保留时间两点校正反相高效液相色谱法测定持久性有机污染物的正辛醇-水分配系数

采用改进的反相高效液相色谱法(RP-HPLC)测定了持久性有机污染物(POPs)包括多环芳烃(PAHs)、多氯二苯并二恶英(PCDDs)、多氯二苯并呋喃(PCDFs)和十溴二苯乙烷(DBDPE)等的正辛醇-水分配系数(logKow)。采用保留时间双点校正法(DP-RTC)校正因色谱柱老化等引起的保留时间漂移。以37种有可靠logKow实验值的苯系物、PAHs、PCDD/Fs类似物为模型化合物,建立了logKow和外推至纯水相的保留因子logkw的定量结构-色谱保留关系(QSRR)模型,回归方程为logKow=(1.18±0.02)logkw+(0.36±0.11),其相关系数(R2)为0.985,交叉验证相关系数(R2cv)为0.983,标准偏差(SD)为0.16。进而,用4个已有可靠logKow实验值的验证化合物(联苯、芴、PCDD 1和PCDF 114)对模型进行了外部验证,表明RP-HPLC测得的logKow值与摇瓶法/慢搅法结果有很好的一致性,尤其是对疏水性强的化合物。采用该模型测定了29种特别受关注的POPs的logKow值,这些化合物的logKow实验值均未见报道。所建立的DP-RTC-HPLC是测定强疏水性POPs的logKow值的一种值得推荐的方法。     

Salting-out gradients in centrifugal partition chromatography for the isolation of chlorogenic acids from green coffee beans

In addition to sample solubility constraints, the use of polarity gradients in normal-phase centrifugal partition chromatography (CPC) for the purification of complex mixtures is also limited by the instability of biphasic systems as a consequence of dramatic changes in the settling times along the gradient, leading in many cases to column bleeding when working under maximum efficiency conditions. In this paper an electrostriction approach is proposed as a strategy in reversed-phase CPC to fractionate intermediate polarity extracts in a single run by bringing its components into the “sweet spot” in a controlled fashion through a stepwise reduction of salt concentration in the aqueous mobile phase. The salting-out gradient method was successfully tested with the separation of the major chlorogenic acids (CGAs, hydroxycinnamoylquinic acids) present in green coffee beans (5-caffeoylquinic acid (5-CQA), 5-feruloylquinic acid (5-FQA) and 3,5-dicaffeoylquinic acid (3,5-diCQA)) using ethyl acetate-hexane as the stationary phase and an ionic gradient of LiCl (5.0, 2.5 and 0.1 M) as the mobile phase in one case and (NH₄)₂SO₄/KNO₃ (3.0 and 1.5 M/1.5 M) in another. Regioisomers of each chlorogenic acid obtained by base-catalyzed isomerisation were also separated by CPC using isocratic elution. The best resolution for both FQAs and diCQAs was achieved with a chloroform–n-butanol–0.01 M pH 2.5 phosphate buffer (84:16:100; v/v) system, while CQAs were best isolated using chloroform–n-butanol–0.01 M pH 2.5 phosphate buffer/5.0 M LiCl (82:18:100; v/v).     

On-line arbitrarily vertex decomposable suns

We give a complete characterization of on-line arbitrarily vertex decomposable graphs in the family of unicycle graphs called suns. A sun is a graph with maximum degree three, such that deleting vertices of degree one results in a cycle. This result has already been used in another paper to prove some Ore-type conditions for on-line arbitrarily decomposable graphs.     

Fall colouring of bipartite graphs and cartesian products of graphs

The question of whether a graph can be partitioned into k independent dominating sets, which is the same as having a fallk-colouring, is considered. For k=3, it is shown that a graph G can be partitioned into three independent dominating sets if and only if the cartesian product G□K₂ can be partitioned into three independent dominating sets. The graph K₂ can be replaced by any graph H such that there is a mapping f:Q_n→H, where f is a type-II graph homomorphism.The cartesian product of two trees is considered, as well as the complexity of partitioning a bipartite graph into three independent dominating sets, which is shown to be NP-complete. For other values of k, iterated cartesian products are considered, leading to a result that shows for what values of k the hypercubes can be partitioned into k independent dominating sets.     

On optimal message vector length for block single parallel partition algorithm in a three-dimensional ADI solver

It has long been recognized that many direct parallel tridiagonal solvers are only efficient for solving a single tridiagonal equation of large sizes, and they become inefficient when naively used in a three-dimensional ADI solver. In order to improve the parallel efficiency of an ADI solver using a direct parallel solver, we implement the single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication costs. The measured performances show that the longest allowable message vector length (MVL) is not necessarily the best choice. To understand this observation and optimize the performance, we propose an improved model that takes the cache effect into consideration. The optimal MVL for achieving the best performance is shown to depend on number of processors and grid sizes. Similar dependence of the optimal MVL is also found for the popular block pipelined method.     

A limit field for orthogonal range searches in two-dimensional random point search trees

We consider the cost of general orthogonal range queries in random quadtrees. The cost of a given query is encoded into a (random) function of four variables which characterize the coordinates of two opposite corners of the query rectangle. We prove that, when suitably shifted and rescaled, the random cost function converges uniformly in probability towards a random field that is characterized as the unique solution to a distributional fixed-point equation. We also state similar results for 2-d trees. Our results imply for instance that the worst case query satisfies the same asymptotic estimates as a typical query, and thereby resolve an open question of Chanzy et al. (2001).     

Star partitions on graphs

Given an undirected graph, a star partition is a partition of the nodes into subsets with at least two nodes so that the subgraph induced by each subset has a spanning star. Star partitions are related to well-known problems concerning domination in graphs and edge covering. We focus on the Constrained Star Partition Problem (CSP) that asks for finding a star partition of given cardinality. The problem is new and presents interesting peculiarities. We explore the relation between the cardinalities of star partitions and domatic bipartitions, showing that there are star partitions of any cardinality between minimum and maximum values, and that a similar but weaker result holds for domatic bipartitions. We study the computational complexity of different versions of star partition and domatic bipartition problems, proving that most of them, in particular CSP, constrained domatic bipartition and balanced domatic bipartition, are NP-complete. We also show that star partition problems are polynomial on trees and, more generally, on bounded treewidth graphs. We introduce an integer linear programming formulation that defines a polytope containing all the star partitions of a graph, showing that its vertices have only integral components for trees, which implies that linear programming can be used to solve weighted star partition problems on trees.     

Arithmetical properties of the number of t-core partitions

Let Λ={λ ₁≥⋅⋅⋅≥λ _s ≥1} be a partition of an integer n. Then the Ferrers-Young diagram of Λ is an array of nodes with λ _i nodes in the ith row. Let λ _j ′ denote the number of nodes in column j in the Ferrers-Young diagram of Λ. The hook number of the (i,j) node in the Ferrers-Young diagram of Λ is denoted by H(i,j):=λ _i +λ _j ′−i−j+1. A partition of n is called a t-core partition of n if none of the hook numbers is a multiple of t. The number of t-core partitions of n is denoted by a(t;n). In the present paper, some congruences and distribution properties of the number of 2 ^t -core partitions of n are obtained. A simple convolution identity for t-cores is also given.