Quasinormal Modes of Self-Dual Warped AdS3_3 Black Hole in Topological Massive Gravity

We consider the various perturbations of self-dual warped AdS$_3$ black hole and obtain the exact expressions of quasinormal modes by imposing the vanishing Dirichlet boundary condition at asymptotic infinity. It is expected that the quasinormal modes agree with the poles of retarded Green's functions of the dual CFT. Our results provide a quantitative test of the warped AdS/CFT correspondence.Comment: 10 pages, no figure, some references and comments on gravitational perturbations are adde

Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpi\'nski gasket

The anisotropic antiferromagnetic Ising model on the fractal Sierpi\'{n}ski gasket is intensively studied, and a number of exotic properties are disclosed. The ground state phase diagram in the plane of magnetic field-interaction of the system is obtained. The thermodynamic properties of the three plateau phases are probed by exploring the temperature-dependence of magnetization, specific heat, susceptibility and spin-spin correlations. No phase transitions are observed in this model. In the absence of a magnetic field, the unusual temperature dependence of the spin correlation length is obtained with $0 \leq$J$_b/$J$_a<1$, and an interesting crossover behavior between different phases at J$_b/$J$_a=1$ is unveiled, whose dynamics can be described by the J$_b/$J$_a$-dependence of the specific heat, susceptibility and spin correlation functions. The exotic spin-spin correlation patterns that share the same special rotational symmetry as that of the Sierpi\'{n}ski gasket are obtained in both the $1/3$ plateau disordered phase and the $5/9$ plateau partially ordered ferrimagnetic phase. Moreover, a quantum scheme is formulated to study the thermodynamics of the fractal Sierpi\'{n}ski gasket with Heisenberg interactions. We find that the unusual temperature dependence of the correlation length remains intact in a small quantum fluctuation.Comment: 9 pages, 12 figure

Synthesis and Optimization of Visible Light Active BiVO 4

Monoclinic BiVO4 powders were synthesized via a novel route using potassium metavanadate (KVO3) prepared by calcination of K2CO3 and V2O5 as a starting material and followed by hydrothermal treatment and were investigated for the degradation of Rhodamine B (RhB) under visible light irradiation. The synthesized BiVO4 particles were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and UV-Visible (UV-Vis) light diffuse reflectance spectrophotometry. The synthesis produced pure monoclinic BiVO4 particles with multimorphological features containing flower-like, flake-ball, flake, cuboid-like, and plate-like shapes and exhibited strong absorption in the visible light range. The BiVO4 prepared via KVO3 possessed excellent photocatalytic activity for the degradation of RhB under visible light. The performance of this catalyst was found to be superior to other BiVO4 photocatalysts prepared via ammonium metavanadate (NH4VO3) using coprecipitation, combustion, and calcination methods reported in literature, respectively

Inner topological structure of Hopf invariant

In light of $\phi$-mapping topological current theory, the inner topological structure of Hopf invariant is investigated. It is revealed that Hopf invariant is just the winding number of Gauss mapping. According to the inner structure of topological current, a precise expression for Hopf invariant is also presented. It is the total sum of all the self-linking and all the linking numbers of the knot family.Comment: 13pages, no figure. Accepted by J.Math.Phy

Sustainable development with geomatics

Learning for service is the main objective in service learning, students in the Hong Kong Polytechnic University (PolyU) are encouraged to apply their learning outcomes to serve the community for rather long term benefits. This paper will discuss how PolyU students with Geomatics knowledge committed a service learning project with local social enterprises-Hosteling International. Together with students from both Peking University and Yunnan University with different disciplines, a group of students from PolyU joined a service learning project in Yunnan. These students applied their knowledge in mapping and other professional skills to serve the community at Yuan Jie Township by enhancing guest reception capabilities of a local Youth Hostel. They crossed over between learning and serving. They learnt the difficulties in local community development with SWOT analysis approach to their collected local information and identified focus of their service through the inter-disciplines dialogues in this student group. They aware that people can use all forms of tools, like web maps to obtain geographical information about the surrounding areas in the well-developed cities, but as the infrastructure was not as well-developed in local as their living community in city. Local community and travelers had no such access in Tuan Jie Township, making the locals difficult to identify the natural resources and assets surrounding them and travelers not able to navigate around during their visits. By using Global Positioning System (GPS) and GeoIT technique, students collected important geographical information, survey the map and painted it on the wall of youth hostel. This helped to empower the local community development in recognizing and promoting their rural assets to visitors and in long-run revitalize the local community for future local cultural conservation and youth development. They also arranged the map application workshop to teach local kids map reading and applications so that they could ascertain the local youth identity and introduce this special community to visitors