A THEOREM ON THE CONVERGENCE OF SUMS OF INDEPENDENT RANDOM VARIABLES

1 IntroductionThroughout this paperl {X., n 2 1} is assumed to be a sequence of independent randomvariables. Fn denotes the distribution function of the partial surns S. = Z Xk. As is known,k = 1oothe series Z X. is said to be essentially convergent (a.s.) if there exists a sequence of constantsn = 1oo{b., n 2 1} such that Z (X. -- 6.) a.s. converges. When this happens we writeClearlyFn(x) = G.(x -- B.). (l.2)Our problem stems from an old conjecture in Probabilistic Number Theory sugges…     

多环芳烃分子结构的距边矢量表征及其气相色谱保留指数预测

 从分子图论拓扑学角度出发 ,提出用六元素组成的分子距边矢量VMDE表达上百个多环芳烃化学结构 ,对 10 0种多环芳烃的毛细管气相色谱保留值进行定量相关性研究 ,发现存在良好的线性相关关系 :IR=a +bVMDE,n =10 0 ,r =0 .988,其中a ,b为回归系数 ,可用于多环芳烃的色谱保留指数的分子建模与定量预测。     

The extremal structures of k-uniform unicyclic hypergraphs on Wiener index

The Wiener index of a connected k-uniform hypergraph is defined as the summation of distances between all pairs of vertices. We determine the unique k-uniform unicyclic hypergraphs with maximum and second maximum, minimum and second minimum Wiener indices, respectively.     

Uniform asymptotic normality of the matrix-variate Beta-distribution

With the upper bound of Kullback-Leibler distance between a matrix variate Beta-distribution and a normal distribution, this paper gives the conditions under which a matrix-variate Beta-distribution will approach uniformly and asymptotically a normal distribution.     

Protein structure prediction from inaccurate and sparse NMR data using an enhanced genetic algorithm

Nuclear Magnetic Resonance Spectroscopy (most commonly known as NMR Spectroscopy) is used to generate approximate and partial distances between pairs of atoms of the native structure of a protein. To predict protein structure from these partial distances by solving the Euclidean distance geometry problem from the partial distances obtained from NMR Spectroscopy, we can predict three-dimensional (3D) structure of a protein. In this paper, a new genetic algorithm is proposed to efficiently address the Euclidean distance geometry problem towards building 3D structure of a given protein applying NMR's sparse data. Our genetic algorithm uses (i) a greedy mutation and crossover operator to intensify the search; (ii) a twin removal technique for diversification in the population; (iii) a random restart method to recover from stagnation; and (iv) a compaction factor to reduce the search space. Reducing the search space drastically, our approach improves the quality of the search. We tested our algorithms on a set of standard benchmarks. Experimentally, we show that our enhanced genetic algorithms significantly outperforms the traditional genetic algorithms and a previously proposed state-of-the-art method. Our method is capable of producing structures that are very close to the native structures and hence, the experimental biologists could adopt it to determine more accurate protein structures from NMR data.     

基于距离相关系数的分层聚类法

随着大数据时代的到来，各个领域涌现出海量数据且结构复杂.如变量的维数不同、尺度不同等.而现实中变量之间往往存在着不确定关系，经典的Pearson相关系数仅能反映两个同维变量间的线性相关关系，不足以完全刻画变量间的相关关系.2007年Szekely等提出的距离相关系数则能描述不同维数变量间的非线性关系.为了探索变量之间的内在信息，本文基于距离相关系数提出了最大距离相关系数法对变量聚类，且有超度量性和空间收缩性.为充分发挥距离相关系数的优势，对上述方法改进得到类整体距离相关系数法.该方法在刻画两类间相似性时，将每类中的所有变量合并成一个整体，再计算这两个不同维数的整体间的距离相关系数.最后，将类整体距离相关系数法应用到几个实际问题中，验证了算法的有效性.     

Effect of binder melt flow on the leading edge flames of solid propellant sandwiches

This study reports the effect of binder melt flow on the burning behaviour, specifically the burning rate controlling sites referred to as the leading edge flames (LEFs), of different types of sandwich propellants, namely, pure, micro-aluminized and nano-aluminized binder. The distance between the LEFs anchored over the lamina interface edges of sandwiches is measured from the combustion images captured under high spatio-temporal resolution. Similarly, the extent of binder melt flow is also measured from the quenched surfaces of sandwiches. The burning rate experiments are performed as well on sandwiches with different middle lamina contents and thicknesses at pressures of 2, 4 and 7 MPa. Two different curing agents are considered to examine the melt flow behaviour of the binder. The curing agent significantly influences the inter-LEF distance mainly in the case of pure binder sandwiches, however, its effect is negligible in aluminized binder sandwiches because of the presence of Al particles that impedes the flow to appreciable extent. Substantial protrusion of the middle lamina relative to the lamina interfaces is observed in micro-aluminized binder sandwiches due to significant accumulation of Al particles on the burning surface. In the case of nano-aluminized binder sandwiches, such protrusion is relatively marginal since nano-Al particles burn quickly, which enables the gas phase flame to locate close to the burning surface, although the extent of Al accumulation is considerably more than in the former case. This causes the nano-aluminized binder sandwiches as a whole to burn significantly faster than the other two cases in the pressure range (<7 MPa) where the LEFs predominantly control the sandwich burning rates.     

Hyperbolic smoothing and penalty techniques applied to molecular structure determination

This work considers the problem of estimating the relative positions of all atoms of a protein, given a subset of all the pair-wise distances between the atoms. This problem is NP-hard, and the usual formulations are nonsmoothed and nonconvex, having a high number of local minima. Our contribution is an efficient method that combines the hyperbolic smoothing and the penalty techniques that are useful in obtaining differentiability and reducing the number of local minima.     

含距离位势的拟线性椭圆方程解的存在性

变分原理证明了一类含距离位势的拟线性椭圆方程齐次Dirichlet边界条件下第一特征值问题的可解性.进一步,利用临界点理论得到了一类含距离位势的非线性椭圆方程非平凡解的存在性.     

Segregation characteristics of irregular binaries in gas solid fluidized beds—An ANN-approach

Binary mixtures of irregular materials of different particle sizes and/or particle densities are fluidized in a 15-cm diameter column with a perforated plate distributor. An attempt has been made in this work to determine the segregation characteristics of jetsam particles for both the homogeneous and heterogeneous binary mixtures in terms of segregation distance by correlating it to the various system parameters, viz. initial static bed height, height of a layer of particles above the bottom grid, superficial gas velocity and average particle size and/or particle densities of the mixture through the dimensional analysis. Correlation on the basis of Artificial Neural Network approach has also been developed with the above system parameters thereby authenticating the development of correlation by the former approach. The calculated values of the segregation distance obtained for both the homogeneous and heterogeneous binary mixtures from both the types of ftuidized beds （i.e. under the static bed condition and the ftuidized bed condition） have also been compared with each other.