Phase measurement accuracy of feedback interferometers

Feedback interferometers are described with specific reference to potential applications in micro-machines. A theoretical analysis is developed to determine the linearity, stability, and noise performance of this type of interferometer. The theoretical analysis was tested using a prototype high-precision feedback interferometer which showed that, at a feedback loop gain which enabled the system to track 6 fringes, the linearity of the interferometer was better than λ/100 and single phase measurements could be made with an accuracy of λ/80.     

Laser spectroscopy of FeO: Rotational analysis of some subbands of the orange system

Extensive laser excitation spectra and rotationally resolved laser-induced fluorescence spectra have been recorded for the “orange system” of gaseous FeO in the wavelength regions 5790–6140 and 5580–5640 Å. Detailed rotational analyses have been performed for about $\text{20}\text{Ω}\text{′}$ substates lying between 16 350 and 18 550 cm^?1. These are found to comprise a very severely perturbed ⁵Δ_i excited electronic state with a bond length of about 1.69 Å (which is responsible for the parallel polarization of the electronic transition from the ⁵Δ_i ground electronic state) and a large number of “extra” $\text{Ω}$ substates with B′ values ranging from 0.38 to 0.50 cm^?1, which almost certainly belong to high vibrational levels of lower-lying electronic states. Evidence about the natures of the “extra” states is confusing, however, with the ⁵⁴FeO⁵⁶FeO isotope shifts apparently being in conflict with the patterns of vibrationally resolved laser-induced fluorescence. Every single $\text{Ω}$ substate that has been analyzed shows rotational perturbations of varying severity. The density and magnitude of the rotational perturbations are quite exceptional for a diatomic molecule, and result in a new type of totally chaotic diatomic spectrum. There is a remarkable similarity to the visible spectrum of NO₂: in NO₂ the complications arise from the high density of perturbing ground state vibrational levels; in FeO there is a correspondingly high density of perturbing electronic states at lower energy. The great complexity of the FeO spectrum arises because the states are in an awkward intermediate spin-coupling case which still resembles Hund's case (a) but shows strong tendencies toward Hund's case (c) coupling.     

Newton's method for nonlinear ordinary and partial differential equations

A unified approach is presented for proving the local, uniform and quadratic convergence of the approximate solutions and a-posteriori error bounds obtained by Newton's method for systems of nonlinear ordinary or partial differential equations satisfying an inverse-positive property. An important step is to show that, at each iteration, the linearized problem is inverse-positive. Many classes of problems are shown to satisfy this property. The convergence proofs depend crucially on an error bound derived previously by Rosen and the author for quasilinear elliptic, parabolic and hyperbolic problems.     

Predissociated rotational structure in the 2490-Å band of 15NO2

The rotational structure of the 000-000 band of the 2490-Å system of ¹⁵NO₂ ($\text{2}{}^2\text{B}{}_2\text{-}\text{X}\text{?}{}^2\text{A}{}_1$) has been analyzed from high dispersion grating spectrograph plates. The band is found to be slightly predissociated, exactly as in the ¹⁴NO₂ isotope, which suggests that it might be usable for laser separation of the isotopes of nitrogen; tables of the wavenumbers of the lines are given. The upper-state molecular constants are close to the values calculated by the isotope relations from those of ¹⁴NO₂.     

Stable constant mean curvature hypersurfaces in ℝ n+1 and ℍ n+1(−1)

In this paper, we show that all complete stable hypersurfaces in ⁿ⁺¹(or ⁿ⁺¹ (-1)) (n = 3, 4, 5) with constant mean curvature H > 0 (or H > 1, respectively) and finite L ² norm of traceless second fundamental form are compact geodesic spheres. Keywords: stable hypersurface, constant mean curvature, isometric immersion, Bernstein theorem.*Supported by PolyU grant G-T575.**Partially supported by CNPq of Brazil.     

High resolution absorption cross-section measurements of the Schumann-Runge bands of O2 by VUV Fourier transform spectroscopy

The photoabsorption spectrum of the O₂ Schumann-Runge bands was measured with resolution comparable to the Doppler widths by using the VUV Fourier transform spectrometer from Imperial College, London, combined with synchrotron radiation as a continuum light source at the Photon Factory, KEK, Japan. The analysis of the (12,0)-(17,0) bands of the Schumann-Runge system provides accurate rotational line positions as well as the line intensities from 185 to 175 nm. Molecular constants of the levels of the state have been determined. The (v^′,0) band oscillator strengths were determined as 2.38, 2.62, 2.70, 2.66, 2.40, and 2.12×10⁻⁵ for the bands from v^′=12 to 17, respectively.     

High throughput fluorescence-based assays for cyclic ADP-ribose,NAADP, and their metabolic enzymes

Cyclic ADP-ribose (cADPR) and nicotinic acid adenine dinucleotide phosphate (NAADP) are two novel Ca(2+) messengers derived respectively from NAD and NADP. Since their discovery in sea urchin eggs, both have now been shown to serve messenger functions in a wide range of cells from plant to human. In this article, a series of fluorimetric assays for cADPR, NAADP and their metabolic enzymes is compiled. The enzyme assay makes use of an analog of NAD, nicotinamide guanine dinucleotide, which is non-fluorescent but is cyclized by the enzymes to a fluorescent analog of cADPR, cyclic GDP-ribose. Other NAD utilizing enzymes are not capable of catalyzing the cyclization and thus produce no interference. The fluorimetric assays for cADPR and NAADP make use of coupled-enzyme amplification and can readily detect nanomolar concentrations of either messenger. All the assays described can be performed in multi-well format, allowing ready automation and use in high throughput screening. An added advantage of these assays is that all the required reagents are commercially available, facilitating general adoption of the techniques by all those who are interested in the physiology and enzymology of the novel Ca(2+) signaling pathways mediated by cADPR and NAADP.     

Ruthenium porphyrin catalyzed intramolecular carbenoid C[bond]H insertion. Stereoselective synthesis of cis-disubstituted oxygen and nitrogen heterocycles

[reaction: see text] A ruthenium porphyrin-catalyzed stereoselective intramolecular carbenoid C[bond]H insertion is described. Using [Ru(II)(TTP)(CO)] as catalyst, aryl tosylhydrazones are converted to 2,3-dihydrobenzofurans, 2,3-dihydroindoles, and beta-lactams in good yields and remarkable cis selectivity (up to 99%). Enantioselective synthesis of 2,3-dihydrobenzofurans is also achieved with [Ru(II)(D(4)-Por*)(CO)] as catalyst, and up to 96% ee is attained.     

Competition between cyclization, cleavage, and reverse hydrogen transfer in 1,4-hydroxybiradicals: crystal structure--solid state reactivity correlations

[reaction: see text] To provide experimental evidence on the relationship between stucture and reactivity in 1,4-hydroxybiradical intermediates, the Norrish type II photochemistry of a homologous series of spirobenzoyladamantane derivatives was investigated in the crystalline state and the outcome correlated with the structures of the compounds as determined by X-ray crystallography. The results provide an unusually detailed and compelling picture of the geometric factors responsible for the partitioning of these reactive intermediates among cleavage, cyclization, and reverse hydrogen transfer.