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.     

Biocompatible polymers for antibody support on gold surfaces

The elimination or minimization of non-specific protein adsorption from serum is critical for the use of surface plasmon resonance (SPR) sensors for in vitro and in vivo analysis of complex biological solutions. The ultimate goals in this application are to minimize non-specific adsorption of protein and to maximize analyte signal. A reduction of the non-specific protein adsorption from serum of up to 73% compared to carboxymethylated-dextran 500 kDa (CM-dextran) was achieved following a survey of eight biocompatible polymers and 10 molecular weights of CM-dextran. These coatings minimize non-specific adsorption on the sensor while also serving as immobilization matrices for antibody fixation to the probes. Polymers including polysaccharides: CM-dextrans, CM-hyaluronic acid, hyaluronic acid, and alginic acid were investigated. Humic acid, polylactic acid, polyacrylic acid, orthopyridyldisuldfide–polyethyleneglycol–N-hydroxysuccinimide (OPSS–PEG–NHS), and a synthesized polymer; polymethacrylic-acid-co-vinyl-acetate (PMAVA) were also used. The non-specific protein adsorption reduction was measured over a 14 day period at 0 °C for each polymer. Calibration curves using some of these polymers were constructed to show the performance and low detection limit possibilities of these new antibody supports. For many of the polymers, this is the first demonstration of employment as an antibody support for an optical or surface active sensor. CM-dextran is the polymer offering the largest signal for the antigen detection. However, the biocompatible polymers demonstrate a greater stability to non-specific binding in serum. These biocompatible polymers offer different alternatives for CM-dextran.     

Half-sandwich and mixed-ring uranium complexes

The monocyclooctatetraene uranium complex [U(COT)(I)₂(THF)₂] (COT=η-C₈H₈; THF=tetrahydrofuran), isolated from the reaction of bis(cyclooctatetraene)uranium with iodine, is a precursor for the synthesis of the alkyl derivatives [U(COT)(CH₂Ph)₂i (HMPA) ₂], [U(COT)(CH₂SiMe₃)₂(HMPA)] (HMPA=hexamethyl phosphorous triamide) and [U(COT)CH₂SiMe₃)₃] [Li(THF)₃] and of the mixed-ring compounds [U(COT)(η-C₅R₅)(I)] (R=H or Me). The last were used to prepare the amide and alkyl complexes [U(COT)(η-C₅H₅)(N{SiMe₃}₂)] and [U(COT)(η-C₅Me₅)(CH₂SiMe₃)].