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.     

Rheological Properties of Mixed Aqueous Solutions of Geminis (12‐3‐12,2Br−) and SDS

The rheological properties of surfactant solutions are the main parameter that affects the surfactant application. In this work, the rheology of the mixed system 12‐3‐12,2Br^?/SDS/H₂O was discussed particularly. The relationship between the microstructure of surfactant aggregates and rheology of mixed solutions was explored. It is shown that the rheological properties of solutions have different behaviors at different molar ratio of two surfactants under given total concentration. With the increase of molar ratio (12‐3‐12,2Br^?/SDS), the solution change from Newtonian liquid into positive thixotropy then to negative thixotropy, at last turn to positive thixotropy again, and ATPS becomes the dividing line. The difference of rheological properties is the embodiment of difference for surfactant aggregates' microstructures. The cryo‐TEM results shown that the solutions containing aggregates with big size, such as rodlike micelles, multilamellar micelles, show positive thixotropy. However, the solutions containing lamellar micelles or liquid crystal will show negative thixotropy. The positive thixotropy endows the mixied system a potential application in enhanced oil recovery.     

An Amino‐Acid‐Based Self‐Healing Hydrogel: Modulation of the Self‐Healing Properties by Incorporating Carbon‐Based Nanomaterials

An amino‐acid‐based (11‐(4‐(pyrene‐1‐yl)butanamido)undecanoic acid) self‐repairing hydrogel is reported. The native hydrogel, as well as hybrid hydrogels, have been thoroughly characterized by using various microscopic techniques, including transmission electron microscopy (TEM), atomic force microscopy (AFM), Raman spectroscopy, fluorescence spectroscopy, FTIR spectroscopy, X‐ray diffraction, and by using rheological experiments. The native hydrogel exhibited interesting fluorescence properties, as well as a self‐healing property. Interestingly, the self‐healing, thixotropy, and stiffness of the native hydrogel can be successfully modulated by incorporating carbon‐based nanomaterials, including graphene, pristine single‐walled carbon nanotubes (Pr‐SWCNTs), and both graphene and Pr‐SWCNTs, within the native gel system. The self‐recovery time of the gel was shortened by the inclusion of reduced graphene oxide (RGO), Pr‐SWCNTs, or both RGO and Pr‐SWCNTs. Moreover, hybrid gels that contained RGO and/or Pr‐SWCNTs exhibited interesting semiconducting behavior.     

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.     

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．     

具无限时滞的周期系统的持久性与正周期解

本文利用比较定理,控制收敛定理和积分平均的方法,讨论一类具有无限时滞的非自治,非卷积的捕食者-食饵系统的一致持久性和正周期解。     

Positivity preserving finite element approximation

We consider finite element operators defined on ``rough' functions in a bounded polyhedron in . Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of and approximating general functions which do not. We give impossibility results for approximation of general functions to more than first order accuracy at extreme points of . We also give impossibility results about invariance of positive operators on finite element functions. This is in striking contrast to the well-studied case without positivity.

     

正线性算子对无穷区间上有界变差函数的点态逼近度

用ＢＶ［０，∞）表示在［０，∞）的每一有限子区间上为有界变差函数的函数构成的空间。用表示ＢＶ［０，∞）上的正线性算子，其中ｄｔＫｎ（ｘ，ｔ）是非负测度且，则有定理如果Ｌｎ（｜ｔ－ｘ｜β，ｘ）≤Ｃ（ｘ）／ｎｖ，，这里β＞０，ｖ≥１，Ｃ（ｘ）是一个与ｘ有关的常数，对ｆ∈ＢＶ［０，∞）和ｘ∈（０，∞）有这里作为应用，给出算子的逼近估计．