[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal ${\cal R}$ matrix can be constructed directly as a quantum double intertwiner, without using Reshetikhin's transformation. An interesting feature automatically appears in the representation theory: it can be divided into two types, one for generic $q$, the other for $q$ being a root of unity. When applying the representation theory to the multiparameter universal ${\cal R}$ matrix, the so called standard and nonstandard colored solutions $R(\mu,\nu; {\mu}', {\nu}')$ of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure

Y(so(5)) symmtry of the nonlinear Schro¨\ddot{o}dinger model with four-cmponents

The quantum nonlinear Schr$\ddot{o}$dinger(NLS) model with four-component fermions exhibits a $Y(so(5))$ symmetry when considered on an infintite interval. The constructed generators of Yangian are proved to satisfy the Drinfel'd formula and furthermore, the $RTT$ relation with the general form of rational R-matrix given by Yang-Baxterization associated with $so(5)$ algebraic structure.Comment: 10 pages, no figure

Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown

Semiclassical results are usually expected to be valid in the semiclassical regime. An interesting question is, in models in which appropriate effective Planck constants can be introduced, to what extent will a semiclassical prediction stay valid when the effective Planck constant is increased? In this paper, we numerically study this problem, focusing on semiclassical predictions for the decay of the quantum Loschmidt echo in deep quantum regions. Our numerical simulations, carried out in the chaotic regime in the sawtooth model and in the kicked rotator model and also in the critical region of a 1D Ising chain in transverse field, show that the semiclassical predictions may work even in deep quantum regions, in particularly, for perturbation strength in the so-called Fermi-Golden-rule regime.Comment: 8 pages, 10 figures. Published versio

Characterization of Zika virus endocytic pathways in human glioblastoma cells

Zika virus (ZIKV) infections can cause microcephaly and neurological disorders. However, the early infection events of ZIKV in neural cells remain to be characterized. Here, by using a combination of pharmacological and molecular approaches and the human glioblastoma cell T98G as a model, we first observed that ZIKV infection was inhibited by chloroquine and NH4Cl, indicating a requirement of low intracellular pH. We further showed that dynamin is required as the ZIKV entry was affected by the specific inhibitor dynasore, small interfering RNA (siRNA) knockdown of dynamin, or by expressing the dominant-negative K44A mutant. Moreover, the ZIKV entry was significantly inhibited by chlorpromazine, pitstop2, or siRNA knockdown of clathrin heavy chain, indicating an involvement of clathrin-mediated endocytosis. In addition, genistein treatment, siRNA knockdown of caveolin-1, or overexpression of a dominant-negative caveolin mutant impacted the ZIKV entry, with ZIKV particles being observed to colocalize with caveolin-1, implying that caveola endocytosis can also be involved. Furthermore, we found that the endocytosis of ZIKV is dependent on membrane cholesterol, microtubules, and actin cytoskeleton. Importantly, ZIKV infection was inhibited by silencing of Rab5 and Rab7, while confocal microscopy showed that ZIKV particles localized in Rab5- and Rab7-postive endosomes. These results indicated that, after internalization, ZIKV likely moves to Rab5-positive early endosome and Rab7-positive late endosomes before delivering its RNA into the cytoplasm. Taken together, our study, for the first time, described the early infection events of ZIKV in human glioblastoma cell T98G