Characterizing and Generating Bivariate Empirical Rank Distributions Satisfying Certain Positive Dependence Concepts

Abstract

This article introduces an approach for characterizing the classes of empirical distributions that satisfy certain positive dependence notions. Mathematically, this can be expressed as studying certain subsets of the class S_N of permutations of 1, …, N, where each subset corresponds to some positive dependence notions. Explicit techniques for it-eratively characterizing subsets of S_N that satisfy certain positive dependence concepts are obtained and various counting formulas are given. Based on these techniques, graph-theoretic methods are used to introduce new and more efficient algorithms for constructively generating and enumerating the elements of various of these subsets of S_N. For example, the class of positively quadrant dependent permutations in S_N is characterized in this fashion.     

Trace formulas for additive and non-additive perturbations

Trace formulas for pairs of self-adjoint, maximal dissipative and accumulative as well as other types of resolvent comparable operators are obtained. In particular, the existence of a complex-valued spectral shift function for a pair {H^′,H}$\{H^{\prime },H\}$ of maximal accumulative operators has been proved. We investigate also the existence of a real-valued spectral shift function. Moreover, we treat in detail the case of additive trace class perturbations. Assuming that H   and H^′=H+V$H^{\prime }=H+V$ are maximal accumulative and V is trace class, we prove the existence of a summable   complex-valued spectral shift function. We also obtain trace formulas for pairs {H,H^?}$\{H,H^{?}\}$assuming only that H and  H^?$H^{?}$are resolvent comparable. In this case the determinant of the characteristic function of H is involved in trace formulas.     

用左手手势巧学常见单糖的结构式*

分享了一种巧用左手手势,结合一首五言口诀快速判断糖分子结构的方法。口诀为:“罗卓葡古塔,甘露艾半乳。核阿木来苏,酮糖果山古”,包含了常见的12种醛糖和6种酮糖。通过该方法,不仅能快速准确写出各种常见糖的Fischer投影式,而且还可应用于糖分子相应的Haworth透视式及椅式构象,值得在糖类教学中进行推广。     

Random k‐SAT and the power of two choices

We study an Achlioptas‐process version of the random k‐SAT process: a bounded number of k‐clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule. We prove the existence of a rule that shifts the satisfiability threshold. This extends a well‐studied area of probabilistic combinatorics (Achlioptas processes) to random CSP's. In particular, while a rule to delay the 2‐SAT threshold was known previously, this is the first proof of a rule to shift the threshold of k‐SAT for . We then propose a gap decision problem based upon this semi‐random model. The aim of the problem is to investigate the hardness of the random k‐SAT decision problem, as opposed to the problem of finding an assignment or certificate of unsatisfiability. Finally, we discuss connections to the study of Achlioptas random graph processes. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 163–173, 2015     

Enhanced Reproducibility of Positive Temperature Coefficient Effect of CB/HDPE/PVDF Composites with the Addition of Ionic Liquid

Developing an effective method for improving the reproducibility of positive temperature coefficient(PTC) effect is of great significance for large-scale application of polymer based PTC composites, owing to its contribution to the security and reliability. Herein, we developed a carbon black(CB)/high density polyethylene(HDPE)/poly(vinylidene fluoride)(PVDF) composite with outstanding PTC reproducibility, by incorporating 1-octyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide([OMIm][NTf_2]) into the composite. After multiple repeated temperature cycles, the PTC performance of as-prepared material keeps almost unchanged and the varition of resistance at room temperature is less than 7%. Our studies revealed that [OMIm][NTf2] contributes to the improvement of PTC reproducibility in two ways:(i)it acts as an efficient plasticizer for refining the co-continuous phase morphology of HDPE/PVDE blends;(ii) it inhibits the crystallization of PVDF through the dilution effect, leading to more overlaps of the volume shrinkage process of HDPE and PVDF melt which results in the decrease of interface gap between HDPE and PVDF. This study demonstrated that ionic liquids as the multifunctional agents have great potential for improving the reproducibility in the application of the binary polymer based PTC composites.     

正电性胶态纳米银中加入凝聚剂后的表面增强拉曼光谱

在柠檬酸还原制备的正电性胶态纳米银中加入凝聚剂HNO₃和NaNO₃后,用波长为633 nm的激光激发,获得了较强的表面增强拉曼散射光谱(SERS谱),通过讨论及实验明确该SERS谱是来自于还原剂中的柠檬酸根离子,并说明该方法制备的纳米银的吸附层是带正电的银离子,扩散层是带负电的柠檬酸根离子。     

聚二巯化合物正极材料的合成及性质的初步研究

固态电池发展至今，许多比能量高、贮存性能好的新型电池产品不断涌向市场，而目前广泛用于正极材料的大多数物质是层状化合物［１］，如聚乙炔，聚苯胺等化合物，它们贮存能量的方式主要是通过插入化学反应来实现，本工作将合成一种高分子材料——２．５－二巯基－１，３...     

高铁酸钾的合成与电化学性能研究

本文主要研究了锂离子电池正极材料高铁酸钾的合成,表征和电化学性质.用次氯酸钾与硝酸铁于碱性介质中反应得到高铁酸钾粗品,重结晶后成纯度大于97%的产品,用XRD和FTIR等方法对高铁酸钾进行表征和分析.初步研究了K2FeO4/Li电池的充放电性能.     

High-performance liquid chromatography with evaporative light-scattering detection for the determination of phospholipid classes in human milk,infant formulas and phospholipid sources of long-chain polyunsaturated fatty acids

We developed and validated a new high-performance liquid chromatographic method for the separation of phospholipid classes in human milk, infant formulas and phospholipidic sources of long-chain polyunsaturated fatty acids (LC-PUFAs) used in paediatric nutrition. Phosphatidylcholine, phosphatidylethanolamine, phosphatidylinositol, phosphatidylserine and sphingomyelin were separated in less than 25 min using an Extrasil silica column (150 x 4.0 mm I.D., 3-microm particle size) by isocratic elution with a mixture of isopropanol-hexane-water. Phospholipids were determined by an evaporative light-scattering detector. Several chromatographic conditions were assayed to optimise the method, whose suitability is shown by the detection limits, linearity ranges and precision rates obtained. The main advantages of the proposed method are its speed and the direct determination of the main phospholipids present in human milk, infant formulas and the phospholipid sources of LC-PUFAs used in paediatric nutrition.     

多物种生态竞争系统周期正解的存在性和全局吸引性

利用重合度理论中的延拓定理和Lyapunov泛函方法讨论了一类具有多个滞量的多物种生态竞争系统周期正解的存在性和全局吸引性,得到了一些新的结果．实例表明我们的结果更加广泛,更加便于应用．