Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation

In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are R +C R = 0 and and . HereR is the Ricci curvature andC is the Weyl conformal curvature; is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship.     

Theoretical studies of the bonding of sulfur to models of the (100) surface of nickel

Electronic wavefunctions have been obtained as a function of geometry for a S atom bonded to Ni clusters consisting of 1 to 4 atoms designed to model bonding to the Ni(100) surface. Electron correlation effects were included using the generalized valence bond and configuration interaction methods. Modeling the (100) surface with four Ni atoms, we find the optimum S position to be 1.33 Å above the surface, in good agreement with the value (1.30 ± 0.10 Å) from dynamic LEED intensity calculations. The bonding is qualitatively like that in H₂S with two covalent bonds to one diagonal pair of Ni atoms. There is a S pπ pair overlapping the other diagonal pair of Ni atoms. [Deleting this pair the S moves in to a position 1.04 Å from the surface.] There are two equivalent such structures, the resonance leading to equivalent S atoms and a c(2 × 2) structure for the S overlayer. The Ni in the layer beneath the surface seems to have little effect (~0.03 Å) on the calculated geometry. Bonding the S directly above a single Ni atom leads to a much weaker bond (D_e = 3.32 eV) than does bonding in a bridge position (D_e = 5.37 eV).     

Oxidation of nickel studied by UV and X-ray photoelectron spectroscopy

The nature of argon-ion bombarded nickel surfaces (polycrystalline, and (111), (110) and (100) single crystals) and their subsequent interaction with oxygen at ordinary temperatures have been studied using X-ray and UV photoelectron spectroscopy, including angular variation measurements and the determination of work function changes, in combination in the same apparatus. Variations between the HeI spectra of the four clean substrates were taken to confirm the presence of substantial order within the depth sampled by UPS. The four surfaces exhibited similar but not identical behaviour during oxidation, resembling that reported by other workers from studies of both annealed single crystals and evaporated polycrystalline films. The initial process was deduced to be essentially dissociative chemisorption: no evidence supporting a previous suggestion of associative adsorption at low coverages was found. Oxygen commenced to penetrate below the surface of all samples before oxygen equivalent to a monolayer had been taken up (~10 L exposure) and further substantial uptake followed resulting in the formation of a stable film (~18 Å) of nickel oxide by ~100 L exposure. This oxide layer was not stoichiometric nickel(II) oxide: it was characterized by the presence of two distinct O 1s signals, the relative intensities of which depended on the crystallographic nature of the surface. It is tentatively suggested that the oxygen signal with the higher BE be associated with Ni^III. Comparison of the X-ray and UV spectra suggests that the oxide film is very non-uniform in thickness, some Ni metal remaining very close to the surface.     

Reducing reflected contributions to ear-canal distortion product otoacoustic emissions in humans

Distortion product otoacoustic emission (DPOAE) fine structure has been attributed to the interaction of two cochlear-source mechanisms (distortion and reflection sources). A suppressor presented near the 2f1-f2 frequency reduces the reflection-source contribution and, therefore, DPOAE fine structure. Optimal relationships between stimulus and suppressor conditions, however, have not been described. In this study, the relationship between suppressor level (L3) and stimulus level (L2) was evaluated to determine the L3 that was most effective at reducing fine structure. Subjects were initially screened to find individuals who produced DPOAE fine structure. A difference in the prevalence of fine structure in two frequency intervals was observed. At 2 kHz, 11 of 12 subjects exhibited fine structure, as compared to 5 of 22 subjects at 4 kHz. Only subjects demonstrating fine structure participated in subsequent measurements. DPOAE responses were evaluated in 1/3-octave intervals centered at 2 or 4 kHz, with 4 subjects contributing data at each interval. Multiple L3's were evaluated for each L2, which ranged from 20 to 80 dB SPL. The results indicated that one or more L3's at each L2 were roughly equally effective at reducing DPOAE fine structure. However, no single L3 was effective at all L2's in every subject.     

A highly Selective Fluorescent Sensor for Monitoring Cu<Superscript>2+</Superscript> Ion: Synthesis,Characterization and Photophysical Properties

A new fluorescent sensor, 4-allylamine-N-(N-salicylidene)-1,8-naphthalimide (1), anchoring a naphthalimide moiety as fluorophore and a Schiff base group as receptor, was synthesized and characterized. The photophysical properties of sensor 1 were conducted in organic solvents of different polarities. Our study revealed that, depending on the solvent polarity, the fluorescence quantum yields varied from 0.59 to 0.89. The fluorescent activity of the sensor was monitored and the sensor was consequently applied for the detection of Cu²⁺ with high selectivity over various metal ions by fluorescence quenching in Tris-HCl (pH = 7.2) buffer/DMF (1:1, v/v) solution. From the binding stoichiometry, it was indicated that a 1:1 complex was formed between Cu²⁺ and the sensor 1. The fluorescence intensity was linear with Cu²⁺ in the concentration range 0.5–5 μM. Moreso, the detection limit was calculated to be 0.32 μM, which is sufficiently low for good sensitivity of Cu²⁺ ion. The binding mode was due to the intramolecular charge transfer (ICT) and the coordination of Cu²⁺ with C = N and hydroxyl oxygen groups of the sensor 1. The sensor proved effective for Cu²⁺ monitoring in real water samples with recovery rates of 95–112.6 % obtained.     

Weakly compact operators on function spaces

S — E, F — . C(S, E) S E. : C(S, E) F C(S) . , C(S, E) C(S).     

Unitarization of symplectics and stability for causal differential equations in Hilbert space

Let Sp($\text{H}$) be the symplectic group for a complex Hibert space $\text{H}$. Its Lie algebra sp($\text{H}$) contains an open invariant convex cone C₀; each element of C₀ commutes with a unique sympletic complex structure. The Cayley transform $\text{C}$: X∈ sp($\text{H}$)→(I + X)¹∈ Sp($\text{H}$) is analyzed and compared with the exponential mapping. As an application we consider equations of the form $\text{(}\text{d}\text{dt}\text{) S = A(t)S,}\text{where}\text{t → A(t) ?}\text{C}\text{?}{}_0$ is strongly continuous, and show that if ∝_?∞^∞ ∥A(t)∥ dt < 2 and ∝_{? t8}^∞A(t) dt?C₀, the (scattering) operator

, where S_t′(t) is the solution such that S_t′(t′) = I, is in the range of $\text{B}$ restricted to C₀. It follows that S leaves invariant a unique complex structure; in particular, it is conjugate in Sp($\text{H}$) to a unitary operator.     

Twistor Geometry of a Pair of Second Order ODEs

We discuss the twistor correspondence between path geometries in three dimensions with vanishing Wilczynski invariants and anti-self-dual conformal structures of signature (2, 2). We show how to reconstruct a system of ODEs with vanishing invariants for a given conformal structure, highlighting the Ricci-flat case in particular. Using this framework, we give a new derivation of the Wilczynski invariants for a system of ODEs whose solution space is endowed with a conformal structure. We explain how to reconstruct the conformal structure directly from the integral curves, and present new examples of systems of ODEs with point symmetry algebra of dimension four and greater which give rise to anti–self–dual structures with conformal symmetry algebra of the same dimension. Some of these examples are (2, 2) analogues of plane wave space–times in General Relativity. Finally we discuss a variational principle for twistor curves arising from the Finsler structures with scalar flag curvature.     

Fiber bragg gratings made with a phase mask and 800-nm femtosecond radiation

High-quality retroreflecting fiber Bragg gratings were written in standard Ge-doped telecom fiber (Corning SMF-28) after a few minutes exposure with pulsed 800-nm, 120-fs laser radiation by use of a deep-etch silica zero-order nulled phase mask optimized for 800 nm. Induced index modulations of 1.9 x 10(-3) were achieved with peak power intensities of 1.2 x 10(13) W/cm2 without any fiber sensitization. The fiber gratings are stable and did not erase after 2 weeks at 300 degrees C. The primary mechanism of induced index change results from a structural modification to the fiber core.