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     

A simplified model joining the sheath and the plasma in electronegative plasmas

An extension of the previous work which only dealt with the sheath zone is used to analyze the wall-plasma interaction in electronegative plasmas. Ionization is introduced as the presheath mechanism. This extension includes the joining of the sheath and the plasma solutions. For certain plasma parameters a stratified presheath is obtained. In this case, the plasma and the sheath solutions are matched in a very simplified way, by introducing a discontinuity in the electric field. This discontinuity is equivalent to consideration of a negatively charged layer between the presheath and the sheath. The parameter space region in which this matching should be made has been delimited. The model includes the previous one in the limiting case of no ionization.     

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.     

Matrix realizations of littlewood—richardson sequences

In this paper we consider the problem of characterizing the invariant factors of three matrices AB, and C, such that AB — C Our matrices have entries over a principal ideal domain or over a local domain. In Section 2 we show that this problem is localizablc

The above problem lias a well-known solution in terms of Littlewood-Richardson sequences. We introduce the concept of a matrix realization of a Littlewood-Richardson sequence. The main result is an explicit construction of a sequence of matrices which realizes a previously given Littlewood Richardson sequence. Our methods offer a matrix theoretical proof of a well-known result of T, Klein on extensions of p-modules.     

Solving the knapsack problem via -transform

Given vectors and , we consider the (unbounded) knapsack optimization problem . We compute the minimum value p^* using techniques from complex analysis, namely Cauchy's Residue Theorem to integrate a function in , and the -transform of an appropriate function related to . The computational complexity depends on s ∑_j=1ⁿa_j, not on the magnitude of b as in dynamic programming based approaches. We also completely characterize the number of solutions with value less than p, as a function of p.     

On separation properties of finite dimensional compact convex sets

In a real finite-dimensional vector space, we study families of sets such that every compact convex set in the space is the intersection of all members of the family that contains it.

     

Mass spectra of some 2-(p-R2-phenyl)-indole-3-carboxaldehyde derivatives

The mass spectra of eight new substituted 2-(p-R²-phenyl)-indole-3-carboxyaldehydes which have potentially useful pharmacological properties, are presented.