模糊数学理论在水库长期径流预报中的应用

本文运用模糊数学的理论方法对汛期径流预报进行了探讨 ,即首先对汛期来水的理论实测资料 ,运用最大树法和软化分法进行了模糊聚类分析 ,得到汛期来水的多个预报模式 ;进而利用Gamma分布和模糊概率的方法 ,预报出汛期的来水流量及其实现的概率     

On covering vertices of a graph by trees

The purpose of this paper is to initiate study of the following problem: Let G be a graph, and k?1. Determine the minimum number s of trees T₁,…,T_s, Δ(T_i)?k,i=1,…,s, covering all vertices of G. We conjecture: Let G be a connected graph, and k?2. Then the vertices of G can be covered by edge-disjoint trees of maximum degree ?k. As a support for the conjecture we prove the statement for some values of δ and k.     

A distance approximating trees

A 1-approximation of connected graph G=(V,E) is a tree T=(V,E^′) with the same vertex set such that for every two vertices |d_G(u,v)−d_T(u,v)|1. A polynomial time algorithm is designed for finding such a tree.     

The Design of Second-order Nonlinear Optical Dendrimers: From “Branch Only” to “Root Containing”

Dendrimers are considered as a promising family of organic second-order nonlinear optical (NLO) polymers because of their well-defined structures,easily modified peripheral functional groups,interior branches and central cores.In order to obtain NLO materials with high performance,dendrimer structures have been optimized in the past years,such as the "branch only" and the "root containing" type dendrimers.This feature article highlights the achievements in exploring the rational design of dendrimers,partially marked by their macroscopic NLO performance.     

A subdiffusive behaviour of recurrent random walk in random environment on a regular tree

We are interested in the random walk in random environment on an infinite tree. Lyons and Pemantle (Ann. Probab. 20, 125–136, 1992) give a precise recurrence/transience criterion. Our paper focuses on the almost sure asymptotic behaviours of a recurrent random walk (X _n ) in random environment on a regular tree, which is closely related to Mandelbrot’s (C. R. Acad. Sci. Paris 278, 289–292, 1974) multiplicative cascade. We prove, under some general assumptions upon the distribution of the environment, the existence of a new exponent such that behaves asymptotically like . The value of ν is explicitly formulated in terms of the distribution of the environment.      

13C discriminations of Pinus sylvestris vs. Pinus ponderosa at a dry site in Brandenburg (eastern Germany): 100-year growth comparison

The carbon isotope composition (δ¹³C, ‰) and discrimination (Δ, ‰) of old grown North American Pinus ponderosa Dougl. Ex P. et C. Laws. and European Pinus sylvestris L. were determined using trees grown under almost identical growing conditions in a mixed stand in Bralitz, Northeast Germany. Single-tree δ¹³C analyses of tree-ring cellulose of both species were carried out at a yearly resolution for the period 1901–2001 and the results compared with growth (basal area increment). Annual mean δ¹³C values for P. ponderosa ranged from?21.6 ‰ to?25.2 ‰ and for P. sylvestris from?21.4 ‰ to?24.4 ‰. Accordingly, ¹³C discrimination (Δ) showed higher values for P. ponderosa throughout the investigation period. Five characteristic periods of Δ were identified for both the tree species, reflecting positive and negative influences of environmental factors. Good growing conditions such as after-thinning events had a positive effect on Δ, reflecting higher values, while poor conditions like aridity and air pollution had a negative influence, reflecting lower values. The dynamics of Δ were likewise reflected in the growth (basal area increment, BAI). Higher ¹³C discrimination values of P. ponderosa led to higher BAIs of P. ponderosa in comparison with P. sylvestris. Correlation function analyses confirmed that P. sylvestris was more dependent on precipitation than P. ponderosa, which showed a closer relationship with temperature. The results confirm that under predominantly dry growing conditions, P. ponderosa showed better growth performance than P. sylvestris, indicating better common intrinsic water-use efficiency and, therefore, higher rates of net photosynthesis at a given transpiration. In view of the prospect of climate change, the results are very significant for assessing both trees’ physiological properties and, hence, their potential for coping with future growing conditions.     

Finite Sholander trees, trees, and their betweenness

We provide a proof of Sholander’s claim [M. Sholander, Trees, lattices, order, and betweenness, Proceedings of the American Mathematical Society 3 (1952) 369–381] concerning the representability of collections of so-called segments by trees, which yields a characterization of the interval function of a tree. Furthermore, we streamline Burigana’s characterization [L. Burigana, Tree representations of betweenness relations defined by intersection and inclusion, Mathematics and Social Sciences 185 (2009) 5–36] of tree betweenness and provide a relatively short proof.     

Mixed effects regression trees for clustered data

This paper presents an extension of the standard regression tree method to clustered data. Previous works extending tree methods to accommodate correlated data are mainly based on the multivariate repeated-measures approach. We propose a “mixed effects regression tree” method where the correlated observations are viewed as nested within clusters rather than as vectors of multivariate repeated responses. The proposed method can handle unbalanced clusters, allows observations within clusters to be split, and can incorporate random effects and observation-level covariates. We implemented the proposed method using a standard tree algorithm within the framework of the expectation-maximization (EM) algorithm. The simulation results show that the proposed regression tree method provides substantial improvements over standard trees when the random effects are non negligible. A real data example is used to illustrate the method.     

Random Sums of Independent Indicators and Generalized Reduced Processes

We consider a random sum of independent and identically distributed Bernoulli random variables. We prove several limit theorems for this sum under some natural assumptions. Using these limit theorems a generalized version of the reduced critical Galton-Watson process will be studied. In particular we find limit distributions for the number of individuals in a given generation the number of whose descendants after some generations exceeds a fixed or increasing level. An application to study of the number of “big” trees in a forest containing a random number of trees will also be discussed.