A reduction of canonical stability index of 4 and 5 dimensional projective varieties with large volume

We study the canonical stability index of nonsingular projective varieties of general type with either large canonical volume or large geometric genus. As applications of a general extension theorem established in the first part, we prove some optimal results in dimensions 4 and 5, which are parallel to some well-known results on surfaces and 3-folds.Comment: Final version, 35 pages, Annales de l'Institut Fourier (to appear

Varieties with vanishing holomorphic Euler characteristic II

We continue our study on smooth complex projective varieties $X$ of maximal Albanese dimension and of general type satisfying $\chi(X, \omega_X)=0$. We formulate a conjectural characterization of such varieties and prove this conjecture when the Albanese variety has only three simple factors.Comment: 27 page

Scaling in the distribution of intertrade durations of Chinese stocks

The distribution of intertrade durations, defined as the waiting times between two consecutive transactions, is investigated based upon the limit order book data of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. A scaling pattern is observed in the distributions of intertrade durations, where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve. The scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions. The ensemble distributions for all stocks are modeled by the Weibull and the Tsallis $q$-exponential distributions. Maximum likelihood estimation shows that the Weibull distribution outperforms the $q$-exponential for not-too-large intertrade durations which account for more than 98.5% of the data. Alternatively, nonlinear least-squares estimation selects the $q$-exponential as a better model, in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities. The distribution of intertrade durations is Weibull followed by a power-law tail with an asymptotic tail exponent close to 3.Comment: 16 elsart pages including 3 eps figure

On varieties of general type with many global k-forms

We study projective $n$-folds of general type with many global $k$-forms ($1\leq k\leq n$). We show that, for any nonsingular projective 3-fold $V$ of general type with either $h^{2, 0}(V)\geq 108\cdot 42^3+4$ or $\chi({\mathcal O}_V)\geq 108\cdot 42^3+5$, the $3$-canonical map is stably birational. Similarly, for any nonsingular projective 4-fold $V$ of general type with sufficiently large $h^{2, 0}(V)$, we prove that the $5$-canonical map is stably birational. We also show that the canonical stability index of any smooth projective general type $n$-fold $X$ with $q(X):=h^1({\mathcal O}_X)>n$ ($n\geq 4$) is less than or equal to the $(n-1)$-th canonical stability index $r_{n-1}$.Comment: 41 pages, comments are welcome

Magic wavelengths for the 6s^2\,^1S_0-6s6p\,^3P_1^o transition in ytterbium atom

The static and dynamic electric-dipole polarizabilities of the 6s^2\,^1S_0 and 6s6p\,^3P_1^o states of Yb are calculated by using the relativistic ab initio method. Focusing on the red detuning region to the 6s^2\,^1S_0-6s6p\,^3P_1^o transition, we find two magic wavelengths at 1035.7(2) nm and 612.9(2) nm for the 6s^2\,^1S_0-6s6p\,^3P_1^o, M_J=0 transition and three magic wavelengthes at 1517.68(6) nm, 1036.0(3) nm and 858(12) nm for the 6s^2\,^1S_0-6s6p\,^3P_1^o, M_J=\pm1 transitions. Such magic wavelengths are of particular interest for attaining the state-insensitive cooling, trapping, and quantum manipulation of neutral Yb atom.Comment: 13 pages, 3 figure