On K-stability of reductive varieties

G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kähler metric of constant scalar curvature. In [D3] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson’s results and computations to a new case, that of reductive varieties.Received: November 2003 Revision: January 2004 Accepted: January 2004     

Effects of reduction temperature and metal-support interactions on the catalytic activity of Pt/gamma-Al2O3 and Pt/TiO2 for the oxidation of CO in the presence and absence of H2

TiO2- and gamma-Al2O3-supported Pt catalysts were characterized by HRTEM, XPS, EXAFS, and in situ FTIR spectroscopy after activation at various conditions, and their catalytic properties were examined for the oxidation of CO in the absence and presence of H2 (PROX). When gamma-Al2O3 was used as the support, the catalytic, electronic, and structural properties of the Pt particles formed were not affected substantially by the pretreatment conditions. In contrast, the surface properties and catalytic activity of Pt/TiO2 were strongly influenced by the pretreatment conditions. In this case, an increase in the reduction temperature led to higher electron density on Pt, altering its chemisorptive properties, weakening the Pt-CO bonds, and increasing its activity for the oxidation of CO. The in situ FTIR data suggest that both the terminal and bridging CO species adsorbed on fully reduced Pt are active for this reaction. The high activity of Pt/TiO2 for the oxidation of CO can also be attributed to the ability of TiO2 to provide or stabilize highly reactive oxygen species at the metal-support interface. However, such species appear to be more reactive toward H2 than CO. Consequently, Pt/TiO2 shows substantially lower selectivities toward CO oxidation under PROX conditions than Pt/gamma-Al2O3.     

Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse

The superluminal group velocity of an ultrashort optical Bessel beam pulse is measured over its entire depth of field, corresponding to approximately 2x10(4) optical wavelengths. The method used is to measure the traveling ionization front induced by the pulse.     

Search for the scalar top quark in pp collisions at square root[s] = 1.8 TeV

We have performed a search for scalar top quark (stop) pair production in the inclusive electron-muon-missing transverse energy final state, using a sample of pp events corresponding to 108.3 pb(-1) of data collected with the D0 detector at Fermilab. The search is done in the framework of the minimal supersymmetric standard model assuming that the sneutrino is the lightest supersymmetric particle. For the dominant decays of the lightest stop, t-->b chi+1 and t-->blnu, no evidence for signal is found. We derive cross-section limits as a function of stop ( t ), chargino ( chi+1), and sneutrino ( nu) masses.     

Role of vortex structures in excitation of condensed system self-oscillatory burning

The effect of free convection and vortex structures arising near the “singing” flame of a gasoline blow torch on excitation of thermal self-oscillations in a resonator tube is studied experimentally. A technique for measuring the oscillation amplitude of the gas column is suggested. It is found that the excitation of acoustic oscillations decreases the height of the singing flame and the mass velocity of burning but raises the gasoline combustion efficiency. The variation of the temperature field of the singing flame over an oscillation cycle is studied by digital photometry. Hysteretic dependences of the acoustic oscillation amplitude on the thermal power of the gasoline diffusion flame are obtained. A mechanism explaining the influence of vortex structures on the self-oscillatory mode of burning in condensed systems is discussed.     

Hydrodynamics of resonance oscillations of columns of inelastic particles

We study oscillations of a one-dimensional (1D) column of N slightly inelastic particles, produced by a piston vibrating at one end of a closed tube. It is found that for large enough vibrational amplitudes of the piston, the column oscillates periodically with the period equal to the vibrational period. The oscillation patterns are governed by the shock waves propagating across the column. The averaged kinetic energy per particle is shown to be proportional to the square of the vibrational frequency, omega. This energy also strongly depends on the vibrational amplitude. The maximal value of this kinetic energy achievable by these external vibrations is found to be of order omega(2)L(2), where L is the total volume (length) of the tube free of particles. The above results on the column resonance oscillations are also predicted by a 3D hydrodynamic model of an inelastic granular gas.     

A generating functional approach to the Hubbard model

The method of generating functional, suggested for conventional systems by Kadanoff and Baym, is generalized to the case of strongly correlated systems, described by the Hubbard X operators. The method has been applied to the Hubbard model with arbitrary value U of the Coulomb on-site interaction. For the electronic Green’s function constructed for Fermi-like X operators, an equation using variational derivatives with respect to the fluctuating fields has been derived and its multiplicative form has been determined. The Green’s function is characterized by two quantities: the self energy Σ and the terminal part Λ. For them we have derived the equation using variational derivatives, whose iterations generate the perturbation theory near the atomic limit. Corrections for the electronic self-energy Σ are calculated up to the second order with respect to the parameter W/U (W width of the band), and a mean field type approximation was formulated, including both charge and spin static fluctuations. This approximation is actually equivalent to the one used in the method of Composite Operators, and it describes an insulator-metal phase transition at half filling reasonably well. The equations for the Bose-like Green’s functions have been derived, describing the collective modes: the magnons and doublons. The main term in this equation represents variational derivatives of the electronic Green’s function with respect to the corresponding fluctuating fields. The properties of the poles of the doublon Green’s functions depend on electronic filling. The investigation of the special case n=1 demonstrates that the doublon Green’s function has a soft mode at the wave vector Q=(π,π,...), indicating possible instability of the uniform paramagnetic phase relatively to the two sublattices charge ordering. However this instability should compete with an instability to antiferromagnetic ordering. The generating functional method with the X operators could be extended to the other models of strongly correlated systems.     

Study of Zgamma events and limits on anomalous ZZgamma and Zgammagamma couplings in pp collisions at square root s = 1.96 TeV

We present a measurement of the Zgamma production cross section and limits on anomalous ZZgamma and Zgammagamma couplings for form-factor scales of lambda = 750 and 1000 GeV. The measurement is based on 138 (152) candidates in the eegamma (mumugamma) final state using 320(290) pb(-1) of pp(-1) collisions at square root of s = 1.96 TeV. The 95% C.L. limits on real and imaginary parts of individual anomalous couplings are /h(10,30)Z/ < 0.23, /h(20,40)Z/ < 0.020, /h(10,30)gamma/ < 0.23, and /h(20,40)gamma/ < 0.019 for lambda = 1000 GeV.     

Measurement of the Lambda0b lifetime in the decay lambda0b--> J/psiLambda0 with the D0 detector

We present measurements of the Lambda(0)(b) lifetime in the exclusive decay channel Lambda(0)(b)--> J/psiLambda(0), with J/psi--> mu(+)mu(-) and Lambda(0)--> ppi(-), the B0 lifetime in the decay B0-->J/psiK(0)(S) with J/psi--> mu(+)mu(-) and K(0)(S)-->pi(+)pi(-), and the ratio of these lifetimes. The analysis is based on approximately 250 pb(-1) of data recorded with the D0 detector in pp collisions at sqrt[s] = 1.96 TeV. The Lambda(0)(b) lifetime is determined to be tau(Lambda(0)(b)) = 1.22(+0.22)(-0.18)(stat) +/- 0.04(syst) ps, the B0 lifetime tau(B0) = 1.40(+0.11)(-0.10)(stat) +/- 0.03(syst) ps, and the ratio tau(Lambda(0)(b))/tau(B0) = 0.87(+0.17)(-0.14)(stat) +/- 0.03(syst). In contrast with previous measurements using semileptonic decays, this is the first determination of the Lambda(0)(b) lifetime based on a fully reconstructed decay channel.