Bounds and Inequalities for General Orthogonal Polynomials on Finite Intervals

AbstractIn this paper using a new effective approach we deduce some bounds and inequalities for general orthogonal polynomials on finite intervals and give their applications to convergence of orthogonal Fourier series, Lagrange interpolation, orthogonal series with gaps, and Hermite-Fejér interpolation, as well as to the L2 version of the principle of contamination. The main results are: we obtain far-reaching generalizations of the important results of P. Nevai on divergence of Lagrange interpolation in Lp with p < 2 ["Orthogonal Polynomials," Memoirs of the Amer. Math. Soc., Vol. 213, Amer. Math. Soc., Providence, RI, 1979, Corollary 10.18, p. 181; J Approx. Theory43 (1985), Theorem, p. 190] and give new answers to Problems VIII and IX of P. Turán [J. Approx. Theory29 (1980), pp. 32-33]; we extend Turán′s Inequality [Anal. Math.1 (1975), 297-311, Lemma II] to "arbitrary" measures supported in [− 1, 1] and solve Problem LXXI of P. Turán [J. Approx. Theory29 (1980), p. 71]

Dynamic analysis of QTLs for green leaf area duration and green leaf number of main stem in wheat

Senescence in a wheat (Triticum aestivum L.) leaf is a programmed degeneration process leading to death. During this process, green leaf area duration (GLAD) and green leaf number of main stem (GLNMS) are gradually reduced. In this study, the two traits of Hanxuan10/Lumai14 DH population at different development stages after anthesis were evaluated under rainfed and irrigated conditions, and QTLs were detected. GLAD and GLNMS of two parents and DH population under rainfed condition were less than those under irrigated condition, and close correlations (P 22-1B-1, QGlad25-1B-1, QGlad28-1B-2 detected under irrigated condition and QGlad25-1B-3, QGlad28-1B-4 mapped under rainfed condition were located at a 20.7 cM marker interval of Xgwm273-EST122 on 1B chromosome. But QTLs for GLNMS were inducibly and specifically expressed at specific developmental stages after anthesis under both water conditions. The findings provide dynamic genetic information related to wheat senescence

Raman spectroscopy study of NaxCoO2 and superconducting NaxCoO2.yH2O

The Raman spectra of the parent compound NaxCoO2 (x=0.75) and the superconducting oxyhydrates NaxCoO2.yH2O with different superconducting temperatures (Tc) have been measured. Five Raman active phonons around 195 cm-1 (E1g), 482 cm-1, 522 cm-1, 616 cm-1 (3E2g), 663 cm-1 (A1g) appear in all spectra. These spectra change systematically along with the intercalation of H2O and superconducting properties. In particular, the Raman active phonons (A1g and E1g) involving the oxygen motions within the Co-O layers show up monotonous decrease in frequency along with superconducting temperature Tc. The fundamental properties and alternations of other active Raman phonons in the superconducting materials have also been discussed.Comment: 16 pages, 4 figures, 2 table

Nucleon-nucleon momentum correlation function for light nuclei

Nucleon-nucleon momentum correlation function have been presented for nuclear reactions with neutron-rich or proton-rich projectiles using a nuclear transport theory, namely Isospin-Dependent Quantum Molecular Dynamics model. The relationship between the binding energy of projectiles and the strength of proton-neutron correlation function at small relative momentum has been explored, while proton-proton correlation function shows its sensitivity to the proton density distribution. Those results show that nucleon-nucleon correlation function is useful to reflect some features of the neutron- or proton-halo nuclei and therefore provide a potential tool for the studies of radioactive beam physics.Comment: Talk given at the 18th International IUPAP Conference on Few-Body Problems in Physics (FB18), Santos, Brasil, August 21-26, 2006. To appear in Nucl. Phys.

Effects of Mn and Ti doping on superconductivity and charge ordering in NaxCoO2 system

The superconductivity in Na0.3Co1-xMxO2.1.3H2O and the charge ordering in Na0.5Co1-xMxO2 have been investigated for M = Mn and Ti substituting for Co. We have first successfully synthesized the single-phase Na0.7Co1-xMxO2(M= Mn and Ti) materials with 0 < = x < = 0.1, then we obtained Na0.5Co1-xMxO2 (0 < = x < = 0.1, M = Mn and Ti) by Na deintercalation and Na0.3Co1-xMxO2.1.3H2O (0 < = x < = 0.1, M = Mn and Ti) by an additional water intercalations. X-ray diffraction measurements revealed that all samples are single-phase materials, their lattice parameters depend systematically on the Ti and Mn contents. Measurements of physical properties indicate that the superconductivity in Na0.3Co1-xMxO2.1.3H2O is suppressed evidently by Co-site doping and killed at x = 0.02 for Mn doping and x = 0.01 for Ti doping. Charge ordering and magnetic properties in Na0.5Co1-xMxO2 were also influenced by M-atom doping.Comment: 22 pages, 3 tables, and 6 figure

Structural Phase Transitions and Sodium Ordering in Na0.5CoO2: a Combined Electron Diffraction and Raman Spectroscopy Study

The nonstoichiometric NaxCoO2 system exhibits extraordinary physical properties that correlate with temperature and Na concentration in its layered lattice without evident long-range structure modification when conventional crystallographic techniques are applied. For instance, Na0.7CoO2, a thermodynamically stable phase, shows large thermoelectric power; water-intercalated Na0.33CoO2.1.3H2O is a newly discovered superconductor with Tc ~ 4K, and Na0.5CoO2 exhibits an unexpected charge ordering transition at around Tco ~ 55 K. Recent studies suggest that the transport and magnetic properties in the NaxCoO2 system strongly depend on the charge carrier density and local structural properties. Here we report a combined variable temperature transmission electron microscopy and Raman scattering investigation on structural transformations in Na0.5CoO2 single crystals. A series of structural phase transitions in the temperature range from 80 K to 1000 K are directly identified and the observed superstructures and modulated phases can be interpreted by Na-ordering. The Raman scattering measurements reveal phase separation and a systematic evolution of active modes along with phase transitions. Our work demonstrates that the high mobility and ordering of sodium cations among the CoO2 layers are a key factor for the presence of complex structural properties in NaxCoO2 materials, and also demonstrate that the combination of electron diffraction and Raman spectroscopy measurements is an efficient way for studying the cation ordering and phase transitions in related systems.Comment: 22 pages, 5 figure

Three-Particle Correlations from Parton Cascades in Au+Au Collisions

We present a study of three-particle correlations among a trigger particle and two associated particles in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV using a multi-phase transport model (AMPT) with both partonic and hadronic interactions. We found that three-particle correlation densities in different angular directions with respect to the triggered particle (`center', `cone', `deflected', `near' and `near-away') increase with the number of participants. The ratio of `deflected' to `cone' density approaches to 1.0 with the increasing of number of participants, which indicates that partonic Mach-like shock waves can be produced by strong parton cascades in central Au+Au collisions.Comment: 9 pages, 6 figures; Final version to appear in Physics Letters

Scaling of anisotropy flows in intermediate energy heavy ion collisions

Anisotropic flows ($v_1$, $v_2$ and $v_4$) of light nuclear clusters are studied by a nucleonic transport model in intermediate energy heavy ion collisions. The number-of-nucleon scalings of the directed flow ($v_1$) and elliptic flow ($v_2$) are demonstrated for light nuclear clusters. Moreover, the ratios of $v_4/v_2^2$ of nuclear clusters show a constant value of 1/2 regardless of the transverse momentum. The above phenomena can be understood by the coalescence mechanism in nucleonic level and are worthy to be explored in experiments.Comment: Invited talk at "IX International Conference on Nucleus-Nucleus Collisions", Rio de Janeiro, Aug 28- Sept 1, 2006; to appear on the proceeding issue in Nuclear Physics

Di-hadron azimuthal correlation and Mach-like cone structure in parton/hadron transport model

In the framework of a multi-phase transport model (AMPT) with both partonic and hadronic interactions, azimuthal correlations between trigger particles and associated scattering particles have been studied by the mixing-event technique. The momentum ranges of these particles are $3< p^{trig}_T< 6$ GeV/$c$ and $0.15< p_{T}^{assoc} < 3$ GeV/$c$ (soft), or $2.5<p^{trig}_T<$ 4 GeV/$c$ and $1< p_{T}^{assoc} < 2.5$ GeV/$c$ (hard) in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. A Mach-like structure has been observed in correlation functions for central collisions. By comparing scenarios with and without parton cascade and hadronic rescattering, we show that both partonic and hadronic dynamical mechanisms contribute to the Mach-like structure of the associated particle azimuthal correlations. The contribution of hadronic dynamical process can not be ignored in the emergence of Mach-like correlations of the soft scattered associated hadrons. However, hadronic rescattering alone cannot reproduce experimental amplitude of Mach-like cone on away-side, and the parton cascade process is essential to describe experimental amplitude of Mach-like cone on away-side. In addition, both the associated multiplicity and the sum of $p_{T}$ decrease, whileas the $$ increases, with the impact parameter in the AMPT model including partonic dynamics from string melting scenario.Comment: 9 pages, 5 figures; Physics Letters B 641, 362-367 (2006

Dynamics of Tachyon and Phantom Field beyond the Inverse Square Potentials

We investigate the cosmological evolution of the tachyon and phantom-tachyon scalar field by considering the potential parameter $\Gamma$($=\frac{V V"}{V'^2}$) as a function of another potential parameter $\lambda$($=\frac{V'}{\kappa V^{3/2}}$), which correspondingly extends the analysis of the evolution of our universe from two-dimensional autonomous dynamical system to the three-dimension. It allows us to investigate the more general situation where the potential is not restricted to inverse square potential and .One result is that, apart from the inverse square potential, there are a large number of potentials which can give the scaling and dominant solution when the function $\Gamma(\lambda)$ equals $3/2$ for one or some values of $\lambda_{*}$ as well as the parameter $\lambda_{*}$ satisfies condition Eq.(18) or Eq.(19). We also find that for a class of different potentials the dynamics evolution of the universe are actually the same and therefore undistinguishable.Comment: 8 pages, no figure, accepted by The European Physical Journal C(2010), online first, http://www.springerlink.com/content/323417h708gun5g8/?p=dd373adf23b84743b523a3fa249d51c7&pi=