The first eigenvalue of the Dirac operator on Kähler manifolds

If M^2m is a closed Kähler spin manifold of positive scalar curvature R, then each eigenvalue λ of type r (r {1, …, [(m + 1)/2]}) of the Dirac operator D satisfies the inequality λ² ≥ rR₀/4r − 2, where R₀ is the minimum of R on M^2m. Hence, if the complex dimension m is odd (even) we have the estimation

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for the first eigenvalue of D. In the paper is also considered the limiting case of the given inequalities. In the limiting case with m = 2r − 1 the manifold M^2m must be Einstein. The manifolds S², S² × S², S² × T², P³( ), F( ), P³( ) × T² and F( ³) × T², where F( ³) denotes the flag manifold and T² the 2-dimensional flat torus, are examples for which the first eigenvalue of the Dirac operator realizes the limiting case of the corresponding inequality. In general, if M^2m is an example of odd complex dimension m, then M^2m × T² is an example of even complex dimension m + 1. The limiting case is characterized by the fact that here appear eigenspinors of D² which are Kählerian twistor-spinors.     

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.     

Considerations concerning the radiative corrections to muon decay in the Fermi and Standard theories

The FAC, PMS, and BLM optimization methods are applied to the QED corrections to the muon lifetime in the Fermi V-A theory. The FAC and PMS scales are close to m_e, while the BLM scale nearly coincides with the geometric average √m_em_μ. The optimized expressions are employed to estimate the third order coefficient in the (m_μ) expansion and the theoretical error of the perturbative series. Using arguments based on effective field theory and a simple examination of Feynman diagrams, it is shown that, if contributions of (m_μ²/M_W²) are neglected, the corrections to muon decay in the SM factorize into the QED correction of the Fermi V-A theory and the electroweak amplitude g²/(1 − Δr), both of which are strictly scale-independent. We use the results to clarify how the QED corrections to muon decay and the Fermi constant G_F should be used in the SM, and what is the natural choice of scales if running couplings are employed.     

Spectral intensities in the ν1 band of NH3

Intensities have been measured for individual transitions in the Q and R branches of the ν₁ band of NH₃ using a difference-frequency laser spectrometer. The data yield an integrated band strength of S⁰_v=219.36±1.03 cm^-2/MPa at 297 K, corresponding to a transition moment of μ_v = 8.535(20) × 10^-32 C·m, and a Herman-Wallis correction factor, (1 + _jm)², where _j = 0.0209(20). The intensities of a few lines for K 7 were noticeably perturbed by a perpendicular Coriolis interaction with 2ν₄ (E, L = 2), so were excluded from the fit. A small sample of ν₃ band lines occurring in the ν₁ band scans also yields a rough estimate of the ν₃ band intensity with evident irregular perturbations.     

Limits of neutrino stability from the γ-ray flux measured in coincidence with neutrinos from SN 1987a

Limits for the neutrino decay ν_H→ν_L+γ, where ν_H and ν_L are assumed to be massive neutrinos withm_VH>m_VL, are presented using data from the Solar Maximum Mission satellite taken in coincidence with the detected neutrino burst from SN 1987A. These limits are essentially independent of supernova models and are and τ/m_νμ,τ>3.3×10¹⁴ s/eV for a thermal spectrum at a temperature .     

Infrared absorbance cross-sections for dinitrogen pentoxide vapour

Laboratory measurements of the ν₁₂ absorption band of gaseous N₂O₅ have been made using Fourier transform infrared (FTIR) spectroscopy at seven different temperatures between 233 and 293 K. Integrated band strengths and absorbance cross-sections per molecule show no significant temperature dependence. Their average values are S_int = (4.09±0.17) × 10^-17 cm molecule ^-1 and σ_peak = (1.90±0.08) × 10^-18 cm² molecule^-1.     

Erbium in silicon–germanium quantum wells

Strained Si_1−xGe_x/Si quantum wells have been doped with erbium by implantation. A comparison is made with strained Si_1−xGe_x/Si quantum wells and relaxed Si_1−xGe_x, with x between 10% and 25%, doped with erbium during MBE growth. The erbium concentration was between 1×10¹⁸ and 5×10¹⁸ cm⁻³ throughout the active regions. Transmission electron microscopy, X-ray diffraction, and photoluminescence studies indicate that good regrowth can been achieved after full amorphisation by implantation of the strained quantum wells. The erbium luminescence is more intense in the Si_1−xGe_x/Si layers, but erbium-implanted samples containing Si_1−xGe_x exhibit defect luminescence in the region of 0.9–1.0 eV. These defects are also present when Si_1−xGe_x/Si quantum wells are implanted with an amorphising dose of silicon, and then regrown. They are attributed to small germanium-rich platelets, rather than to erbium-related defects. Electroluminescence is presented from a forward biased erbium-implanted Si_0.87Ge_0.13/Si structure at a drive current density of only 1.8 mA/cm².     

Effective activation energy Ue(T,J,H) in textured Bi1.84Pb0.4Sr2Ca2Cu3Oy silver-clamped thick films

We have measured the resistivity of textured Bi_1.84Pb_0.4Sr₂Ca₂Cu₃O_y silver-clamped thick films as a function of temperature, current density ranging from 10 to 1×10³ A/cm² and magnetic field up to 0.3 T. We find that the effective activation energy U_e follows U_e(T,J,H)=U₀(1−T/T_p)^mln(J_c0/J)H⁻ with m=1.75 for Hab-plane and 2.5 for Hc-axis and =0.76 for Hab and 0.97 for Hc, for the current density regime above 100 A/cm², where T_p is a function of applied magnetic field and current density. This result suggests the effective activation energy U_e be correlated with the temperature, current density and magnetic field. The possible dissipative mechanisms responsible for the temperature, current density and magnetic field dependence of the effective activation energy are discussed.     

WnNim(n+m=8)团簇轨道能级与芳香性的理论研究

用密度泛函理论(DFT)中的b3lyp方法,在Lanl2dz基组水平上对W_nNi_m(n+m=8)团簇的各种可能构型进行几何参数全优化,得到它们的基态构型;并对基态构型的轨道能级分布、能隙、HOMO、LUMO能级、芳香性和热力学性质进行分析,结果表明:团簇W₅Ni₃和W₆Ni₂的Alpha轨道和Beta轨道是完全简并的,所有电子都是严格两两配对的;团簇W₂Ni₆能隙最小,化学活性最强,组成前线轨道的成分基本相同;W₆Ni₂能隙最大,化学活性最弱;团簇W₁Ni₇,W₅Ni₃,W₆Ni₂,W₇Ni₁具有芳香性,W₂Ni₆具有反芳香性;团簇的生成焓都是负值,为放热反应,热力学上是稳定的.     

On the electroweak and gluonic corrections to the hadronic width of the Z boson

The electroweak corrections to the Z-boson hadronic width are presented in a simple analytical form for the width itself, Λ_h, for its ratio to the leptonic width, R_l = Λ_h/Λ_l, for the Λ_b/Λ_h ratio, and for the total width Λ_Z. The rational parametrization, advocated in our recent papers on leptonic decays, simplifies the analysis of the hadronic decays too. There are two main results of this analysis: (1) All electroweak precision measurements agree within 1 σ with the electroweak Born approximation if the gluon coupling constant . Thus the electroweak radiative corrections have not been observed experimentally. The unexpected smallness of electroweak radiative corrections is caused by the mutual cancellation of the large positive contribution of a heavy top quark and the large negative contribution of all other virtual particles. (2) With electroweak radiative corrections being taken into account, the value of extracted from the experimental value of Λ_Z differs by 3σ from that obtained from R_l, if m_t 200 GeV; they agree within 1σ if m_t 150 GeV. Thus a low upper limit on m_t can be obtained from hadronic decays of the Z-boson alone, even without data on its leptonic decays.     

Density profile and flow of miscible fluid with dissimilar constituent masses

A computer simulation model is used to study the density profile and flow of a miscible gaseous fluid mixture consisting of differing constituent masses (m_A=m_B/3) through an open matrix. The density profile is found to decay with the height ∝exp (−m_A(B)h), consistent with the barometric height law. The flux density shows a power-law increase ∝(p_c−p)^μ with μ2.3 at the porosity 1−p above the pore percolation threshold 1−p_c.     

N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E₆ models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M⁴×S¹/(Z₂×Z₂′)×S¹/(Z₂×Z₂′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)², SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)³ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A² and disc D², we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)³ models for the zero modes, and give the simplest model with Z₉ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.     

Supersymmetric left-right model and its tests in linear colliders

We investigate phenomenological implications of a supersymmetric left-right model based on SU(2)_L × SU(2)_R × U(1)_B–L gauge symmetry testable in the next generation linear colliders. We concentrate in particular on the doubly charged SU(2)_R triplet higgsino , which we find very suitable for experimental search. We estimate its production rate in e⁺e⁻, e⁻e⁻, e⁻γ and γγ collisions and consider its subsequent decays. These processes have a clear discovery signature with a very low background from other processes.     

Remarks on stochastic non-linear birth and death models

The first part of this paper is an attempt to formulate and motivate additional work on the important problem of obtaining global bounds applicable to the controlled truncation of the paper relates specifically to the linear birth, quadratic death model. Asymptotic results are given for the first finite difference ΔT_m where T_m is the exactly known mean time to extinction starting from state m (m= 0,1,…). These results are in terms of the environmental carrying capacity n^* taken to be large. For m near zero ΔT_me^n*/(n^*)²; whereas, for m near n^*ΔT_m ≈ (π/2)^1/2/(n^*)^3/2. This indicates the vastly different time scales in those two regions of state space - with considerably slower action near extinction than near n^*.     

Chiral perturbation theory: Expansions in the mass of the strange quark

In a previous paper, we have shown how to systematically determine the low-energy structure of the Green functions in QCD. The present article extends this framework to expansions in the mass of the strange quark. We construct the generating functional of U(3)×U(3) which allows us to calculate the Green functions up to and including terms of order p⁴ (at fixed radio m_quark/p²) in terms of a few coupling constants which chiral symmetry leaves undetermined. We calculate the first non-leading term in the quark mass expansion of the order parameters , and of the masses and decay constants in the pseudoscalar octet. The three coupling constants which are not fixed by experimental low-energy information are estimated by invoking large-N_c arguments.     

Determination of different oxygen transport mechanisms and measurement of the oxygen ion conductivity of Y1Ba2Cu3O7−x

By undertaking AC electrochemical impedance experiments on yttria stabilised zirconia electrolytes with polished Y₁Ba₂Cu₃O_7−x electrodes, the activation energy for oxygen ion transport within the bulk of Y₁Ba₂Cu₃O_7−x, in air, over the temperature range 823 K–1043 K, was determined to be 1.50 ± 0.05 eV. At 1000 K the oxygen ionic conductivity was calculated to be around one order of magnitude lower than that in yttria stabilised zirconia. Typical calculated values were σ=5×10⁻⁵ (ω cm)⁻¹ and 6×10⁻³ (ω cm)⁻¹ at the respective temperatures 823 K and 1043 K. By employing a similar cell but with Y₁Ba₂Cu₃O_7−x paste electrodes, oxygen transfer between the Y₁Ba₂Cu₃O_7−x and the electrolyte was found to occur via a surface diffusional processes. Over the temperature range 873 K–1098 K, in air, the activation energy for in-diffusion at the surface was found to be 1.4±0.1 eV and that for out-diffusion at the surface to be 1.76±0.05 eV.     

A hybrid mode of one- and two-surface multipactor on grooved dielectric surface

A hybrid mode of one- and two-surface multipactor on the grooved dielectric surface is studied in detail using both an analytical approach and two-dimensional particle-in-cell(2D PIC) simulations. When the groove width L eE_0/(4πm_ef~2),there are one-surface multipactor and one-order two-surface multipactor on the grooved dielectric surface, and only one slope of the groove has the multipactor anytime. When L eE0/(4πme f~2), both slopes may have the multipactors. The electron surface density of the multipactor discharge has a sharp increase at the length L = eE_0/(4πm_ef~2).     

On nonanalytic solitary waves formed by a nonlinear dispersion

We study the prototypical, genuinely nonlinear, K(m, n) equation, u_t ± a(u^m)_x + (uⁿ)_xxx = 0, a = const, which exhibits a number of remarkable dispersive effects. In particular, the distinguished subclass wherein m = n + 2 is transformed into a new, purely dispersive equation free of convection. In addition to compactons, the K(m, n) can support both kinks and solitons with an infinite slope(s), periodic waves and dark solitons with cusp(s) all being manifestations of nonlinear dispersion in action. For n < 0 the enhanced dispersion at the tail may generate algebraically decaying patterns.     

The effect of nitrogen ion implantation on tungsten surfaces

X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) were used to study the phase, composition and chemical states of elements at the tungsten surface. The measurement results indicate that nitrogen-containing phase of tungsten were formed by nitrogen ion implantation (energy 40 keV, implantation doses of 4×10¹⁷, 8×10¹⁷ and 1.6×10¹⁸ ions/cm²). The formation of the W_x(O,N) and WN in the surface layer occurred as a result of nitrogen ion irradiation. A decrease in concentration of W_x(O,N) is observed with increasing N⁺ while that WN increases. Due to residual oxygen in the chamber WO₃ still exists at the surface of the specimen.