Synthesis of enantiomerically enriched β-hydroxy selenides by catalytic asymmetric ring opening of meso-epoxides with (phenylseleno)silanes

The first example of the enantioselective ring opening of meso-epoxides by (phenylseleno)silanes using salen(Cr)complexes as catalyst is described. This desymmetrization reaction constitutes a simple and convenient approach to synthetically versatile optically active β-hydroxy selenides.     

Microwave-assisted synthesis of 4-quinolylhydrazines followed by nickel boride reduction: a convenient approach to 4-aminoquinolines and derivatives

Nickel(II) chloride/sodium borohydride combination was employed for the reduction of 4-hydrazinoquinoline derivatives to the corresponding anilines. This reductive protocol was efficiently applied for the reductive cleavage of monosubstituted hydrazines. We described herein the microwave-assisted synthesis of 4-hydrazinoquinolines, which furnished a high yielding and rapid two-step procedure for the synthesis, under mild conditions, of 4-aminoquinolines as antimalarial precursors.     

Evaluation of a spectroscopic tandem method using information theory

To obtain vital spectroscopic data, a specific tandem spectroscopic method consisting of excitation in the DC are separated from the evaporation process was applied. Recently developed tandem spectroscopic methods require a complex evaluation process that can be described by metrological characteristics and from them derived parameters. Evaluation of the novel method optimization process is a part of the application of some chosen, specific, and generally accepted statistical methods. For this purpose, it is suitable to determine parameters of the information theory. It is necessary to compare experimental parameters of the information theory with tolerance parameters representing the values which are supposed to be achieved. To evaluate the given parameters, influence of the concentration range used was taken into account.     

The complex of pant decompositions of a surface

We exhibit a set of edges (moves) and 2-cells (relations) making the complex of pant decompositions on a surface a simply connected complex. Our construction, unlike the previous ones, keeps the arguments concerning the structural transformations independent from those deriving from the action of the mapping class group. The moves and the relations turn out to be supported in subsurfaces with 3g−3+n=1,2 (where g is the genus and n is the number of boundary components), illustrating in this way the so-called Grothendieck principle.     

A new summation method for power series with rational coefficients

We show that an asymptotic summation method, recently proposed by the authors, can be conveniently applied to slowly convergent power series whose coefficients are rational functions of the summation index. Several numerical examples are presented.

     

A Lower Bound for the Rectilinear Crossing Number

We give a new lower bound for the rectilinear crossing number of the complete geometric graph K_n. We prove that and we extend the proof of the result to pseudolinear drawings of K_n. Dedicated to the memory of our good friend and mentor Víctor Neumann-Lara. Received: April, 2003 Final version received: March 18, 2005     

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n ^−1/2, n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.     

Analysis of some injection bounds for Sobolev spaces by wavelet decomposition

We consider the Sobolev spaces $H^s(\Omega )$ and $H_0^s(\Omega )$ and the Besov spaces $B_{2,\infty }^{1/2}(\Omega )$, where Ω is a sufficiently regular (see Lemma 2) subdomain of ${\mathbb{R}}^2$. It is well known that for the values of $s\in [0,1/2)$ the two Sobolev spaces coincide, with equivalence of the norms, and that the inclusion $B_{2,\infty }^{1/2}(\Omega )?H^s(\Omega )$ holds. The Note is concerned with the explicit analysis of the constants appearing in the continuity bounds for the injections $H^s(\Omega )?H_0^s(\Omega )$ and $B_{2,\infty }^{1/2}(\Omega )?H^s(\Omega )$ and of their dependence on the regularity s of the spaces. The analysis is carried out by using the wavelet characterization of the corresponding norms.