Identity for harmonic oscillator brackets

An identity satisfied by the harmonic oscillator (Talmi-Moshinsky) brackets is derived from two equivalent methods for evaluating an integral often encountered in cluster model studies.

Generalization of Dynkin's Identity and Some Applications

Let X(t) be a right continuous temporally homogeneous Markov pro- cess, Tt the corresponding semigroup and A the weak infinitesimal genera- tor. Let g(t) be absolutely continuous and r a stopping time satisfying E.( S f I g(t) I dt) < oo and E.( f " I g'(t) I dt) < oo Then for f e 9iJ(A) with f(X(t)) right continuous the identity Exg(r)f(X(z)) - g(O)f(x) = E( 5 " g'(s)f(X(s)) ds) + E.( 5 " g(s)Af(X(s)) ds) is a simple generalization of Dynkin's identity (g(t) 1). With further restrictions on f and r the following identity is obtained as a corollary: Ex(f(X(z))) = f(x) + k! Ex~rkAkf(X(z))) + n-1E + (n ) )!.E,(so un-1Anf(X(u)) du). These identities are applied to processes with stationary independent increments to obtain a number of new and known results relating the moments of stopping times to the moments of the stopped processes.

A matrix identity and perturbation expressions

An identity expressing formally the diagonal and off-diagonal elements of an inverse of a matrix is deduced employing operator techniques. Several well-known perturbation expressions for the self-energy are deduced as special cases. A new approximation and other applications following from the above formalism are briefly indicated through illustrations from a perturbed harmonic oscillator, chemisorption approximations and Kelly's result in the problem of electron correlation.

Both Surface Proteins (VP4 and VP7) of an Asymptomatic Neonatal Rotavirus Strain (1321) Have High Levels of Sequence Identity with the Homologous Proteins of a Serotype 10 Bovine Rotavirus

The nucleotide sequence of genes 4 and 9, encoding the outer capsid proteins VP4 and VP7 of a serotype 10 tissue culture-adapted strain, 1321, representative of asymptomatic neonatal rotaviruses isolated from neonates in Bangalore, India, were determined. Comparison of nucleotide and deduced amino acid sequences of 1321 VP4 and VP7 with previously published sequences of various serotypes revealed that both genes were highly homologous to the respective genes of serotype 10 bovine rotavirus, B223. The VP4 of 1321 represents a new human P serotype and the 1321 and related strains represent the first description of neonatal rotaviruses that appear to derive both surface proteins from an animal rotavirus.

Identity, energetics, dynamics and environment of interfacial water molecules in a micellar solution

The structure and energetics of interfacial water molecules in the aqueous micelle of cesium perfluorooctanoate have been investigated, using large-scale atomistic molecular dynamics simulations, with the primary objective of classifying them. The simulations show that the water molecules at the interface fall into two broad classes: bound and free, present in a ratio of 9:1. The bound water molecules can be further categorized on the basis of the number of hydrogen bonds (one or two) that they form with the surfactant headgroups. The hydrogen bonds of the doubly hydrogen-bonded species are found to be, on the average, slightly weaker than those in the singly bonded species. The environment around interfacial water molecules is more ordered than that in the bulk. The surface water molecules have substantially lower potential energy, because of interaction with the micelle. In particular, both forms of bound water have energies that are lower by �2.5-4.0 kcal/ mol. Entropy is found to play an important role in determining the relative concentration of the species.

Dung as a potential medium for inter-sexual chemical signaling in Asian elephants (Elephas maximus)

Chemical signaling is a prominent mode of male-female communication among elephants, especially during their sexually active periods. Studies on the Asian elephant in zoos have shown the significance of a urinary pheromone (Z7-12:Ac) in conveying the reproductive status of a female toward the opposite sex. We investigated the additional possibility of an inter-sexual chemical signal being conveyed through dung. Sixteen semi-captive adult male elephants were presented with dung samples of three female elephants in different reproductive phases. Each male was tested in 3 separate trials, within an interval of 1-3 days. The trials followed a double-blind pattern as the male and female elephants used in the trials were strangers, and the observer was not aware of the reproductive status of females during the period of bioassays. Males responded preferentially (P < 0.005), in terms of higher frequency of sniff, check and place behavior toward the dung of females close to pre-ovulatory period (follicular-phase) as compared to those in post-ovulatory period (luteal-phase). The response toward the follicular phase samples declined over repeated trials though was still significantly higher than the corresponding response toward the non-ovulatory phase in each of the trials performed. This is the first study to show that male Asian elephants were able to distinguish the reproductive phase of the female by possibly detecting a pre-ovulatory pheromone released in dung. (C) 2012 Elsevier B.V. All rights reserved.

A taxonomic mystery for more than 180 years: the identity and systematic position of Brachysaura minor (HARDWICKE & GRAY, 1827)

Brachysaura is a monotypic genus of agamid lizard found in the Indian subcontinent; the identity and systematic position of B. minor has been long debated, and it has at times been subsumed into Agama, Charasia and Laudakia, with some authors suggesting affinities to Calotes. We constructed nuclear and mitochondrial phylogenetic trees including Brachysaura and allied agamid genera to resolve its phylogenetic position. We also compared osteology and external morphology with the genera Agama, Calotes and Laudakia. Hemipenial morphology was compared with Calotes and some other agamids from South Asia. Both nuclear and mitochondrial phylogenies demonstrate that Brachysaura is nested within the widespread South and Southeast Asian genus Calotes, with which it also shares certain external morphological, osteological and hemipenial characters. Adaptations to ground dwelling in Brachysaura minor has resulted in unique modifications to its body plan, which is likely why generic allocation has been long confused. This study also highlights the need for an integrated systematic approach to resolve taxonomic ambiguity in Asian agamids.

Generic identity of Camptorrhiza indica (Colchicaceae) based on cytogenetics and molecular phylogenetics

The tribe Iphigenieae (Colchicaceace, Liliales) includes two genera, viz. Camptorrhiza and Iphigenia, which are distributed in Africa, India, and Australasia. Iphigenia is represented by 12 species, of which six occur in India while Camptorrhiza comprises one species each in Africa (C. strumosa) and India (C. indica). The genus Camptorrhiza possesses a knee-shaped tuber attached to the corms, filaments with a thick bulge in the middle and styles with single stigma. Iphigenia on the other hand lacks knee-shaped tuber, bears linear filaments and has styles with three stigmas. Camptorrhiza indica possesses ovoid corms, linear filaments and styles with a single stigma. These characters are intermediate between Iphigenia and Camptorrhiza and hence we studied the cytogenetics and phylogenetic placement of this species to ascertain its generic identity. Somatic chromosome count (2n = 22) and karyotypic features of C. indica are very similar to that of Iphigenia species. Molecular phylogenetic studies based on atpB-rbcL, rps16, trnL, and trnL-F regions showed that C. indica is nested within a lineage of Indian Iphigenia species. Thus, C. indica was reduced to a species of Iphigenia, i.e., I. ratnagirica. Camptorrhiza is now a monotypic genus restricted only to southern Africa. A key to the Indian Iphigenia species is provided. In addition, a new combination Wurmbea novae-zelandiae is proposed for Iphigenia novae-zelandiae.