Gravitational Collapse of Self-Similar Perfect Fluid in 2 + 1 Gravity

Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. These include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind, and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth and second kinds. It is found that some of these solutions represent gravitational collapse, and the final state of the collapse can be either a black hole or a null singularity. It is also shown that one solution can have two different kinds of kinematic self-similarity.     

利用模式的对称性研究光子晶体光纤的色散

由光子晶体光纤的对称性可以得到模式分布的对称性，根据模式的对称性选择适当的展开函数，可以使计算量大大减少。计算了六角结构光子晶体光纤的色散特性，得到了波长在1．55pm处色散为零时，光子晶体光纤的结构参量所满足的方程。     

多目标半定规划的互补弱鞍点和G-鞍点最优性条件

对于含矩阵函数半定约束和多个目标函数的多目标半定规划问题，给出Lagrange函数在弱有效意义下的互补弱鞍点和Geofrrion恰当有效意义下的G-鞍点的定义及其等价定义．然后，在较弱的凸性条件下，利用含矩阵和向量约束的择一性定理，建立多目标半定规划的互补弱鞍点和G-鞍点充分必要条件．     

Hydrogen indium vacancy complex VInH4 in n-type InP studied by positron-lifetime

Positron-lifetime experiments have been carried out on two undoped n-type liquid encapsulated Czochralski (LEC)-grown InP samples with different stoichiometric compositions in the temperature range 10-300 K. For temperatures below 120 K for P-rich InP and 100 K for In-rich InP, the positron average lifetime began to increase rapidly and then leveled off, which was associated with the charge state change of hydrogen indium vacancy complexes from (V_InH₄)⁺ to (V_InH₄)⁰. This phenomenon was more obvious in P-rich samples that have a higher concentration of V_InH₄. The transformation temperature of approximately 120 K suggests that the complex V_InH₄ is a donor defect and that the ionization energy is about 0.01 eV. The ionization of neutral V_InH₄ accounted for the decrease of the positron average lifetime when the sample was illuminated with a photon energy of 1.32 eV at 70 K. These results provide evidence for hydrogen complex defects in undoped LEC InP.     

Ultrafast carrier dynamics in ferromagnetic InGaMnAs

We have carried out an ultrafast time-resolved differential reflectivity study of a ferromagnetic semiconductor InGaMnAs and made a systematic comparison with low-temperature grown and high-temperature grown InGaAs reference films. Very short carrier lifetimes (2 ps) were observed in InGaMnAs and the low-temperature grown InGaAs film, but not in the high-temperature grown InGaAs film. We attribute the short lifetimes to carrier trapping by mid-gap states introduced during low-temperature MBE growth. Furthermore, at long times, we observed periodic oscillations in the differential reflectivity signal with period 20 ps, which we interpret as coherent acoustic phonons.     

一类非线性退化方程混合问题解的渐进性态

本文利用比较原理以及一种特殊变换研究了一类非线性退化方程的混合问题，得到了这类复杂问题解的渐进性质。     

Enhancement of the Kerr effect for a quantum dot in a cavity

Nonlinear susceptibility of a quantum dot (QD) embedded in a two-sided cavity, is studied theoretically from a weak-coupling to a strong-coupling regime. In the relevance of a quantum logic gate, the corresponding nonlinear phase shifts (Kerr effect) are estimated for coherent wavepackets including one photon on average. In the weak-coupling regime, the phase shift enhances strongly as a function of a coupling constant between the cavity photon and QD, and eventually saturates in the strong-coupling regime. We also show transmission spectra to evaluate the efficiency of the phase shift. Although the efficiency decreases monotonically in the weak-coupling regime, it rises in the strong-coupling regime.     

Optimal Path Planning Based on Visibility

Various problems associated with optimal path planning for mobile observers such as mobile robots equipped with cameras to obtain maximum visual coverage of a surface in the three-dimensional Euclidean space are considered. The existence of solutions to these problems is discussed first. Then, optimality conditions are derived by considering local path perturbations. Numerical algorithms for solving the corresponding approximate problems are proposed. Detailed solutions to the optimal path planning problems for a few examples are given.     

Pressure induced transitions in calcium: a tight-binding approach

A tight-binding (TB) hamiltonian for calcium is built with a high precision parametrization technique based on density functional calculations of the energy bands and the total energy at various lattice volumes. The new set of TB parameters is appropriate to study phenomena under pressures as high as 20 GPa. Specifically, both the metal to nonmetal transition at 4 GPa and the structural transition fcc to bcc at 19 GPa are well reproduced. These transitions and several static properties are in excellent agreement with experiments. Phonon frequencies, plasmon energy, melting temperature and the coefficient of thermal expansion were calculated with a molecular dynamics scheme of this TB hamiltonian.     

20-relative neighborhood graphs are hamiltonian

For any two points p and q in the Euclidean plane, define LUN_pq = { v | v ∈ R², d_pv < d_pq and d_qv < d_pq}, where d_uv is the Euclidean distance between two points u and v . Given a set of points V in the plane, let LUN_pq(V) = V ∩ LUN_pq. Toussaint defined the relative neighborhood graph of V, denoted by RNG(V) or simply RNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of RNG(V) if and only if LUN_pq (V) = ?. The relative neighborhood graph has several applications in pattern recognition that have been studied by Toussaint. We shall generalize the idea of RNG to define the k-relative neighborhood graph of V, denoted by kRNG(V) or simply kRNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of kRNG(V) if and only if | LUN_pq(V) | < k, for some fixed positive number k. It can be shown that the number of edges of a kRNG is less than O(kn). Also, a kRNG can be constructed in O(kn₂) time. Let E_c = {e_pq| p ∈ V and q ∈ V}. Then G_c = (V,E_c) is a complete graph. For any subset F of E_c, define the maximum distance of F as max_epq∈Fd_pq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph G_c whose maximum distance is the minimum among all Hamiltonian cycles in graph G_c. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian.