Gazeau-Klauder type coherent states for hypergeometric type operators

The hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitly described in the general case. Some additional shape invariant operators depending on several parameters are defined in a natural way by starting from this general factorization. The mathematical properties of the eigenfunctions and eigenvalues of the operators thus obtained depend on the values of the involved parameters. We study the parameter dependence of orthogonality, square integrability and of the monotony of eigenvalue sequence. The obtained results allow us to define certain systems of Gazeau-Klauder coherent states and to describe some of their properties. Our systematic study recovers a number of well-known results in a natural unified way and also leads to new findings.Comment: An error occurring in Theorem 12 and Theorem 13 has been correcte

Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis $-\infty<E<\infty$ instead of being bounded from below $0\leq E <\infty$ (``Fermi's approximation''). Then the Fourier transform of the extended Lorentzian becomes the exponential, but only for times $t\geq 0$, a time asymmetry which is in conflict with the unitary group time evolution of standard quantum mechanics. Extending the Fourier transform from distributions to generalized vectors, we are led to Gamow kets, which possess a Lorentzian energy distribution with $-\infty<E<\infty$ and have exponential time evolution for $t\geq t_0 =0$ only. This leads to probability predictions that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.

Using Propagules to Restore Coastal Marine Ecosystems

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High-precision calculations of van der Waals coefficients for heteronuclear alkali-metal dimers

Van der Waals coefficients for the heteronuclear alkali-metal dimers of Li, Na, K, Rb, Cs, and Fr are calculated using relativistic ab initio methods augmented by high-precision experimental data. We argue that the uncertainties in the coefficients are unlikely to exceed about 1%.Comment: 11 pages, 2 figs, graphicx.st

Phenotypic cha- racterization of pig genetic resources in the departments of Oueme and Plateau in Benin

L’élevage porcin est très pratiqué au Sud-Bénin et implique une diversité de races ou de populations. L’objectif de l’étude était de caractériser les différents porcs sur le plan morphométrique et phénotypique. Ainsi, les données phéno- typiques ont été collectées sur 149 porcs, dont 14 améliorés, 91 croisés et 44 locaux. Les porcs de type génétique local ont présenté des mesures morpho- logiques significativement inférieures (p < 0,05) à celles des porcs améliorés et des animaux issus des croisements entre les porcs améliorés et les porcs locaux. Les poils des porcs locaux étaient significativement plus courts (p < 0,05) que ceux des porcs améliorés et des croisés. La couleur de la robe a varié d’un type génétique à l’autre. La couleur la plus rencontrée a été le blanc uniforme, suivi du noir uniforme chez tous les types génétiques. Le profil de la tête était plus rectiligne chez les porcs locaux, et plus concave chez les porcs améliorés et chez les croisés. Les oreilles dressées étaient moins observées chez les croisés. Elles étaient orientées vers l’avant chez les porcs améliorés et chez les croisés alors qu’elles étaient dressées et orientées vers l’arrière chez les porcs locaux. La queue en tire-bouchon a été significativement (p < 0,05) plus présente chez les porcs améliorés que chez les porcs croisés, et elle a été plus présente chez ces derniers que chez les porcs locaux. La ligne dorsale droite a été davantage observée chez les porcs locaux et chez les croisés que chez les porcs amélio- rés chez lesquels la ligne était plus creuse. Les porcs croisés ont présenté une grande similarité avec les porcs améliorés

Restore or Redefine:Future Trajectories for Restoration

Global habitat deterioration of marine ecosystems has led to a need for active interventions to halt or reverse the loss of ecological function. Restoration has historically been a key tool to reverse habitat loss and restore functions, but the extent to which this will be sufficient under future climates is uncertain. Emerging genetic technologies now provide the ability for restoration to proactively match adaptability of target species to predicted future environmental conditions, which opens up the possibility of boosting resistance to future stress in degraded and threatened habitats. As such, the choice of whether to restore to historical baselines or anticipate the future remains a key decision that will influence restoration success in the face of environmental and climate change. Here, we present an overview of the different motives for restoration – to recover or revive lost or degraded habitats to extant or historical states, or to reinforce or redefine for future conditions. We focus on the genetic and adaptive choices that underpin each option and subsequent consequences for restoration success. These options span a range of possible trajectories, technological advances and societal acceptability, and represent a framework for progressing restoration of marine habitat forming species into the future