Near-wall model for boundary layer turbulence

The evolution of an intermittently created isolated three-dimensional turbulent eddy near a wall is followed in space and time on the assumption that its structure evolves on three separate time scales, a shear interaction one, a viscous one, and a nonlinear one. The large-time limit of the solution for the shear interaction stage shows many of the observed features of the near-wall turbulence structure such as the formation of shear layers, of streaks, and of streamwise vortices. It also provides initial conditions for the viscous and nonlinear stages showing viscous decay of convected structures and the possibility of a singularity in the nonlinear development. The eddy model is also used to construct a new model for the turbulent shear stress showing strong similarity to Prandtl's mixing-length model.     

Apollonius coordinates,theN-body problem,and continuation of periodic solutions

This paper treats theN-body problem and its relation to various restricted problems. For each solution of the Kepler problem a generalization of the pulsating coordinates used to express the Hamiltonian of the elliptic restricted three-body problem is given. These coordinates are called Apollonius coordinates. The method of symplectic scaling is used to give a precise derivation of the elliptic restricted problem showing the precise asymptotic relationship between the restricted problem and the full three-body problem. This derivation obviates the proof of the fact that a nondegenerate periodic solution of the elliptic restricted three-body problem can be continued into the full three-body problem under mild nonresonance assumptions. Also, the method of symplectic scaling is used to give a precise derivation of the elliptic Hill lunar equation showing the precise relationship between the elliptic Hill lunar equation and the full three-body problem. A similar continuation theorem is established.     

中国微量元素科学研究现状、意义、问题和对策

通过"从统计数字看现状"、"从科研成果看意义"、"从社会现象看问题"和"为持续发展想对策"等四个方面高度概括了中国微量元素科学研究走过的30多年历程,为该学科今后的持续发展提供了方向性的意见和讨论的基础。     

2-（1,3-Diphenylpropen-1,3-diolato）-1,3,2-（5-formylbenzo）dioxaborol： A ＇Whole-molecule Disorder＇ Crystal Structure

The boron atom in C22H15BO5 is O,O’-chelated by the anions in a tetrahedral geometry, with the planar five-and six-membered chelate rings being orthogonal to each other. The molecule lies on a two-fold rotation axis. The molecule is disordered with respect to another molecule in a 93:7 ratio; the treatment of the ‘whole-molecule disorder’ by employing a large number of restraints is described. Crystal data: C22H15BO5, monoclinic C2/c, a = 17.1804(5), b = 12.9409(4), c = 9.8842(3) , β = 124.832(2)o, V = 1803.82(9) 3 at –173 K.     

Modelling diffraction patterns from one‐dimensionally disordered structures of AIIBVI crystals by Monte Carlo Technique IV. The 6H structure with different kinds of stacking faults

To investigate the one‐dimensionally disordered structures (ODDS) in the close packed (cp) crystals, the Monte Carlo computer simulation technique has been applied. Calculations of the diffraction intensity distributions along the 10.L reciprocal lattice row from the 6H(33) structure with the four different kinds of the stacking faults (SFs): growth, deformation, layer displacement and extrinsic fault are presented. In particular, using the simple frequency functions of the fault to fault distances, both random and non‐random distributions of the SFs are considered. Distinctive features of the diffraction patterns corresponding to the chosen examples of the transformations from the parent 6H(33) structure into another small‐period polytypes are discussed in detail. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantum annealing of the graph coloring problem

Quantum annealing extends simulated annealing by introducing artificial quantum fluctuations. The path-integral Monte Carlo version chosen is population-based and designed to be implemented on a classical computer. Its first application to the graph coloring problem is presented in this paper. It is shown by experiments that quantum annealing can outperform classical thermal simulated annealing for this particular problem. Moreover, quantum annealing proved competitive when compared with the best algorithms on most of the difficult instances from the DIMACS benchmarks. The quantum annealing algorithm has even found that the well-known benchmark graph dsjc1000.9 has a chromatic number of at most 222. This is an improvement on its best upper-bound from a large body of literature.     

高师院校复变函数课程教学改革的探索

结合多年的教学实践和高师院校的特点,分析了复变函数课程教学中存在的问题,并提出了一些教学改革设想,如改革课程内容,进行教材建设,渗透数学文化,加强网络教学等,期望能为该课程的教学改革抛砖引玉.     

一类具幂零奇点的五次系统中心条件及极限环分支

In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 8 quasi Lyapunov constants are deduced. As a result, the necessary and sufficient conditions to have a center are obtained. The fact that there exist 8 small amplitude limit cycles created from the three-order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems.     

具线性退化特征场对角型方程组Goursat问题的奇性形成机制

For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C^1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C^1 classical solution to the Goursat problem with C^1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C^0 compatibility conditions at the origin.