Oscillations of Higher Order Neutral Differential Equations with Variable Coefficients

We obtain sufficient conditions for the oscillation of all solutions of the higher order neutral differential equation dⁿ/d^m[y(t) + P(t) y(t - μ)] + Q(t) y(t ?σ) = 0, t ≧ t₀ where n ≧ 1, P ? C[t₀, ∞), R ], Q ? C[t₀, ∞), R ] and τ, μ ? R ⁺. Our results extend and improve several known results in the literature.     

XeAuF

XeAuF has been detected and characterized using microwave rotational spectroscopy. It was prepared by laser ablation of Au in the presence of Xe and SF(6), and stabilized in a supersonic jet of Ar. The spectrum was measured with a cavity pulsed jet Fourier transform microwave spectrometer, in the frequency range 6-26 GHz. Rotational constants, centrifugal distortion constants, and (131)Xe and (197)Au nuclear quadrupole coupling constants have been evaluated. The molecule is linear, with a short XeAu bond (2.54 A), and is rigid. The (131)Xe nuclear quadrupole coupling constant (NQCC) is large (-135 MHz). The (197)Au NQCC differs radically from that of uncomplexed AuF. The results are supported by those of ab initio calculations which have given an XeAu dissociation energy approximately 100 kJ mol(-1), plus Mulliken and natural bond orbital populations, MOLDEN plots of valence orbitals, and an energy density distribution. All evidence is consistent with XeAu covalent bonding in XeAuF.     

Organic functional group analysis via gas chromatography. III

Summary A gas Chromatographic procedure for the analysis of carbamates is described. A specially prepared reaction tube, packed with a 10 % mixture of potassium hydroxide in glass beads, is placed inside the injection port of a Perkin-Elmer 900 Gas Chromatograph, in front of the Chromatographic column packed with Porapak Q. S.A solution of the carbamates (0.01–0.1mol) is injected directly into the gas Chromatograph. The carbamates are reacted with the alkali present in the reaction tube and the alcohols produced are separated, detected and recorded. Standard calibration graphs of the alcohols are prepared in the same manner and the quantities of carbamates are determined. The procedure is fast and quantitative.

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Zusammenfassung Ein gaschromatisches Verfahren für die Analyse von Carbamaten wurde beschrieben. Ein spezielles Reaktionsrohr, beschickt mit 10% iger Kalilauge auf Glasperlen, wird innerhalb der Injektionsöffnung eines Gaschromatographen Perkin-Elmer 900 vor dem mit Poropak Q. S. gefüllten Chromatographierohr angebracht. Die Carbamatlösung (0,01 bis 0,1 Mol) wird direkt injiziert. Die Carbamate reagieren mit dem im Reaktionsrohr befindlichen Alkali, die dabei entstandenen Alkohole werden getrennt, nachgewiesen und registriert. In gleicher Weise ermittelte Standard-Eichkurven der Alkohole dienen zur Bestimmung der Carbamate. Das Verfahren ist rasch und quantitativ.

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For Part II see Mikrochim. Acta [Wien]1966, 55. Inquiries and requests for reprints of this series of papers should be addressed to Prof. T. S. Ma, Department of Chemistry, City University of New York, Brooklyn, N.Y. 11210, U.S.A.     

The microwave spectrum of bromine isocyanate,Brnco: Determination of rotational constants from quadrupole hyperfine structure

A novel method has been developed to evaluate accurate rotational constants from the microwave spectrum of the unstable molecule bromine isocyanate, using perturbations in nuclear quadrupole hyperfine structure. It has been applied to this prolate near-symmetric rotor to determine A_v and x_ab accurately, entirely from a-type R branches. The method has been made possible by the development of a special computer program for global léast-squares fitting to rotational and centrifugal distortion constants, along with all components of the Br nuclear quadrupole coupling tensor.     

Proposal for generating Fock states in traveling wave fields

We describe a proposal for the generation of a single-mode photonic number state, |N〉$|N〉$, in a traveling wave optical field. The state is obtained by state reduction from an input coherent state using Kerr media. Our method is based on a previous scheme used for hole burning in the Fock space by minimizing the Mandel Q parameter. The same method was used by Maia et al., but ours is different, it requires only one single photon injected in the entire setup and one photon detection at the end.     

Microwave spectra, geometries, and hyperfine constants of OCAgX (X = F, Cl, Br)

A pulsed jet cavity Fourier transform microwave spectrometer has been used to measure the rotational spectra of OCAgX (X = F, Cl, Br) in the frequency range 5-22 GHz. Metal atoms were generated via laser ablation and were allowed to react with CO and a halide precursor, prior to stabilization of the products within a supersonic jet of argon. These are the first experimental observations of OCAgF and OCAgBr, and the first high resolution spectroscopic study of OCAgCl. All three molecules are linear. Accurately determined rotational constants have been used to evaluate the various internuclear distances, which are found to be consistent with trends established for OCAuX and OCCuX species. The C-O distances are short, and the M-C distances are significantly longer than those in other molecules containing a metal-carbonyl bond. Precise values of centrifugal distortion constants and halogen nuclear quadrupole coupling constants have also been determined. The coupling constants are compared with the results of previous studies of OCCuX and OCAuX and are used to infer trends in the electron distributions of the molecules. Ab initio calculations have been performed and employed to predict the geometries, vibrational frequencies, and Mulliken valence orbital populations of the various species.     

Oscillations of first-order neutral delay differential equations

Consider the neutral delay differential equation (*) (d/dt)[y(t) + py(t − τ)] + qy(t − σ) = 0, t t₀, where τ, q, and σ are positive constants, while p ε (−∞, −1) (0, + ∞). (For the case p ε [−1, 0] see Ladas and Sficas, Oscillations of neutral delay differential equations (to appear)). The following results are then proved. Theorem 1. Assume p < − 1. Then every nonoscillatory solution y(t) of Eq. (*) tends to ± ∞ as t → ∞. Theorem 2. Assume p < − 1, τ > σ, and q(σ − τ)/(1 + p) > (1/e). Then every solution of Eq. (*) oscillates. Theorems 3. Assume p > 0. Then every nonoscillatory solution y(t) of Eq. (*) tends to zero as t → ∞. Theorem 4. Assume p > 0. Then a necessary condition for all solutions of Eq. (*) to oscillate is that σ > τ. Theorem 5. Assume p > 0, σ > τ, andq(σ − τ)/(1 + p) > (1/e). Then every solution of Eq. (*) oscillates. Extensions of these results to equations with variable coefficients are also obtained.