Construction of Wavelet Sets Using Integral Self-Affine Multi-tiles

Gabardo and Yu first considered using integral self-affine tiles in the Fourier domain to construct wavelet sets and they produced a class of compact wavelet sets with certain self-similarity properties. In this paper, we generalize their results to the integral self-affine multi-tiles setting. We characterize some analytic properties of integral self-affine multi-tiles under certain conditions. We also consider the problem of constructing (multi)wavelet sets using integral self-affine multi-tiles.     

Hydrogen Migration and Reductive Elimination of Alkyne in Fe(CO)4 P(tBu) (C °CPh)H Induced by the Action of Co2 (CO)8

Abstract

One of the possible ways of getting phosphacumulene complexes could be the complexation of phosphinoalkynes, which might induce the migration of hydrogen from phosphorus to the β carbon of the alkynyl group.     

[HFe(CO)4 – A Versatile Reagent toward Dichlorophosphines,Phosphenium Salts,Phospha-alkenes and Diphosphenes

Abstract

A new entry to non classical phosphorus complexes is reported.     

Regulation of births for viability of populations governed by age-structured problems

We assume that the evolution of the population is governed by a controlled McKendrick age-structured partial differential equation where the mortality rate and immigrated population levels are no longer known coefficients, but contingent regulation parameters chosen for a given purpose, for instance, for requiring that the population satisfies prescribed viability constraints depending on time and age. The Lotka renewal equation relating the boundary condition (number of births) to the integral with respect to age of the population is replaced by the introduction of another regulation parameter in the boundary condition, regarded as a natality policy. We may control it by its derivative, regarded as a natality decision. We then construct a regulation map, associating with the population level, the time and the age the subset of natality policies, a mortality rates and an immigration levels needed for governing viable evolutions of the population.