粒子-转子模型和推转壳模型中的能谱统计分析

用粒子–转子模型和推转壳模型研究了6个粒子分别填充在单j壳和双j壳上的混沌行为.分析了单j壳和双j壳情况下能谱的最近邻能级间距分布和谱刚度随自旋及推转频率的变化,结果表明,当组态空间大小不变时,系统在双j壳(g_7/2+d_5/2)情况下比在单j壳(i_13/2)情况下更规则,而当组态空间从单j壳(i_13/2)扩大到双j壳(i_13/2+g_9/2)时,系统的混沌程度变化不大.同时比较了将6个粒子的两体相互作用分别取为δ力和对力时的系统的混沌行为     

Searching for a near neighbor particle in DSMC cells using pseudo-subcells

LeBeau et al. (2003) [4] introduced the ‘virtual-subcell’ (VSC) method of finding a collision partner for a given DSMC particle in a cell; all potential collision partners in the cell are examined to find the nearest neighbor, which becomes the collision partner. Here I propose a modification of the VSC method, the ‘pseudo-subcell’ (PSC) method, whereby the search for a collision partner stops whenever a ‘near-enough’ particle is found, i.e. whenever another particle is found within the ‘pseudo-subcell’ of radius δ centered on the first particle. The radius of the pseudo-subcell is given by δ = Fd_n, where d_n is the expected distance to the nearest neighbor and F is a constant which can be adjusted to give a desired trade-off between CPU time and accuracy as measured by a small mean collision separation (MCS). For 3D orthogonal cells, of various aspect ratios, d_n/L ≈ 0.746/N^0.383 where N is the number of particles in the cell and L is the cube root of the cell volume. There is a good chance that a particle will be found in the pseudo-subcell and there is a good chance that such a particle is in fact the nearest neighbor. If no particle is found within the pseudo-subcell the closest particle becomes the collision partner.     

Increasing the polynomial reproduction of a quasi-interpolation operator

Quasi-interpolation is an important tool, used both in theory and in practice, for the approximation of smooth functions from univariate or multivariate spaces which contain , the d-variate polynomials of degree ≤m. In particular, the reproduction of Π_m leads to an approximation order of m+1. Prominent examples include Lagrange and Bernstein type approximations by polynomials, the orthogonal projection onto Π_m for some inner product, finite element methods of precision m, and multivariate spline approximations based on macroelements or the translates of a single spline.For such a quasi-interpolation operator L which reproduces and any r≥0, we give an explicit construction of a quasi-interpolant which reproduces Π_m+r, together with an integral error formula which involves only the (m+r+1)th derivative of the function approximated. The operator is defined on functions with r additional orders of smoothness than those on which L is defined. This very general construction holds in all dimensions d. A number of representative examples are considered.     

QSPR Modeling of Gibbs Free Energy of Organic Compounds by Weighting of Nearest Neighboring Codes

We examine the encoding of chemical structure of organic compounds by Labeled Hydrogen-Filled Graphs (LHFGs). Quantitative Structure-Property Relationships (QSPR) for a representative set of 150 organic molecules have been derived by means of the optimization of correlation weights of local invariants of the LHFGs. We have tested as local invariants Morgan extended connectivity of zero- and first order, numbers of path of length 2 (P2) and valence shells of distance of 2 (S2) associated with each atom in the molecular structure, and the Nearest Neighboring Codes (NNC). The best statistical characteristics for the Gibbs free energy has been obtained for the NNC weighting. Statistical parameters corresponding to this model are the following n = 100, r² = 0.9974, s = 5.136 kJ/mol, F = 38319 (training set); n = 50, r² = 0.9990, s = 3.405 kJ/mol, F = 48717 (test set). Some possible further developments are pointed out.     

A proof of Markov's theorem for polynomials on Banach spaces

Our object is to present an independent proof of the extension of V.A. Markov's theorem to Gâteaux derivatives of arbitrary order for continuous polynomials on any real normed linear space. The statement of this theorem differs little from the classical case for the real line except that absolute values are replaced by norms. Our proof depends only on elementary computations and explicit formulas and gives a new proof of the classical theorem as a special case. Our approach makes no use of the classical polynomial inequalities usually associated with Markov's theorem. Instead, the essential ingredients are a Lagrange interpolation formula for the Chebyshev nodes and a Christoffel-Darboux identity for the corresponding bivariate Lagrange polynomials. We use these tools to extend a single variable inequality of Rogosinski to the case of two real variables. The general Markov theorem is an easy consequence of this.     

两点正则问题的多元H—B插值

研究两点正则问题的多元Ｈ－Ｂ插值，给出其插值算子及余项表达式。     

On an extreme class of real interpolation spaces

We investigate the limit class of interpolation spaces that comes up by the choice θ=0 in the definition of the real method. These spaces arise naturally interpolating by the J-method associated to the unit square. Their duals coincide with the other extreme spaces obtained by the choice θ=1. We also study the behavior of compact operators under these two extreme interpolation methods. Moreover, we establish some interpolation formulae for function spaces and for spaces of operators.