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     

集值映射多目标半定规划问题的epsilon-弱有效性

对于集值映射多目标半定规划问题, 在近似锥-次类凸的框架下, 建立了含矩阵和向量的择一性定理, 给出了问题的epsilon-弱有效解的epsilon-Lagrange乘子定理及标量化定理和epsilon-弱鞍点定理．     

The fourth power mean of the general 2-dimensional Kloostermann sums mod <Emphasis Type="Italic">p</Emphasis>

The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 2-dimensional Kloostermann sums mod p, and give an exact computational formula for it.     

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.     

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.     

K3 surfaces,Picard numbers and Siegel disks

If a K3 surface admits an automorphism with a Siegel disk, then its Picard number is an even integer between 0 and 18. Conversely, using the method of hypergeometric groups, we are able to construct K3 surface automorphisms with Siegel disks that realize all possible Picard numbers. The constructions involve extensive computer searches for appropriate Salem numbers and computations of algebraic numbers arising from holomorphic Lefschetz-type fixed point formulas and related Grothendieck residues.     

A multistep collocation method for solving advection equations with delay

Advection equations with delay are appeared in the modeling of the dynamics of structured cell populations. In this article, we construct an efficient two-dimensional multistep collocation method for the numerical solution of a class of advection equations with delay. Equations with aftereffect and equations with both aftereffect and retardation of a state variable are considered. Computability of the algorithm and convergence properties of the proposed numerical method are analyzed for solutions in appropriate Sobolev spaces, and it is shown that the proposed scheme enjoys the spectral accuracy. Numerical examples are given and comparison with other existing methods in the literature is made to demonstrate the efficiency, superiority and high accuracy of the presented method.     

多组件学习器实现有机分子沸点的精准预测

沸点(BP)是有机分子液体的基本物理化学量, 也是化学工业生产中的重要参数. 有机分子的沸点由分子结构决定, 呈现复杂的结构-沸点关系, 函数法(Function Method)、基团贡献法(Group Contribution Method)等传统方法无法应对复杂多样有机分子结构的预测, 应用范围狭窄, 预测精度低. 本研究中, 我们利用基于人工神经网络(ANN)和支持向量机(SVM)的多组件学习器实现有机分子沸点的精准预测. 我们构建了基于可解释性描述符的ANN、基于相关性描述符的ANN及基于复合分子指纹的SVM三个异质模型, 并通过包含4550个各种类别的有机分子沸点的数据集进行训练得到了三个异质性学习器, 最后集成三个学习器对有机分子沸点进行预测. 相比于传统方法和此前的定量结构性质关系(QSPR)模型, 多组件模型结合了三种模型的优点, 展现出很好的预测精度和泛化能力以及低的过拟合, 实现了对多种类型有机分子的沸点的有效预测.