Commutator representations of differential calculi on the quantum group SUq(2)

Let (Γ, d) be the 3D-calculus or the 4D_±-calculus on the quantum group SU_q (2). We describe all pairs (π, F) of a ^*-representation π of (SU_q(2)) and of a symmetric operator F on the representation space satisfying a technical condition concerning its domain such that there exist a homomorphism of first order differential calculi which maps dx into the commutator [iF, π(x)] for x ε (SU_q (2)). As an application commutator representations of the two-dimensional left-covariant calculus on Podles quantum 2-sphere S_qc² with c = 0 are given.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

Ultrasonic and viscometric studies of molecular interactions in binary mixtures of formamide with ethanol, 1-propanol, 1,2-ethanediol and 1,2-propanediol at different temperatures

The ultrasonic speeds, u and viscosities, η of binary mixtures of formamide (FA) with ethanol, 1-propanol, 1,2-ethanediol, and 1,2-propanediol, including those of pure liquids, over the entire composition range were measured at 293.15, 298.15, 303.15, 308.15, 313.15, and 318.15 K. From the experimental values of u and η, the deviations in isentropic compressibility, Δk_s, in ultrasonic speed, Δu, and in viscosity, Δη were calculated. The variation of these parameters with composition and temperature of the mixtures are discussed in terms of molecular interaction in these mixtures. The observed trends in Δk_s values indicate the presence of specific interactions between FA and alkanol molecules. The Δk_s values follow the order: ethanol < 1-propanol < 1,2-propanediol < 1,2-ethanediol. It is observed that the Δk_s values depend upon the number of hydroxyl groups and alkyl chain length in these alkanol molecules. Furthermore, the free energies, ΔG, enthalpies, ΔH and entropies, ΔS of activation of viscous flow have also been obtained by using Eyring viscosity equation and their dependence on composition of the mixtures have been discussed.     

Reactions of π-allyl with atomic oxygen and hydroxyl on Ag(110)

The oxidation of the adsorbed π-allyl (η³-C₃H₅), prepared on atomic oxygen- and hydroxyl-covered Ag(110) by dissociation of allyl chloride (C₃H₅Cl), is investigated with temperature-programmed desorption and high-resolution electron energy loss spectroscopy. Allyl chloride adsorbs molecularly on oxygen-covered Ag(110) at 110 K. Upon heating to 180 K, some allyl chloride dissociates to form π-allyl and atomic chlorine, and the remainder desorbs molecularly. The π-allyl undergoes combustion to form hydroxyl or carbonate until all of the free oxygen is consumed by 200 K. Migratory insertion of hydroxyl into excess π-allyl commences near 220 and finishes by 250 K, forming adsorbed allyl alcohol (C₃H₅OH), which reacts either with excess hydroxyl near 240 K to form allyl alkoxy (η¹(O)-C₃H₅O) and water, or with π-allyl at 250 K to form allyl alkoxy and propylene (C₃H₆). Th allyl alkoxy evolves acrolein (C₃H₄O) by β-hydrogen elimination near 285 K, and propylene is evolved concurrently as the hydrogen released by this reaction rapidly scavenges π-allyl. Finally, the remaining π-allyl dimerizes to form 1,5-hexadiene (C₆H₁₀), which desorbs at 315 K. The gross observations of reaction pathways and temperatures are used to evaluate important aspects of the thermochemistry of these reactions.     

Study of activation parameters and NMR spin-lattice relaxation time in some substituted amines

The present communication reports the experimental values of NMR spin-lattice relaxation time (T₁) and dielectric relaxation time (τ) of piperidine, pyrrole, pyridine, diethylamine, triethylamine and pyrrolidine. The values of activation energy (ΔE_A) obtained using dielectric relaxation time, have been correlated with calculated values of ΔE_A obtained using Arrhenius equation of NMR relaxation time (T₁) for pyridine, diethylamine and pyrrole. Authors have also established a correlation between the experimental values of NMR spin-relaxation time (T₁) with its calculated values obtained using different equations of dielectric relaxation time (τ).     

Unusual observation of nitrogen chemical shift anisotropies in tetraalkylammonium halides by 14N MAS NMR spectroscopy

¹⁴N Magic-angle spinning (MAS) NMR spectra for a number of polycrystalline, symmetrical tetraalkylammonium halides with short alkyl chains (C₂H₅– to n-C₄H₉–) have been recorded following a careful setup of the experimental conditions. Analysis of the spectra demonstrates the presence of ¹⁴N chemical shift anisotropies (CSAs) on the order of |δ_σ|=10–30 ppm along with ¹⁴N quadrupole coupling constants in the range of 10–70 kHz. The magnitude and sign of the CSAs determined from ¹⁴N MAS NMR are confirmed by recording and analysis of the corresponding slow-speed spinning (500–650 Hz) ¹⁵N CP/MAS NMR spectra. Most interestingly, it is observed experimentally and demonstrated theoretically and by simulations, that these CSAs are reflected in the spinning sideband (ssb) intensities of the ¹⁴N MAS spectra at much higher spinning speeds than can be applied to retrieve the corresponding ¹⁵N CSAs from the ssb pattern in the ¹⁵N CP/MAS spectra.     

Desorption of H2 from W(110) and Fe covered W(110) surfaces

The kinetics of H₂ desorption from H/W(110) and H/Fe₁/W(110) were studied by measuring work function changes Δø vs time at a number of temperatures. Combination with previously determined Δø vs coverage data and differentiation at various fixed coverages gave rate vs T data from which activation energies of desorption could be obtained. E vs coverage results agree well with previously determine ΔH_des results. In the case of H/Fe₁/W(110) this includes a rise from 20 to 30 kcal mol⁻¹ of H₂ at H/Fe = H/W > 0.3. Plots of rate −dθ/dt vs θ (θ being coverage in units of H/W) vary much more steeply than θ² at most coverages for both systems. The θ dependence can be explained almost quantitatively in terms of the variations of ΔH_des and surface entropy S_s with coverage, by assuming that rates of desorption are equal to the equilibrium rates of adsorption. The latter can be formulated thermodynamically, except for a sticking coefficient, s. Values for s(θ, T) can also be obtained and show relatively little temperature dependence.     

Time-dependent magnetization in co-precipitated cobalt ferrite

A study of the magnetic aftereffect in co-precipitated cobalt ferrite is presented. Measurements of the magnetic viscosity S were performed at room temperature along the demagnetization curve for different applied fields H_ap over a wide range of fields (0 kOe<H_ap<−7 kOe). The interrelation function η=(∂M_rev/∂M_irr)_Hi between the DCD reversible M_rev and irreversible M_irr magnetization components was determined as well. The experimental results for S_η(H_i), where H_i is the internal field, showed a broad distribution with a maximum at H_i=2.7 kOe. However, the irreversible susceptibility χ_irr displays a maximum at H_c=0.75 kOe, the coercivity of the material. The experimental behavior of η and the non-proportionality between S_η and χⁱ_irr suggest that the magnetic viscosity in this material is principally supplied by events of nucleation of inverse domains and the depinning of domain walls. When the main mechanism of reversal magnetization changes to rotation of magnetic moments for all the grains, the magnetic viscosity decreases.     

Dielectric behavior of hexaferrites BaCo2−xZnxFe16O27

The dielectric constant (′) and dielectric loss (tan δ) for hexaferrites BaCo_2−xZn_xFe₁₆O₂₇ have been studied as a function of frequency (f), temperature (T) and composition (x). The experimental results indicate that ′ and tan δ above the relaxation frequency only decrease as the frequency increases and as the temperature decreases. Tan δ shows the dielectric relaxation at certain critical frequencies which rise as temperature increases. The activation energy for the dielectric relaxation (E_D), ′, and tan δ are found to be minimum for x = 0.8.     

Asymptotics of eigenvalues of the Schrödinger operator with a strong δ-interaction on a loop

In this paper we investigate the operator H_β=−Δ−βδ(·−Γ) in , where β>0 and Γ is a closed C⁴ Jordan curve in . We obtain the asymptotic form of each eigenvalue of H_β as β tends to infinity. We also get the asymptotic form of the number of negative eigenvalues of H_β in the strong coupling asymptotic regime.     

Exploring leptonic CP violation by reactor and neutrino superbeam experiments

We point out the possibility that reactor measurement of θ₁₃, when combined with high-statistics ν_e appearance accelerator experiments, can detect leptonic CP violation. Our proposal is based on a careful statistical analysis under reasonable assumptions on systematic errors, assuming 2 years running of the neutrino mode J-PARC → Hyper-Kamiokande experiment and a few years running of a reactor experiment with 100 t detectors at the Kashiwazaki–Kariwa nuclear power plant. We show that the method can be arranged to be insensitive to the intrinsic parameter degeneracy but is affected by the one due to unknown sign of Δm²₃₁.     

Thermoelectric power and irreversibility field of (Hg,Tl)2Ba2Can−1CunOy (n=2–5) superconductors

We have measured the thermoelectric power, S, and the irreversibility field, H_irr, of the superconducting samples of (Hg,Tl)₂Ba₂Ca_n−1Cu_nO_y (n=2–5). S values for the (Hg,Tl)-22(n−1)n above their T_c's drastically increase with increasing n. Judging from the S values at room temperature, the n=2 and 3 samples are located in the overdoped region, the n=4 is in the almost optimally doped and the n=5 is in the underdoped region. H_irr values for the n=4 and 5 samples are higher than those for the as-synthesized and annealed n=3 samples. It is considered that the enhancement in H_irr is due not only to the increase of hole concentration but to the increase in the number of CuO₂ sheets.     

Stokes parameters measurement of light over a wide wavelength range by judicious choice of azimuthal settings of quarter-wave plate and linear polarizer

The Stokes parameters (S_p, S₁, S₂, S₃) of light are measured at an arbitrary wavelength over a wide wavelength range. The Stokes parameters S₁ and S₂ are easily obtained. But the Stokes parameter S₃ at the arbitrary wavelength is affected by the phase difference error Δ₁ of the quarter-wave plate mismatch and the Stokes parameters S₁ or S₂. Therefore, in this paper, S₃ is obtained from both the intensity measurements by the circular polarizer rotating the quarter-wave plate by 0° and 90°. Then, S₃ is obtained by considering only Δ₁, but is not affected by S₁ and S₂. Also, though Δ₁ is not accounted for, S₃ is measured more accurately.     

Molecular parameters describing intermolecular interactions in the electrooptical Kerr effect

Electrooptical Kerr effect has been studied in binary solutions of a dipolar liquid (-picoline, β-picoline) in a non-dipolar solvent (benzene, p-xylene) and 1,4-dioxane in the full range of concentrations of the dipolar component (0 ≤ f₂ ≤ 1). The experimental Kerr constant K_s of the solutions, refraction index n_s, density ρ_s and the dielectric constant ε_s have been measured and used for the calculation of the molar Kerr constants K_S^M within the Onsager local field model. Analysis of changes in the molar Kerr constants as a function of the solute concentration by fits of theoretical functions to the experimental ones has permitted a determination of the parameters characterizing intermolecular interactions in binary solutions.     

Neutrino oscillations induced by two-loop radiative mechanism

Two-loop radiative mechanism, when combined with an U(1)_L′ symmetry generated by L_e − L_μ − L_τ (=L′), is shown to provide an estimate of Δm²/Δm²_atm εm_e/m_τ, where ε measures the U(1)_L′-breaking. Since Δm²_atm 3.5×10⁻³ eV², we find that Δm² ε10⁻⁶ eV², which will fall into the allowed region of the LOW solution to the solar neutrino problem for ε 0.1.     

Auger electron spectroscopy and electron energy loss spectroscopy studies on carbonization of Si(100) and (111) surfaces with ethylene

The reactions of Si(100) and Si(111) surfaces at 700 °C (973 K) with ethylene (C₂H₄) at a pressure of 1.3×10⁻⁴ Pa for various periods of time were studied by using Auger electron spectroscopy (AES) and electron energy loss spectroscopy (ELS). For a C₂H₄ exposure level, the amount of C on the (111) surface was larger than that on the (100) surface. The formation of β-SiC grain was deduced by comparing the C_KLL spectra from the sample subjected to various C₂H₄ exposure levels, and from β-SiC crystal.     

Conductivity relaxation parameters of some H and K conducting in the polycrystalline compound KDyHP3O10

Polycrystalline samples of KDyHP₃O₁₀ was obtained by heating for 12 hour at 553 K a mixture containing K₂CO₃, Dy₂O₃ and H₃PO₄. Samples were characterized through X-ray diffraction, examined by IR vibrational spectroscopy and impedance and modulus spectroscopy techniques. The conductivity relaxation parameters of some H⁺ and K⁺ conducting in this compound have been determined from an analysis of ac conductivity data measured in a wide temperature range. Transport properties in this material appears as due to H⁺ and K⁺ ions hopping mechanism. The stretched exponential function exp[−(t/τ_σ)^β] has been used to describe the conductivity relaxation. The relaxation parameters have been investigated as a function of the nature of mobile ions. The results obtained are shown to be in good agreement with the predictions of the Ngai coupling model.     

Kondo screening in gapless magnetic alloys

The low-energy physics of a spin- Kondo impurity in a gapless host, in which the density of band states ρ₀(ε)=|ε|^r/(|ε|^r+β^r) vanishes at the Fermi level ε=0, is studied by the Bethe ansatz. It is shown that the growth of the parameter Γ_r=βg^−1/r (where g is an exchange coupling constant) drives the ground state of the system from the Kondo regime with a screened impurity spin to the Anderson regime, where the impurity spin is unscreened. However, in a weak magnetic field H, the impurity spin exceeds its free value, , due to a strong coupling to a band.     

Fabrication, microstructure and critical current density of screen-printed Ag-(Bi, Pb)2Sr2Ca2Cu3Ox superconducting tapes

The influence of the sintering conditions on the microstructure and critical current density J_c has been studied on screen-printed Ag-(Bi, Pb)₂Sr₂Ca₂Cu₃O_x tapes with a ceramics mono-layer core. Three kinds of fabrication processes, which consist of a combination of cold working (rolling and/or pressing) and sintering, are applied. Four times repetition of pressing and sintering after the pre-sintering produces the highest c-axis alignment and achieves J_c= 1.5 × 10⁴ A/cm² (77 K, 0 T). The J_c versus θ data with an angle θ between B and the c-axis elucidate the relation between the anisotropy ratio γ=J_c(Bc)/J_c(B|c and the half-height angular width Δθ of a peak for Bc. This is related to both grain alignment and the J_c value. An increase in J_c, which comes from an improvement for grain alignment, enhances γ and narrows Δθ. The J_c versus θ data are fitted to the expression J_c(B, θ)=J _c(B, 90°)/[(γ−1)|cos θ|ⁿ+1] by regarding both γ and n as adjustable parameters. Fabrication of screen-printed tapes with multilayers (1≤N≤5) is presented, where the critical current increases from 8.0 A to 30.2 A at 77 K and 0 T as N increases.