Applicability of the Friedberg-Lee-Zhao method

Friedberg, Lee and Zhao proposed a method for effectively evaluating the eigenenergies and eigen wavefunctions of quantum systems. In this work, we study several special cases to investigate applicability of the method. Concretely, we calculate the ground-state eigenenergy of the Hellmann potential as well as the Cornell potential, and also evaluate the energies of the systems where linear term is added to the Coulomb and harmonic oscillator potentials as a perturbation. The results obtained in this method have a surprising agreement with the traditional method or the numerical results. Since the results in this method have obvious analyticity compared to that in other methods, and because of the simplicity for calculations this method can be applied to solving the Schr\"{o}dinger equation and provides us better understanding of the physical essence of the concerned systems. But meanwhile applications of the FLZ method are restricted at present, especially for certain potential forms, but due to its obvious advantages, it should be further developed.Comment: 14 pages,no figure

Addendum to "Maximal regularity and Hardy spaces"

We correct an inaccuracy in a previous article [Auscher, Pascal; Bernicot, Fr\'ed\'eric; Zhao, Jiman. Maximal regularity and Hardy spaces. Collect. Math. 59 (2008), no. 1, 103-127.

Building galaxy models with Schwarzschild method and spectral dynamics

Tremendous progress has been made recently in modelling the morphology and kinematics of centers of galaxies. Increasingly realistic models are built for central bar, bulge, nucleus and black hole of galaxies, including our own. The newly revived Schwarzschild method has played a central role in these theoretical modellings. Here I will highlight some recent work at Leiden on extending the Schwarzschild method in a few directions. After a brief discussion of (i) an analytical approach to include stochastic orbits (Zhao 1996), and (ii) the ``pendulum effect'' of loop and boxlet orbits (Zhao, Carollo, de Zeeuw 1999), I will concentrate on the very promising (iii) spectral dynamics method, with which not only can one obtain semi-analytically the actions of individual orbits as previously known, but also many other physical quantities, such as the density in configuration space and the line-of-sight velocity distribution of a superposition of orbits (Copin, Zhao & de Zeeuw 1999). The latter method also represents a drastic reduction of storage space for the orbit library and an increase in accuracy over the grid-based Schwarzschild method.Comment: 11 pages including 3 ps figures, Contribution to IAU Colloquium 172 on ``Impact of Modern Dynamics in Astronomy'', July 6-11, 1998, Namur, Belgium; ed. S. Ferraz-Mello (Dordrecht:Kluwer

Soft Power to Whom? A Critical Analysis of the Publicity Film “CPC (Communist Party of China) is With You Along the Way” in Relation to China’s Soft Power Project

The existing literature on China’s soft power is mainly concerned with its success or failure, ignoring the ideological tensions between the Chinese state's international pursuit of soft power and its efforts at reviving the popularity of socialist ideology at home in a country profoundly transformed by modernisation and globalisation processes. This article argues that such ideological tensions should be contextualised and critically analysed by employing an approach informed by critical globalisation studies, particularly by the power-to-whom critique. It offers a critical analysis of the CPC is With You Along the Way film, a notable recent example of the CPC’s publicity videos in the context of its pursuit of soft power. Borrowing Reisigl and Wodak’s discourse-historical approach (DHA) in addition to the analytical devices for the study of ideology from Eagleton and van Dijk, the article argues that CPC is With You Along the Way illustrates a shift in the party’s ideological approach to the question ‘(soft) power to whom?’

Monotonicity and 1-dimensional symmetry for solutions of an elliptic system arising in Bose-Einstein condensation

We study monotonicity and 1-dimensional symmetry for positive solutions with algebraic growth of the following elliptic system: $$\begin{cases} -\Delta u = -u v^2 & \text{in $\R^N$}\\ -\Delta v= -u^2 v & \text{in $\R^N$}, \end{cases}$$ for every dimension $N \ge 2$. In particular, we prove a Gibbons-type conjecture proposed by H. Berestycki, T. C. Lin, J. Wei and C. Zhao

Oxygen-isotope effect on the in-plane penetration depth in underdoped Y_{1-x}Pr_xBa_2Cu_3O_{7-delta} as revealed by muon-spin rotation

The oxygen-isotope (^16O/^18O) effect (OIE) on the in-plane penetration depth $\lambda_{ab} (0)$ in underdoped Y_{1-x}Pr_xBa_2Cu_3O_{7-delta} was studied by muon-spin rotation. A pronounced OIE on $\lambda_{ab}^{-2}(0)$ was observed with a relative isotope shift of $\Delta\lambda^{-2}_{ab}/\lambda^{-2}_{ab}$=-5(2)% for x =0.3 and -9(2)% for x=0.4. It arises mainly from the oxygen-mass dependence of the in-plane effective mass $m_{ab}^{\ast}$. The OIE exponents of T_{c} and of $\lambda_{ab}^{-2}(0)$ exhibit a relation that appears to be generic for cuprate superconductors.Comment: 4 pages, 4 eps figures, RevTex