Asymptotics on Two-dimensional Recursion Sequences

In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.     

化学计量是传感器系统开发的关键

介绍了化学计量技术——组合分析在灵敏传感器系统元件优选中的应用     

第二类Stirling数的一个公式

In this paper, We propose and prove the following equation, where is a Stirling number of the second kind, when n≥3 is given.     

变系数二元线性差分方程解的显式表示

文章讨论了变系数二元线差分方程求解公式,并给出两个应用实例。     

一类超椭圆方程的整数解

设ｍ，ｎ∈Ｎ；ｍ≥２，ｎ≥２，ｍｎ≥６，ｆ（ｘ）＝ｘｍ＋ａ１ｘｍ－１＋…＋ａｍ∈Ｚ［ｘ］，Ｈ＝ｍａｘ（｜ａ１｜，…，｜ａｍ｜）．本文运用组合分析方法证明了：当ｍ≡０（ｍｏｄｎ），ａ１，…，ａｍ不全为零，而且其中第一个非零系数ａｓ与ｎ互素时，方程ｆ（ｘ）＝ｙｎ，ｘ，ｙ∈Ｚ，仅有有限多组解（ｘ，ｙ），而且这些解都满足｜ｘ｜＜（４ｍＨ）２ｍ／ｎ＋１以及｜ｙ｜＜（４ｍＨ）４ｍ２／ｎ２＋ｍ／ｎ＋１     

Depth in bucket recursive trees with variable capacities of buckets

We consider bucket recursive trees of sizen consisting of all buckets with variable capacities1,2,...,b and with a specifc stochastic growth rule.This model can be considered as a generalization of random recursive trees like bucket recursive trees introduced by Mahmoud and Smythe where all buckets have the same capacities.In this work,we provide a combinatorial analysis of these trees where the generating function of the total weights satisfes an autonomous frst order diferential equation.We study the depth of the largest label（i.e.,the number of edges from the root node to the node containing label n）and give a closed formula for the probability distribution.Also we prove a limit law for this quantity which is a direct application of quasi power theorem and compute its mean and variance.Our results for b=1 reduce to the previous results for random recursive trees.     

A new triterpenoid saponin from the leaves and stems of Panax quinquefolium L.

One new triterpenoid saponin,quinquenoside L_(17)(1),was isolated from the leaves and stems of Panax quinquefolium L.,and its structure was elucidated as 20-O-[(β-D-xylopyranosyl-(1-6)-O-β-D-glucopyranosyl)]-6-O-β-D-glucopyranosyl-dammar-24-ene- 3,6,12,20-tetraol,by the combination analysis of one-dimensional NMR and two-dimensional NMR,mass spectrometry,CD spectrum and chemical evidences.     

组合分析浅释

组合分析是为研、发新化学品(特别是新药)服务的,研、发新化学品历来遵循两条路线①是设计路线,即从主观思维出发,在经受客观检验的过程中进行不断修改,以求得主、客观的统一;②是筛选路线,即从客观出发,进行“神农尝百草”的寻找。这两条路线的缺点是明显的,旷日持久,宛如大海捞针,很可能徒劳无功,研、发的风险很大。     

关于组合和的超几何级数方法

本文旨在通过精选的例证,阐明关于组合和计算的一种极受重视的有效方法,即超几何级数的嵌入法。最后一节对三种典型方法作了简要的比较分析,述及作者自己的成果及见解。