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.     

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.     

Hydroboration of Alkenes Catalysed by a Nickel N-Heterocyclic Carbene Complex: Reaction and Mechanistic Aspects

The pentamethylcyclopentadienyl N-heterocyclic carbene nickel complex [Ni(η⁵-C₅Me₅)Cl(IMes)] (IMes=1,3-dimesitylimidazol-2-ylidene) efficiently catalyses the anti-Markovnikov hydroboration of alkenes with catecholborane in the presence of a catalytic amount of potassium tert-butoxide, and joins the very exclusive club of nickel catalysts for this important transformation. Interestingly, the regioselectivity can be reversed in some cases by using pinacolborane instead of catecholborane. Mechanistic investigations involving control experiments, ¹H and ¹¹B NMR spectroscopy, cyclic voltammetry, piezometric measurements and DFT calculations suggest an initial reduction of the Ni^II precursor to a Ni^I active species with the concomitant release of H₂. The crucial role of the alkoxo-catecholato-borohydride species resulting from the reaction of potassium tert-butoxide with catecholborane in the formation of an intermediate nickel-hydride species that would then be reduced to the Ni^I active species, is highlighted.     

Potent Anticancer Efficacy of First-In-Class CuII and AuIII Metaled Phosphorus Dendrons with Distinct Cell Death Pathways

First-in-class Cu^II and Au^III metaled phosphorus dendrons were synthesized and showed significant antiproliferative activity against several aggressive breast cancer cell lines. The data suggest that the cytotoxicity increases with reducing length of the alkyl chains, whereas the replacement of Cu^II with Au^III considerably increases the antiproliferative activity of metaled phosphorus dendrons. Very interestingly, we found that the cell death pathway is related to the nature of the metal complexed by the plain dendrons. Cu^II metaled dendrons showed a potent caspase-independent cell death pathway, whereas Au^III metaled dendrons displayed a caspase-dependent apoptotic pathway. The complexation of plain dendrons with Au^III increased the cellular lethality versus dendrons with Cu^II and promoted the translocation of Bax into the mitochondria and the release of Cytochrome C (Cyto C).     

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.     

Mereologies as the grammars of chemical discourses

Mereology is the logic of part—whole concepts as they are used in many different contexts. The old chemical metaphysics of atoms and molecules seems to fit classical mereology very well. However, when functional attributes are added to part specifications and quantum mechanical considerations are also added, the rules of classical mereology are breached in chemical discourses. A set theoretical alternative mereology is also found wanting. Molecular orbital theory requires a metaphysics of affordances that also stands outside classical mereology.