以香草素为内标之气相层析光谱法定量牛樟木精油指标成分松油醇的快速分析方法

牛樟精油具有独特浓郁的香气,其中以α-松油醇(α-terpineol)为牛樟精油主要成分。由于樟树精油制品可依种类、变种、亚种等不同而有不同成分,以松油醇最具独特性,可作为牛樟木精油品质重要指标成分,应用以区别牛樟树与冇樟以及香樟等木材精油的方法,因此建立市售牛樟木精油指标成分α-松油醇含量的简便快速又准确的检验方法便有其必要性。该研究拟以市售精油液体样品,不经任何前处理,加入适当之内标准溶液溶解后,直接注入气相层析光谱仪中,配合适当的分离管柱及气相层析条件,以期建立简便快速又准确的牛樟木精油指标成分α-松油醇之定量方法。毛细管柱气相层析具有高解析度及高灵敏度等优点,仍为现代最重要分析技术之一,因此研究建立了以香草素为内标准定量牛樟木精油指标成分α-松油醇(α-terpineol)之气相色谱层析法的快速分析方法。牛樟木精油液体样品,加入适当量之香草素内标准溶液混合溶解后,即可直接注入配有广口径之毛细管柱(megabore column)气相色谱仪中分析,相当简便,每分析一个样品仅需约30 min。结果显示松油醇之最低定量浓度（limit of quantitation, LOQ）为1 μg·mL-1左右。在添加回收试验中添加松油醇1.0及10.0 mg 于市售冇樟精油及牛樟精油中,其回收率在98%~103%,变异系数均在10.8%以下,显示该方法的精密度相当高。以该研究建立的方法分析15件市售牛樟精油中松油醇含量,结果显示,市售牛樟木精油的松油醇含量最高约51.6%及最低为21.3%左右,此结果显示以定量松油醇作为市售牛樟精油品质指标是一快速、准确且可行的方法。     

树和单圈图的斜谱矩

给定图$G$,对图$G$的每条边确定一个方向,称为$G$的定向图$G^\sigma$, $G$称为$G^\sigma$的基础图. $G^\sigma$的斜邻接矩阵$S(G^\sigma)$是反对称矩阵,其特征值是0或纯虚数. $S(G^\sigma)$所有特征值的$k$次幂之和称为$G^\sigma$的$k$阶斜谱矩,其中$k$是非负整数.斜谱矩序列可用于对图进行排序.本文主要研究定向树和定向单圈图的斜谱矩,并对这两类图的斜谱矩序列依照字典序进行排序.首先确定了直径为$d$的树作为基础图的所有定向树中,斜谱矩序最大的$2\lfloor\frac{d}{4}\rfloor$个图; 然后确定以围长为$g$的单圈图作为基础图的所有定向单圈图中, 斜谱矩序最大的$2\lfloor\frac{g}{4}\rfloor+1$个图.     

具有最小反对称分割指数的化学树

设图$G$,其中边集为$E(G)$,顶点集$V(G)$.反对称分割指数被定义为$ISDD(G)=\sum_{uv \in E(G)}\dfrac{d_ud_v}{d_u^2+d_v^2}$,其中$d_u$, $d_v$分别为顶点$u,v$的度.化学树就是顶点的度不超过4的树.在本文中,我们刻画出具有最小反对称分割指数的$n$阶化学树.     

Addendum to: “Hamilton-laceable bi-powers of locally finite bipartite graphs” [Discrete Math. 345 (2022) 112777]

In this addendum we give a short and easy negative answer to the two questions raised in the original article.     

云格环境下基于P2P的动态资源发现机制

为在云计算平台上实现大数据的高效并行处理与访问,针对动态增长的异构资源所具有的集成与共享所形成的超强计算力结合网格计算,从基于服务计算的角度分析了云计算与网格计算2个不同框架体系的集成问题,探讨了一种资源与服务的统一描述机制,提出了云格体系下的一种分组生成树的P2P网络动态资源与服务发现算法,可实现海量数据的高效处理与访问.实验表明该算法具有一定的可行性与针对性.     

A New Statistical Aspect of the Cluster Variation Method for Lattice Systems

This paper presents an alternative statistical way to derive the cluster variation method (CVM) for lattice systems. The formulation is developed for a series of different clusters, each of which is the largest overlap cluster between two clusters of the next larger type. We arrive at the CVM expression of the lattice configuration factor by deriving the number of different ways of distributing clusters of a selected type in the lattice so that they overlap each other at the largest overlap clusters in a physically correct manner. The essential assumption employed is that individual overlapping events are statistically independent of each other. This reveals a new statistical aspect of the CVM: The CVM is based on a Bethe tree of clusters of the selected type.     

关于树的补图的色多项式

本文证明了,由树的特征多项式可立即求出其补图的色多项式.     

一个用于支持经济预测决策的EP—ESS模型

本文论述了EP-ESS的结构及其各部分之间的关系,并给出了ES部分推理的数学模型及其实现的流程图。     

Topological properties of stock market networks: The case of Brazil

This paper investigates the topological properties of the Brazilian stock market networks. We build the minimum spanning tree, which is based on the concept of ultrametricity, using the correlation matrix for a variety of stocks of different sectors. Our results suggest that stocks tend to cluster by sector. We employ a dynamic approach using complex network measures and find that the relative importance of different sectors within the network varies. The financial, energy and material sectors are the most important within the network.     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.