Synthesis,characterization and antibacterial activity of 3‐(2‐methoxyphenyl)‐2‐sulfanylpropenoic acid and di‐isopropylammonium [3‐(2‐methoxyphenyl)‐2‐sulfanylpropenoato] triphenylstannate(IV). The crystal structure of [HQ][SnPh3(o‐mpspa)]

Reaction of 3‐(2‐methoxyphenyl)‐2‐sulfanylpropenoic acid [H₂(o‐mpspa)] with SnPh₃OH in the presence of di‐isopropylamine resulted in the formation of the complex [HQ][SnPh₃(o‐mpspa)] (where HQ = di‐isopropylammonium cation and o‐mpspa = 3‐(2‐methoxyphenyl)‐2‐sulfanylpropenoato), which was characterized by mass spectrometry and vibrational spectroscopy, as well as by ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy. The single‐crystal X‐ray structural analysis of the new complex shows a trigonal‐bipyramidal coordination geometry around the Sn atom where o‐mpspa behaves as a bidentate chelating ligand. Dimeric units arise from the existence of N? H…O hydrogen bonds between the NH₂ group of the di‐isopropylammonium cation and the oxygen atoms of the two neighbouring carboxylato groups. The bacteriostatic activity of the complex is also reported. Copyright © 2007 John Wiley & Sons, Ltd.     

Positive definite completions of partial Hermitian matrices

The question of which partial Hermitian matrices (some entries specified, some free) may be completed to positive definite matrices is addressed. It is shown that if the diagonal entries are specified and principal minors, composed of specified entries, are positive, then, if the undirected graph of the specified entries is chordal, a positive definite completion necessarily exists. Furthermore, if this graph is not chordal, then examples exist without positive definite completions. In case a positive definite completion exists, there is a unique matrix, in the class of all positive definite completions, whose determinant is maximal, and this matrix is the unique one whose inverse has zeros in those positions corresponding to unspecified entries in the original partial Hermitian matrix. Additional observations regarding positive definite completions are made.     

Linear programming approaches to the measurement and analysis of productive efficiency

Invited by J. T. Pastor     

Higher dimensional classicalW-algebras

ClassicalW-algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel'fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension. TheseW-algebras are the Poisson structures associated with a higher dimensional version of the Khokhlov-Zabolotskaya hierarchy (dispersionless KP-hierarchy). The two dimensional case is worked out explicitly and it is shown that the role of DiffS(1) is taken by the algebra of generators of local diffeomorphisms in two dimensions.     

Maximin location: Discretization not always works

In this note we show by means of a simple example that, if the maximin problem with (nonlinear) concave increasing utility functions is solved by inspecting the extreme points of the (generalized) Voronoi diagram (as usually proposed), one may have to inspect an infinite number of candidate points. The research of the second and third authors is partially supported by Grant PB96-1416-C02-02 of Ministerio de Educación y Cultura, Spain     

Asymptotics for a weighted least squares estimator of the disease onset distribution function for a survival-sacrifice model

In carcinogenicity experiments with animals where the tumor is not palpable it is common to observe only the time of death of the animal, the cause of death (the tumor or another independent cause, as sacrifice) and whether the tumor was present at the time of death. These last two indicator variables are evaluated after an autopsy. A weighted least squares estimator for the distribution function of the disease onset was proposed. Asymptotic properties of that estimator are established here. We demonstrate its strong uniform consistency. A minimax lower bound for the estimation of the disease onset distribution is obtained, as well as the local asymptotic distribution for their estimator.     

Synthesis and spectral properties of 4-(ortho-R-benzylideneamine)-5-[2-(2-pyridyl)ethenyl]-3-methylisoxazole

The preparation of several 5,4-disubstituted 3-methylisoxazoles is described. The structure of all products was corroborated by ir, ¹H-nmr and mass spectrometry.