Pattern‐avoiding permutations and Brownian excursion part I: Shapes and fluctuations

Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study the scaling limits of a random permutation avoiding a pattern of length 3 and their relations to Brownian excursion. Exploring this connection to Brownian excursion allows us to strengthen the recent results of Madras and Pehlivan [25] and Miner and Pak [29] as well as to understand many of the interesting phenomena that had previously gone unexplained. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 394–419, 2017     

2-距离空间中平方型压缩映象的一个新的耦合公共不动点定理

在2-距离空间的框架下, 利用映象对的ω-相容性条件, 建立了一类新的平方型压缩条件, 讨论了此类映象耦合公共不动点的存在性和唯一性.证明了一个新的耦合公共不动点定理, 也提供了一个有效的例子来支持该文的新结果.该文的结果改善了之前文献中的相关结果.     

ATIS和道路收费下混合SUE相对于SSO的效率损失

在ATIS和道路收费共同作用的异质性交通网络中,基于用户在信息接受程度与时间价值上的异质性,对用户进行合理分类,所有用户均按照随机方式进行择路.构建了多用户混合随机均衡等价的变分不等式模型,以及多用户随机社会最优模型.以用户感知的总出行成本作为系统性能评价的指标,当收费作为系统总成本的一部分时,分别在时间准则与费用准则下研究了多用户混合随机均衡相对于随机社会最优的绝对效率损失问题.研究结果表明,时间准则下的绝对效率损失上界与路段出行时间函数和混合随机均衡时系统的实际总出行时间有关,费用准则下的绝对效率损失上界还与出行者的社会经济特性和随机社会最优时系统的实际总出行时间有关.     

一类奇异非线性多重调和方程存在正整解的充分必要条件

研究一类奇异非线性多重调和方程?~mu=f(|x|,u,|▽u|)u~(-β),给出了方程存在正的径向对称整体解的充分必要条件和解的性质.     

Self-maps of <Emphasis Type="Italic">S</Emphasis><Superscript>2</Superscript> homotopic to a smooth map with a single <Emphasis Type="Italic">n</Emphasis>-periodic point

We show for which (d,n) ∈ Z×N there exists a smooth self-map f:S² → S² so that deg(f)=d and Fix(fⁿ) is a point.     

New results for the Liebau phenomenon via fixed point index

We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a simple model. Our methodology relies on the use of classical fixed point index. Some examples are provided to illustrate our theory. We improve and complement previous results in the literature.     

A lubricated stagnation point flow of nanofluid with heat and mass transfer phenomenon: Significance to hydraulic systems

The improved thermal association of heat transfer is considerably observed due to interaction of nanoparticles in recent days. The lubrication phenomenon with heat and mass transfer effects plays a key role in the hydraulic systems. In current research, the thermal impact of nanofluid over a lubricated stretching surfaces near a stagnation point analytical has been studied. A thin layer of lubricating fluid with a variable thickness provides lubrication. The inspection of thermophoresis and Brownian motion phenomenon is illustrated via Boungrino model. The analytical finding of refurbished boundary layer ordinary differential equations is obtained by a reliable and proficient technique namely variational iteration method (VIM). The Lagrange Multiplier is a potent tool in proposed technique to reduce the computational work. In addition, a numerical comparison is presented to show the effectiveness of this study. The range of flow parameters is based on theoretical flow assumptions. Physical inspection of involved parameters on velocities, temperatures, concentrations, and other quantities of interest when lubrication is presented. The current results present applications in polymer process, manufacturing systems, heat transfer and hydraulic systems.     

基于曲线问题情境的信息化教学尝试*——以“沉淀溶解平衡”为例

基于高中生对实验曲线理解困难的现状,为挖掘实验曲线的教学价值,以沉淀溶解平衡为例,结合课堂演示实验和教学软件,设计了“宏观微观符号曲线”多重表征教学为一体的实验探究课。根据沉淀溶解平衡实验证据,绘制实验曲线,构建微观模型和图像,从而培养学生的证据收集与应用意识,提高学生对曲线的分析和理解能力,领会各种变化曲线的来源。在曲线理解的基础上建立“溶解平衡转化”思维模型,以此为开展“曲线融入式”的问题引导型实验教学提供参考案例。     

Determination of thermodynamic parameters for cloud point extraction of Arsenazo-III and Magdala Red dyes using mixed micelles: An essential requirement for high performance

A simple and low cost method for extraction and preconcentration of Arsenazo-III (ARS-III) and Magdala Red (MR) was developed by an efficient cloud point extraction (CPE) method using mixed micelles of Triton X–114 (TX–114) and cetyltrimethyl ammonium bromide (CTAB). Various parameters, such as pH/concentration of H₂SO₄, surfactant concentrations (TX-114 and CTAB), equilibrium temperature and time have been studied to maximise efficiency. Thermodynamic quantities like change in Gibbs free energy (ΔG⁰), change in enthalpy (ΔH⁰) and change in entropy (ΔS⁰) were calculated. The results show that the CPE of ARS-III and MR dye is feasible, spontaneous, and endothermic in the temperature range of (50–80) °C indicating good recoveries for the developed method. The effect of temperature, surfactant concentration and dye concentration on various thermodynamic quantities was investigated and it was found that ΔG⁰ values increased with temperature but decreased with surfactant and dye concentration. ΔH⁰ and ΔS⁰ values increased as surfactant concentration increased and decreased as dye concentration decreased. The recoveries were found to be the range from 90.02 – 101.03 % for ARS-III and 86.07–99.46 % for MR dyes which proves that the method is highly efficient.