Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

A Raman study of multiferroic LuMnO3

Magnetic and dielectric measurements confirm the multiferroic nature of LuMnO3. Raman spectra of LuMnO3 have been recorded in the 77-800 K range covering both the antiferromagnetic transition at 90 K and the ferroelectric-paraelectric transition at 750 K. The changes in the phonon modes frequencies and band-widths indicate the presence of phonon-spin coupling in the antiferromagnetically ordered phase. The ferroelectric-paraelectric transition is accompanied by the broadening and disappearance of many of the phonon modes. Some of the phonon modes also show anomalies at the ferroelectric transition.

Electron-beam melting and centrifugal splat-quenching technique for rapid solidification of titanium alloys

An electron-beam melting and centrifugal splat-quenching technique for the production of microflakes of Ti-6A1-4V (wt%) alloy quenched at an average cooling rate of about 105 K sec–1 is described. The effect of substrate angle on the shape, size, microstructure and average cooling rate of the flakes of major sieve fractions is discussed. Morphologies of particles of minor sieve fractions are dealt with briefly.

Structural effects on the vaporization of high molecular weight esters

To understand the effect of molecular weight and branching on the heats of vaporization (AH,) and their flow behavior, AH, and viscosity (7) were measured at different temperatures in the high molecular weight ester series: linear flexible di-n-alkyl sebacates and compact branched triglycerides with molecular weight ranging from 300 to 900. AHv" values (AHv corrected to 298 K) have been obtained with experimental AH, and also computed according to the group additivity method; a smaller-CH,- group value of 3.8 kJ mol-' compared to the normal value of 5.0 kJ mol-' is found to give good agreement with the experimental data (within 2-5% error). Both ester series have the same AH," irrespective of their molecular features, namely,shape, flexibility, and polarity, suggesting the coiling of the molecules during vaporization. The segmental motion of these ester series during their flow and its dependence on their molecular features unlike AH,' are demonstrated by the correlation of the enthalpy of activation for viscous flow (AH*) and the ratio AE,/AH* = n (AE, is the energy of vaporization) with molecular weight.

Reactivity switching and selective activation of C-1 or C-3 in 2,3-unsaturated thioglycosides

Reactivity switching and selective activation of C-1 or C-3 in 2,3-unsaturated thioglycosides, namely, 2,3-dideoxy-1-thio-D-hex-2-enopyranosides are reported. The reactivity switching allowed activation of either C-1 or C-3, with the use of either N-iodosuccinimide (NIS)/triflic acid (TfOH) or TfOH alone. C-1 glycosylation with alcohol acceptors occurred in the presence of NIS/TfOH, without the acceptors reacting at C-3. On the other hand, reaction of 2,3-unsaturated thioglycosides with alcohols mediated by triflic acid led to transposition of C-1 ethylthio-moiety to C-3 intramolecularly, to form 3-ethylthio-glycals. Resulting glycals underwent glycosylation with alcohols to afford 3-ethylthio-2-deoxy glycosides. However, when thiol was used as an acceptor, only a stereoselective addition at C-3 resulted, so as to form C-1, C-3 dithio-substituted 2-deoxypyranosides. (C) 2011 Elsevier Ltd. All rights reserved.

Analysis of the temperature-dependent current-voltage characteristics and the barrier-height inhomogeneities of Au/GaN Schottky diodes

In this report, the currentvoltage (IV) characteristics of Au/GaN Schottky diodes have been carried out in the temperature range of 300510?K. The estimated values of the Schottky-barrier height (SBH) and the ideality factor of the diodes based on the thermionic emission (TE) mechanism were found to be temperature dependent. The barrier height was found to increase and the ideality factor to decrease with increasing temperature. The conventional Richardson plot of ln(Is/T2) versus 1/kT gives the SBH of 0.51?eV and Richardson constant value of 3.23?X?10-5?A?cm-2?K-2 which is much lower than the known value of 26.4?A?cm-2?K-2 for GaN. Such discrepancies of the SBH and Richardson constant value were attributed to the existence of barrier-height inhomogeneities at the Au/GaN interface. The modified Richardson plot of ln(Is/T2)q2 sigma 2/2k2T2 versus q/kT, by assuming a Gaussian distribution of barrier heights at the Au/GaN interface, provided the SBH of 1.47?eV and Richardson constant value of 38.8?A?cm-2?K-2. The temperature dependence of the barrier height is interpreted on the basis of existence of the Gaussian distribution of the barrier heights due to the barrier-height inhomogeneities at the Au/GaN interface.

Structural and kinetic studies on adenylosuccinate lyase from Mycobacterium smegmatis and Mycobacterium tuberculosis provide new insights on the catalytic residues of the enzyme

Adenylosuccinate lyase (ASL), an enzyme involved in purine biosynthesis, has been recognized as a drug target against microbial infections. In the present study, ASL from Mycobacteriumsmegmatis (MsASL) and Mycobacteriumtuberculosis (MtbASL) were cloned, purified and crystallized. The X-ray crystal structure of MsASL was determined at a resolution of 2.16 angstrom. It is the first report of an apo-ASL structure with a partially ordered active site C3 loop. Diffracting crystals of MtbASL could not be obtained and a model for its structure was derived using MsASL as a template. These structures suggest that His149 and either Lys285 or Ser279 of MsASL are the residues most likely to function as the catalytic acid and base, respectively. Most of the active site residues were found to be conserved, with the exception of Ser148 and Gly319 of MsASL. Ser148 is structurally equivalent to a threonine in most other ASLs. Gly319 is replaced by an arginine residue in most ASLs. The two enzymes were catalytically much less active compared to ASLs from other organisms. Arg319Gly substitution and reduced flexibility of the C3 loop might account for the low catalytic activity of mycobacterial ASLs. The low activity is consistent with the slow growth rate of Mycobacteria and their high GC containing genomes, as well as their dependence on other salvage pathways for the supply of purine nucleotides. Structured digital abstract andby()

On the systematic position of some Asian enigmatic genera of Asclepiadoideae (Apocynaceae)

The phylogenetic structure of Asclepiadoideae (Apocynaceae) has been elucidated at the tribal and subtribal levels in the last two decades. However, to date, the systematic positions of seven Asian genera, Cosmostigma, Graphistemma, Holostemma, Pentasachme, Raphistemma, Seshagiria and Treutlera, have not been investigated. In this study, we examine the evolutionary relationships among these seven small enigmatic Asian genera and clarify their positions in Asclepiadoideae, using a combination of plastid sequences of rbcL, rps16, trnL and trnL- F regions. Cosmostigma and Treutlera are resolved as members of the non-Hoya clade of Marsdenieae with strong support (maximum parsimony bootstrap support value BSMP = 96, maximum likelihood bootstrap support value BSML = 98, Bayesian-inferred posterior probability PP = 1.0). Pentasachme is resolved as sister of Stapeliinae to Ceropegieae with moderate support (BSMP = 64, BSML = 66, PP = 0.94). Graphistemma, Holostemma, Raphistemma and Seshagiria are all nested in the Asclepiadeae-Cynanchinae clade (BSMP = 97, BSML = 100, PP = 1.0). The study confirms the generally accepted tribal and subtribal structure of the subfamily. One exception is Eustegia minuta, which is placed here as sister to all Asclepiadeae (BSMP = 58, BSML = 76, PP = 0.99) and not as sister to the Marsdenieae + Ceropegieae clade. The weak support and conflicting position indicate the need for a placement of Eustegia as an independent tribe. In Asclepiadeae, a sister group position of Cynanchinae to the Asclepiadinae + Tylophorinae clade is favoured (BSMP = 84, BSML = 88, PP = 1.0), whereas Schizostephanus is retrieved as unresolved. Oxystelma appears as an early-branching member of Asclepiadinae with weak support (BSMP = 52, BSML = 74, PP = 0.69). Calciphila and Solenostemma are also associated with Asclepiadinae with weak support (BSMP = 37, BSML = 45, PP = 0.79), but all alternative positions are essentially without support. The position of Indian Asclepiadoideae in the family phylogeny is discussed. (c) 2014 The Linnean Society of London, Botanical Journal of the Linnean Society, 2014, 174, 601-619.