Electron-ion collisional dissociative recombination at high ambient ammonia densities

A plot of the measured electron—ion recombination coefficient against the number density of ambient ammonia shows an unexpectedly early fall which, it is suggested, may be due to the collisional coupling between the dissociative states and the other states being weakened by the growth in the clustering.     

Absorption spectra of diatomic molybdenum nitride (MoN), molybdenum oxide (MoO), and molybdenum dimer (Mo2) molecules isolated in Ar,Ne, and Kr matrices

MoN and MoO molecules produced in a hollow cathode discharge have been trapped in Ne, Ar, and Kr matrices at 4.2 and 13 K and investigated by optical spectroscopy. Bands attributed to MoN were identified in the red and blue spectral regions and assigned by comparison with gas phase results to the A⁴π → X⁴Σ^? (a) and B⁴Σ → X⁴Σ^? (a) transitions, respectively. The ground state of Mo¹⁴N has been identified as ⁴Σ^? with ω_e = 1040 cm^?1 in an Ar matrix. Absorptions assigned to MoO in the red spectral region form the (0-0) and (1-0) bands of at least one electronic transition, but could not definitely be correlated with the gas phase results. The ground state vibrational frequency for Mo¹⁶O in an Ar matrix is 893.5 cm^?1. Additionally, Mo₂ absorptions centered at 19 305 cm^?1 were shown to be part of a vibrational progression with an average spacing of 181 cm^?1.     

Astronomical speckle imaging

The many methods suggested and (some of them) tried out experimentally and/or observationally for imaging celestial objects through the Earth's atmosphere are reviewed. Their theoretical and physical bases are examined. Most attention is paid to Labeyrie's speckle interferometry and its several extensions devised during the past decade-astrophysical results obtained with the aid of these techniques are listed. Other forms of optical interferometry are discussed, as are related techniques in radio astronomy and ultrasonics.     

Preparation of niobium and tantalum organoimido complexes from reactions of the pentahalides with amines: The crystal and molecular structure of bis(t-butylamine)bis(t-butylimido)bis(μ-ethoxy)tetrachloroditantalum

MCl₅ (M = Nb, Ta) reacts with 2 equivalents of Me₃SiNHCMe₃ to give [M(NCMe₃)Cl₃(NH₂CMe₃)] from which [M(NCMe₃)Cl₃(PMe₃)₂] is obtained on addition of PMe₃. One equivalent of Me₃SiNHCMe₃ reacts with MCl₅ in the presence of 3 equivalents of PMe₃ to give [M(NCMe₃)Cl₃(PMe₃)₂] and PMe₃HCl. MCl₅ reacts with excess RNH₂ (R = CMe₃, CHMe₂, CH₂Me) to give [M(NR)(NHR)Cl₂(NH₂R)] and 3 equivalents of RNH₃Cl. One equivalent of alcohol replaces the amido ligand in [M(NCMe₃)(NHCMe₃)Cl₂(NH₂CMe₃)] to give [M(NCMe₃)(OR)Cl₂(NH₂CMe₃)]₂ (M = Nb, R = OCMe₃; M = Ta, R = OEt). The structure of [Ta(NCMe₃)(μ-OEt)Cl₂(NH₂CMe₃)]₂ was determined by single-crystal X-ray diffraction methods. Crystals are triclinic, space group P$\text{1}$ with a = 9.900(5), b = 10. 161(17), c = 9.017(6) Å and α = 103.91(8), β = 97.77(4), γ = 64.40(7)°. The structure was solved by Patterson and Fourier methods and refined to an R value of 0.062 for 1319 observed data. The TaN_imido and TaN_amino bond lengths are 1.70(2) Å and 2.28(2) Å, respectively; the bridging TaO bond lengths are 2.01(2) Å and 2.32(2) Å, the longer one lying trans to the imido function.     

Lower closure and existence theorems for optimal control problems with infinite horizon

Lower closure theorems are proved for optimal control problems governed by ordinary differential equations for which the interval of definition may be unbounded. One theorem assumes that Cesari's property (Q) holds. Two theorems are proved which do not require property (Q), but assume either a generalized Lipschitz condition or a bound on the controls in an appropriateL _p-space. An example shows that these hypotheses can hold without property (Q) holding.     

Studies of translational diffusion in the smectic A phase of a Gay-Berne mesogen using molecular dynamics computer simulation

Molecular dynamics computer simulations are used to determine the self-diffusion coefficients for a Gay-Berne model mesogen GB (4.4,20,1,1) in the isotropic, nematic and smectic A phases along two isobars. The values of the parallel and perpendicular diffusion coefficients, D(parallel) and D(perpendicular), are calculated and compared in the different phases. For the phase sequence isotropic-smectic A, D(perpendicular)*> or =D(parallel)* over the whole smectic A range with the ratio D(parallel)*/D(perpendicular)* decreasing with decreasing temperature. At a higher pressure, a nematic phase is observed between these two phases and we find that D(parallel)*>D(perpendicular)* throughout the nematic region and the inequality D(parallel)*>D(perpendicular)* remains on entering the smectic A phase. However, the ratio D(parallel)*/D(perpendicular)* decreases with decreasing temperature within the smectic A range and eventually this ratio inverts such that D(perpendicular)*>D(parallel)* at low temperatures. The temperature dependence of the parallel diffusion coefficient in the smectic A phase for this model mesogen is compared to that predicted by a theoretical model for diffusion subject to a cosine potential.     

Invariant foliations near normally hyperbolic invariant manifolds for semiflows

Let be a compact manifold which is invariant and normally hyperbolic with respect to a semiflow in a Banach space. Then in an -neighborhood of there exist local center-stable and center-unstable manifolds and , respectively. Here we show that and may each be decomposed into the disjoint union of submanifolds (leaves) in such a way that the semiflow takes leaves into leaves of the same collection. Furthermore, each leaf intersects in a single point which determines the asymptotic behavior of all points of that leaf in either forward or backward time.

     

An extension of the Dirac theory of constraints

Constructions introduced by Dirac for singular Lagrangians are extended and reinterpreted to cover cases when kernel distributions are either nonintegrable or of nonconstant rank, and constraint sets need not be closed.