vitamin B12: Part VII. Role of the base-off/base-on reaction in the oxido-reduction in the B12r-B12s couple in non-aqueous solvents

The cyclic voltammetric study of vitamin B_12r in DMSO shows the importance of the base-on/base-off reaction in the electrochemical reduction mechanism. Depending upon the flux of electrons flowing through the system. part of the base-on complex is reduced through prior opening of the nucleotide side-chain which gives rise to the more easily reduced DMSO-Co(II) complex. The quantitative analysis of the variations of the peak heights with the sweep rate allows the thermodynamic and kinetic characterization of the base-on/base-off reactions to be determined. DMSO thus appears as a stronger ligand toward Co(II) than water, leading to an increased participation of the base-off complex in the reduction process. The greater stability of the DMSO complex is also related to the observation that electron transfer is significantly slower than in the case of the water complex. The importance of the ligand exchange reactions in the reduction of B_12r is confirmed by the effect of pyridine additions. Three complexes then participate in the reduction process, their reduction potentials lying in the order DMSO >Py >Bzm. The reduction mechanism involving the interconversion of the three complexes is described as a function of the electrode potential, the flux of electrons and the pyridine concentration. An estimation of the equilibrium and rate constants of the three ligand exchange reactions is made, based on the variations of the cyclic voltammograms with the sweep rate and the pyridine concentration.