Algebraic cycles and topology of real Enriques surfaces

For a real Enriques surface Y we prove that every homology class in H₁(Y (R), Z/2) can be represented by a real algebraic curve if and only if all connected components of Y(R) are orientable. Furthermore, we give a characterization of real Enriques surfaces which are Galois-Maximal and/or Z-Galois-Maximal and we determine the Brauer group of any real Enriques surface Y.     

Frequency stability of an optically pumped cesium beam frequency standard

Results obtained in an experimental optically pumped cesium beam frequency standard in which a single semiconductor laser is used for the state selection and the atom detection are reported. The separation between the two interaction regions is equal to 21 cm. This gives a 500 Hz linewidth which is observed with a signal to noise ratio equal to 10,000 in a 1 Hz noise bandwidth. A quartz crystal oscillator is frequency controlled by the atomic transition. The measured short term frequency stability is given by _y()=2×10^–12–1/2 for 1 s<500 s. Prospects for improvement of this frequency stability are discussed.     

A novel palladium-mediated coupling approach to 2,3-disubstituted benzo(b)thiophenes and its application to the synthesis of tubulin binding agents

[structure: see text]. Flexible, convergent access to 2,3-disubstituted benzo[b]thiophenes has been developed. The most concise approach involves sequential coupling of o-bromoiodobenzenes with benzylmercaptan and zinc acetylides to give benzyl o-ethynylphenyl sulfides which react with iodine to give 3-iodobenzo[b]thiophenes in a 5-endo-dig iodocyclization. These iodides can be further elaborated using palladium-mediated coupling and/or metalation techniques. This method has been applied to the synthesis of some novel tubulin binding agents.     

A proximal point algorithm for control approximation problems

We consider the optimization problem $$f(x): = (c,x) + \sum\limits_{i = 1}^n {\alpha _i \parallel A^i x - a^i \parallel ^{\beta _i } \to \mathop {\min }\limits_{x \in D} ,} $$ which is an extension of a problem studied by Idrissi, Lefebvre and Michelot [7]. This class of problems contains many practically important special cases so as approximation, location and optimal control problems, perturbed linear programming problems and surrogate problems for linear programming. Necessary and sufficient optimality conditions are derived using the sub-differential calculus. A proximal point algorithm is modified by the method of partial inverse [13] in order to solve the optimality conditions.     

Regioselective Synthesis of Mixed Indole 2,3-Bis(sulfides). A Study of the Mechanism of the Second Sulfenylation of Indole

Sulfenylation of indole using sulfenyl chlorides leads to the initial formation of a 3-indolyl sulfide, while excess reagent introduces a second sulfide at the 2-position of the ring. The mechanism of this second sulfenylation has not, to date, been rigorously elucidated. The development of the first, regioselective synthesis of mixed indole 2,3-bis(sulfides) has allowed the study of the sulfenylation of 3-indolyl sulfides using a different sulfenyl chloride. Our results afford evidence that the reaction proceeds via an intermediate 3,3-disulfenylated indolenine species, with subsequent migration of one of the sulfide groups to the 2-position.     

A general method for the preparation of N-monosubstituted-3-isothiazolamines

We describe here a novel and general high yield method for the synthesis of 3-alkyl and arylaminoisothiazoles, a previously unknown group of isothiazoles, by the reaction of ammonia with 3-halo-2-alkylisothiazolium salts. The mechanism of the reaction probably involves a ring opening followed by a recyclization to the title compounds.