Thermodynamics of Third Order Lovelock Anti-de Sitter Black Holes Revisited

We compute the mass and temperature of third order Lovelock black holes with negative Gauss-Bonnet coefficient a2 〈 0 in anti-de Sitter space and perform the stability analysis of topological black holes. When k = -1, the third order Lovelock black holes are thermodynamically stable for the whole range r＋. When k = 1, we found that the black hole has an intermediate unstable phase for D = 7. In eight dimensional spacetimes, however, a new phase of thermodynamically unstable small black holes appears if the coefficient a is under a critical value. For D ≥ 9, black holes have similar the distributions of thermodynamically stable regions to the case where the coefficient ＆ is under a critical value for D = 8. It is worth to mention that all the thermodynamic and conserved quantities of the black holes with fiat horizon do not depend on the Loveloek coefficients and are the same as those of black holes in general gravity.

sl(1|2)Super-Toda Fields

Explicit exact solution of supersymmetric Toda fields associated with the Lie superalgebra s/（2｜ 1） is constructed. The approach used is a super extension of Leznov-Saveliev algebraic analysis, which is based on a pair of chiral and antichiral Drienfeld-Sokolov systems. Though such approach is well understood for Toda field theories associated with ordinary Lie algebras, its super analogue was only successful in the super Liouville case with the underlying Lie superalgebra osp（1｜2）. The problem lies in that a key step in the construction makes use of the tensor product decom- position of the highest weight representations of the underlying Lie superalgebra, which is not clear until recently. So our construction made in this paper presents a first explicit example of Leznov-Saveliev analysis for super Toda systems associated with underlying Lie superalgebras of the rank higher than 1.

Long-Lived Rogue Waves and Inelastic Interaction in Binary Mixtures of Bose–Einstein Condensates

We investigate bright,dark and two rogue waves in two-component Bose–Einstein condensates.It is found that one rogue wave of a new structure that contains two humps and two valleys around one center in the temporal-spatial distribution interacts with the conventional rogue wave.We present an effective way to obtain long-lived rogue waves through managing the nonlinear interaction with modulating trapping frequency and interchange atoms between thermal clouds and condensates.The results provide many possibilities to manipulate rogue waves experimentally in the condensate system.

Thermodynamics of Slowly Rotating Charged Black Holes in Anti-de Sitter Einstein-Gauss-Bonnet Gravity

By using a new approach,we demonstrate the analytic expressions for slowly rotating Gauss-Bonnet charged black hole solutions with one non-vanishing angular momentum in higher-dimensional anti-de Sitter spaces.Up to linear order of the rotating parameter a,the mass,Hawking temperature and entropy of the charged black holes get no corrections from rotation.

Static spherically symmetric star in Gauss-Bonnet gravity

We explore static spherically symmetric stars in Gauss-Bonnet gravity without a cosmological constant, and present an exact internal solution which attaches to the exterior vacuum solution outside stars. It turns out that the presence of the Gauss-Bonnet term with a positive coupling constant completely changes thermal and gravitational energies, and the upper bound of the red shift of spectral lines from the surface of stars. Unlike in general relativity, the upper bound of the red shift is dependent on the density of stars in our case. Moreover, we have proven that two theorems for judging the stability of equilibrium of stars in general relativity can hold in Gauss-Bonnet gravity.

A Note on Homogenization of Parabolic Equation in Perforated Domains

We are concerned with a class of parabolic equations in periodically perforated domains with a homogeneous Neumann condition on the boundary of holes.By using the periodic unfolding method in perforated domains, we obtain the homogenization results under the conditions slightly weaker than those in the corresponding case considered by Nandakumaran and Rajesh（Nandakumaran A K, Rajesh M. Homogenization of a parabolic equation in perforated domain with Neumann boundary condition. Proc. Indian Acad. Sci.（Math. Sci.）, 2002, 112（1）： 195–207）. Moreover,these results generalize those obtained by Donato and Nabil（Donato P, Nabil A. Homogenization and correctors for the heat equation in perforated domains. Ricerche di Matematica L. 2001, 50： 115–144）.

Unitary Transformation in kq Representation

In this paper,we discuss the unitary transformation induced by Z_6 rotations of noncommutative space onthe states |k,q,s〉,which plays a key role in construction for noncommutative solitons T^2/Z_6 by GHS method.As aresult,we prove a well-known 'Gauss Sum' formula in the number theory through a concise way.

关于高压液压油输送管在渣土环境中使用的寿命研究

针对隧道掘进机高压液压油输送管在渣土环境中表面容易被磨损的问题,通过选取不同的保护措施,通过相关材质及制造工艺的分析及比较,为了提高使用寿命,提出了一种新形式的组合保护方案,为高压液压油输送管的制作提供了可借鉴方案。

Dynamics of Nonautonomous Dark Solitons

We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton （∈2 ≠ 1） while it has no effects on the wave central position. Moreover, the precise expressions of a nonautonomous black soliton＇s （∈2 = 1） width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton＇s evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.