Powers of Euler's Product and Related Identities

Ramanujan's partition congruences can be proved by first showing that the coefficients in the expansions of (q; q) ^r satisfy certain divisibility properties when r = 4, 6 and 10. We show that much more is true. For these and other values of r, the coefficients in the expansions of (q; q) ^r satisfy arithmetic relations, and these arithmetic relations imply the divisibility properties referred to above. We also obtain arithmetic relations for the coefficients in the expansions of (q; q) ^r (q ^t; q ^t) ^s , for t = 2, 3, 4 and various values of r and s. Our proofs are explicit and elementary, and make use of the Macdonald identities of ranks 1 and 2 (which include the Jacobi triple product, quintuple product and Winquist's identities). The paper concludes with a list of conjectures.     

氧化亚氮3000—0200和1001—0110跃迁带在高温下的线强度

采用乘积近似法计算了氧化亚氮分子的总配分函数，其中转动配分函数考虑了离心扭曲修正，振动配分函数采用谐振子近似. 利用计算所得的配分函数和实验振动跃迁矩平方及Herman-Wallis因子系数，计算了氧化亚氮3000—0200和1001—0110跃迁带在常温和高温下的线强度. 结果显示，当温度高达3000K时，计算所得线强度与实验值及HITRAN数据库提供的结果仍符合较好. 这表明高温下的分子配分函数和线强度的计算是可靠的. 还进一步计算了氧化亚氮3000—0200和1001—0110跃迁带在更高温度(40 关键词： 氧化亚氮 配分函数 线强度 高温     

地下洞室围岩弹塑性仿真反演分析方法

地下洞室围岩弹塑性反演分析方法是长期以来反分析理论研究的一个难题。文中详细分析了实施弹塑性反分析所存在的3个难点,并针对这3个问题,假定围岩是理想弹塑性介质,通过参数对位移的灵敏度分析,现场实测将弹塑性位移进行分离,从而探索围岩弹塑性反分析的新途径;之后阐述了本文采用的仿真反分析的概念、实施思路及流程;最后说明了该方法的应用与检验思路,结合工程实例证明该方法的可靠性。     

基于OBS网络的一种最少冗余包的组播树共享算法

为了减少组播树共享算法(TS-MCAST)产生冗余包,有效地利用链路网络带宽,提出了一种基于光突发交换(OBS)网络的最少冗余包的组播树共享算法(LRP-MCAST-TS)。该算法实现过程中,引入了树分割规则,将满足分割条件的组播树分割成森林,然后根据重叠大小将汇聚的组播会话划分成多个组播共享类。通过理论分析,证明了LRP-MCAST-TS算法设计的正确性,达到了减少冗余包的目的。     

Impact of dissolved humic acid on the bioavailability of acenaphthene and chrysene assessed by membrane-based passive samplers

Dissolved organic carbon (DOC) is known to reduce the bioavailability of hydrophobic organic compounds (HOCs) in aqueous environments. This reduction occurs as a result of adsorption to DOC, apparently reducing the freely dissolved concentration of HOCs. In the present study, triolein-embedded cellulose acetate membrane (TECAM) and Japanese medaka (Oryzias latipes) were used to measure the uptake of acenaphthene and chrysene in the presence of commercial humic acid (HA) at different concentrations (0―15 mg C·L-1) under controlled laboratory conditions. Apparent uptake rate constants for PAHs in TECAM and medaka were compared and DOC-water partition coefficients (KDOCs) of two PAHs were calculated with different sampling methods by model fit. Results showed that HA present in water significantly reduced the uptake of PAHs in TECAM and medaka. The obtained values of log KDOC of acenaphthene and chrysene measured by TECAM were 4.63 and 5.83, respectively, whereas biologically determined values were 4.52 and 5.76, respectively. These log KDOC values were comparable to earlier published KDOCs toward commercial HA, thereby indicating that TECAM accumulated only the freely dissolved fraction of chemicals and uptake PAHs in a manner similar to that of fish. All these results suggested that the TECAM method can provide a good means for assessing the impact of DOC on bioavailability of PAHs in the aqueous environment.     

一类典型模糊逻辑控制器的输出结构

研究一类特殊的多输入单输出的模糊逻辑控制器 ,其组成规则中的输入输出语言变量的语言值均取正规的三角形隶属函数 ,且分别作成其相应论域的模糊划分 ,在其输入输出之间存在一种特殊的映射关系———线性规则映射 .经分析得到结论 :模糊逻辑控制器的输出可以表示成输入的凸组合函数 .这一结论建立了模糊逻辑控制器的精确数学模型 ,对于模糊逻辑控制器的分析和调整提供了直接依据 .     

Balanced decomposition of a vertex-colored graph

A balanced vertex-coloring of a graph G is a function c from V(G) to {−1,0,1} such that ∑{c(v):v∈V(G)}=0. A subset U of V(G) is called a balanced set if U induces a connected subgraph and ∑{c(v):v∈U}=0. A decomposition V(G)=V₁∪?∪V_r is called a balanced decomposition if V_i is a balanced set for 1≤i≤r.In this paper, the balanced decomposition number f(G) of G is introduced; f(G) is the smallest integer s such that for any balanced vertex-coloring c of G, there exists a balanced decomposition V(G)=V₁∪?∪V_r with |V_i|≤s for 1≤i≤r. Balanced decomposition numbers of some basic families of graphs such as complete graphs, trees, complete bipartite graphs, cycles, 2-connected graphs are studied.     

Set Partition Complexes

The Hom complexes were introduced by Lovász to study topological obstructions to graph colorings. The vertices of Hom(G,K _n ) are the n-colorings of the graph G, and a graph coloring is a partition of the vertex set into independent sets. Replacing the independence condition with any hereditary condition defines a set partition complex. We show how coloring questions arising from, for example, Ramsey theory can be formulated with set partition complexes. It was conjectured by Babson and Kozlov, and proved by Čukić and Kozlov, that Hom(G,K _n ) is (n−d−2)-connected, where d is the maximal degree of a vertex of G. We generalize this to set partition complexes.     

Amalgamation of partitions from multiple segmentation bases: A comparison of non-model-based and model-based methods

The segmentation of customers on multiple bases is a pervasive problem in marketing research. For example, segmentation service providers partition customers using a variety of demographic and psychographic characteristics, as well as an array of consumption attributes such as brand loyalty, switching behavior, and product/service satisfaction. Unfortunately, the partitions obtained from multiple bases are often not in good agreement with one another, making effective segmentation a difficult managerial task. Therefore, the construction of segments using multiple independent bases often results in a need to establish a partition that represents an amalgamation or consensus of the individual partitions. In this paper, we compare three methods for finding a consensus partition. The first two methods are deterministic, do not use a statistical model in the development of the consensus partition, and are representative of methods used in commercial settings, whereas the third method is based on finite mixture modeling. In a large-scale simulation experiment the finite mixture model yielded better average recovery of holdout (validation) partitions than its non-model-based competitors. This result calls for important changes in the current practice of segmentation service providers that group customers for a variety of managerial goals related to the design and marketing of products and services.     

A major index for matchings and set partitions

We introduce a statistic pmaj(P) for partitions of [n], and show that it is equidistributed with cr₂, the number of 2-crossings, over all partitions of [n] with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inv and maj.