Properties of the Central Points in Linear Programming Problems

In this paper we list several useful properties of central points in linear programming problems. We study the logarithmic barrier function, the analytic center and the central path, relating the proximity measures and scaled Euclidean distances defined for the primal and primal–dual problems. We study the Newton centering steps, and show how large the short steps used in path following algorithms can actually be, and what variation can be ensured for the barrier function in each iteration of such methods. We relate the primal and primal–dual Newton centering steps and propose a primal-only path following algorithm for linear programming.     

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.     

Synthesis and molecular structures of dialkylselenonium methylide complexes of indium tribromide

The reaction of bromomethyl-dibromo-indium(III), Br₂InCH₂Br with dialkylselenides, R¹SeR² (R¹ = CH₃, R² = CH₂C₆H₅; R¹ = C₂H₅, R² = CH₂C₆H₅; R¹ = R² = CH₂C₆H₅) afforded the corresponding dialkylselenonium methylide complexes of indium tribromide, Br₃InCH₂SeR¹R², which were fully characterized by NMR spectroscopy and single crystal X-ray diffraction studies.     

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.     

Indium(I) bromide-mediated coupling of dibromoacetonitrile with aldehydes followed by Boord elimination of bromine and oxygen of β-bromo alkoxides for preparation of 3-organyl-2-alkenenitriles

The organoindium compound derived from indium monobromide and dibromoacetonitrile reacts with carbonyl compounds to afford the corresponding 2-bromo-2-cyano-indium(III) alkoxide. The action of a second equivalent of indium monobromide onto the alkoxides derived from aldehydes promotes the Boord elimination of the β-related oxygen and bromine atoms leading to 2-alkenenitriles.     

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.