Abstract:
Spatial topology rule is the primary method to insure the consistency and validity of spatial topology relation in GIS software. Topology rule can be divided into three categories according to geographic entity’s geometric shape: point topology rule, line topology rule and polygon topology rule. At first, this paper summarizes the various linear geographic entities’ topological relations which have practical application, then designs a series of linear entity topology rules detailedly. Based on these rules, this paper proposes a topology rule checking algorithm using quadtree, which is designed on the basis of MAPGIS7.4 spatial data model. The algorithm has already been applied to MAPGIS platform and gained good effects.

Abstract:
The study in this paper
analyzes and compares the distribution on the global engine active seismic zone
and cooling seismic belt basing on the ANSS earthquake catalog from Northern
California Earthquake Data Center. An idea of the seismogenesis and earthquake
prediction research is achieved by showing the stratigraphic structure in the
hot engine belt. The results show that the main engine and its seismic cones
are the global seismic activity area, as well as the subject of global
geological disaster. Based on the conjecture of other stratum structure, the
energy of crustal strong earthquake and volcano activities probably originates
from the deep upper mantle. It is suggested that the research on earthquake and
volcano prediction should focus on the monitor and analysis on the sub-crustal
earthquake activities.

Abstract:
In this paper we use the semiclassical Boltzmann equation to investigate the transport properties of Dirac fermion on the surface of topological insulator with magnetic impurities. The results obtained show that there is also a minimal conductivity in this system as in graphene. We also argue the low temperature transport property, and find that there is no low temperature anomaly known as Kondo effect when the temperature is T>10^{-6}K.

Abstract:
We generalize the calculation of Casimir interaction between topological insulators with opposite topological magnetoelectric polarizabilities and finite surface band gaps to finite Temperature cases. We find that finite temperature quantitatively depress the repulsive peak and enlarge the critical surface gap $m_c$ for repulsive Casimir force. However the universal property $m_c a \sim 1/2$ is still valid for various oscillation strength, temperature region and topological magnetoelectric polarizabilities.

Abstract:
We propose three possible momentum-dependent pairing potentials for candidate of topological superconductor (for example Cu$_x$Bi$_2$Se$_3$), and calculate the surface spectral function and surface density of state with these pairing potentials. We find that the first two can give the same spectral functions as the fully-gapped and node-contacted pairing potentials given in [Phys. Rev. Lett. 105, 097001], and that the third one can obtain topological non-trivial case which exists flat Andreev bound state and preserves the $C_3$ rotation symmetry. We hope our proposals and results be judged by future experiment.

Abstract:
We study the star lattice with Rashba spin-orbit coupling and exchange field and find that there exists the quantum anomalous Hall effect in this system and there are five energy gaps at Dirac points and quadratic band crossing points. We calculate the Berry curvature distribution and obtain the Hall conductivity (Chern number $\nu$) quantized as integers, and find that $\nu=-1,2,1,1,2$, respectively, when the Fermi level lies in these five gaps. Our model can be view as a general quantum anomalous Hall system and, in limit cases, can give what the honeycomb lattice and kagome lattice gave. We also find there exists a nearly flat band with $\nu=1$ which may provide an opportunity to realize the fractional quantum anomalous Hall effect. Finally, the chiral edge states on a zigzag star lattice are given numerically to confirm the topological property of this system.

Abstract:
We show that (1) the newly discovered supernova remnant (SNR), GRO J0852--4642/RX J0852.0--4622, was created by a core-collapse supernova of a massive star, and (2) the same supernova event which produced the $^{44}$Ti detected by COMPTEL from this source is probably also responsible for a large fraction of the observed $^{26}$Al emission in the Vela region detected by the same instrument. The first conclusion is based on the fact that the remnant is currently expanding too slowly given its young age for it to be caused by a Type Ia supernova. If the current SNR shell expansion speed is greater than 3000 km/s, a $15 M_\odot$ Type II supernova with a moderate kinetic energy exploding at about 150 pc away is favored. If the SNR expansion speed is lower than 2000 km s$^{-1}$, as derived naively from the X-ray data, a much more energetic supernova is required to have occurred at $\sim250$ pc away in a dense environment at the edge of the Gum nebula. This progenitor has a preferred ejecta mass of $\le10 M_\odot$ and therefore, it is probably a Type Ib or Type Ic supernova. However, the required high ambient density of $n_H \ge 100 cm^{-3}$ in this scenario is difficult to reconcile with the regional CO data. A combination of our estimates of the age/energetics of the new SNR and the almost perfect positional coincidence of the new SNR with the centroid of the COMPTEL $ ^{26}$Al emission feature of the Vela region strongly favors a causal connection. If confirmed, this will be the first case where both $^{44}$Ti and $^{26}$Al are detected from the same young SNR and together they can be used to select preferred theoretical core-collapse supernova models.

Abstract:
Casimir interaction between topological insulators with opposite topological magnetoelectric polarizabilities and finite surface band gaps has been investigated. For large surface band gap limit$(m\rightarrow\infty)$, we can obtain results given in [Phys. Rev. Lett. \textbf{106}, 020403 (2011)]. For small surface band gap limit$(m\rightarrow0)$, Casimir interaction between topological insulators is attractive and analogy to ideal mental in short separation limit. Generally, there is a critical value $m_c$ and when the surface band gap is greater than the critical value, the Casimir force is repulsive in an intermediate separation region. We estimate the critical surface band gap $m_c \sim 1/(2a)$, where $a$ is a critical separation where Casimir force vanishes.

Abstract:
This paper describes a technique to determine the linear well-posedness of a general class of vector elliptic problems that include a steady interface, to be determined as part of the problem, that separates two subdomains. The interface satisfies mixed Dirichlet and Neumann conditions. We consider ``2+2'' models, meaning two independent variables respectively on each subdomain. The governing equations are taken to be vector Laplacian, to be able to make analytic progress. The interface conditions can be classified into four large categories, and we concentrate on the one with most physical interest. The well-posedness criteria in this case are particularly clear. In many physical cases, the movement of the interface in time-dependent situations can be reduced to a normal motion proportional to the residual in one of the steady state interface conditions (the elliptic interior problems and the other interface conditions are satisfied at each time). If only the steady state is of interest, one can consider using other residuals for the normal velocity. Our analysis can be extended to give insight into choosing residual velocities that have superior numerical properties. Hence, in the second part, we discuss an iterative method to solve free boundary problems. The advantages of the correctly chosen, non-physical residual velocities are demonstrated in a numerical example, based on a simplified model of two-phase flow with phase change in porous media.

Abstract:
Covering model provides a general framework for granular computing in that overlapping among granules are almost indispensable. For any given covering, both intersection and union of covering blocks containing an element are exploited as granules to form granular worlds at different abstraction levels, respectively, and transformations among these different granular worlds are also discussed. As an application of the presented multi-granular perspective on covering, relational interpretation and axiomization of four types of covering based rough upper approximation operators are investigated, which can be dually applied to lower ones.