On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

基于XPS对硫铁矿去除SeO2-3的机理研究

硒是动植物及人体生长必需的十五种微量元素之一，具有清除体内自由基、抗氧化、增强免疫力等功能，但其安全剂量的范围却很窄。利用扫描电子显微镜（SEM）和X射线衍射仪（XRD）对湿法球磨制备的硫铁矿形貌进行了表征。SEM观测发现加乙醇助磨后的硫铁矿为粒径大小较均匀的球形颗粒团聚体，粒径范围在17～200 nm之间，平均粒径138 nm。XRD衍射图谱中的特征峰与FeS₂衍射图谱中各峰位置基本一致，因此判定硫铁矿中主要化学组分为FeS₂，且图谱中基本没有杂峰，表明制备过程中并未混入杂质，样品纯度较高。实验结果表明，该法制备的硫铁矿具有颗粒粒径小、比表面积大、反应活性高等优点。研究中利用X射线光电子能谱仪（XPS）对硫铁矿去除水体中SeO2-₃的机理进行了研究。研究结果表明, （1）在较为广泛的实验pH范围（pH 2.2～11.5），硫铁矿均能有效去除水体中SeO2-₃，去除效率（除pH值7.8以外）均达到90%以上；（2）硫铁矿与SeO2-₃发生反应后，其主要组成元素的XPS特征峰结合能有所减小，表明硫铁矿表面发生了一定化学变化；（3）酸碱环境下硫铁矿去除SeO2-₃的机理不完全相同，酸性环境下，硫铁矿对SeO2-₃的去除是单纯的氧化还原过程，即硫铁矿中被酸活化的S2-₂将SeO2-₃还原为单质Se(0)，并且酸性越强，SeO2-₃去除效果越好；碱性环境下，SeO2-₃的去除过程中氧化还原与络合反应并存，硫铁矿表面有络合态Fe(OH)SeO₃和单质Se(0)两种存在形态，且碱性越强，络合态Fe(OH)SeO₃含量越高。以上研究结果为硫铁矿去除固定水体和土壤中以SeO2-₃为代表的可变价金属阴离子提供重要理论依据和应用基础。     

A branch-and-bound method for the minimum k−enclosing ball problem

The minimum k-enclosing ball problem seeks the ball with smallest radius that contains at least k of m given points. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of k points to solve this problem. Our method is able to solve the problem exactly in a short amount of time for small and medium sized datasets.     

基于2,5-二溴对苯二甲酸配体的锌/钴配合物合成、晶体结构及性质

将有机物2,5-二溴对苯二甲酸(H₂L₁)和2,2′-联吡啶(L₂)作为双配体,使用溶剂热法和七水合硫酸锌(ZnSO₄·7H₂O)、六水合硝酸钴(Co(NO₃)₂·6H₂O)分别反应,得到配合物[Zn(L₁)(L₂)(H₂O)]_n(1)和配合物[Co(L₁)(L₂)(H₂O)]_n(2)。采用单晶X射线衍射、元素分析、红外光谱、紫外光谱、荧光光谱、热重分析等测试方法对这两种物质进行分析研究。单晶测试结果表明配合物1是单斜晶系,以Zn²⁺配位连接L^2-₁与L₂形成一维链状结构,各条链在分子间氢键和π…π共轭作用下有规律地堆叠形成三维网络结构。配合物2是三斜晶系,Co1离子和Co1ⁱ离子由H₂L₁上的羧酸氧原子O4和O4ⁱ连接,形成双齿螯合的配位结构单元,以Co²⁺配位连接 L^2-₁和L₂形成二维网格结构,各层在O—H…O分子间氢键和范德瓦耳斯力作用下有规律的堆叠形成三维网络结构。配合物1和2均含有芳香杂环、羧基杂环和氮杂环,具有良好的荧光性质和热稳定性,最大发射波长分别为345 nm和333 nm。     

Study on the Relationship between Emulsion Properties and Interfacial Rheology of Sugar Beet Pectin Modified by Different Enzymes

The contribution of rheological properties and viscoelasticity of the interfacial adsorbed layer to the emulsification mechanism of enzymatic modified sugar beet pectin (SBP) was studied. The component content of each enzymatic modified pectin was lower than that of untreated SBP. Protein and ferulic acid decreased from 5.52% and 1.08% to 0.54% and 0.13%, respectively, resulting in a decrease in thermal stability, apparent viscosity, and molecular weight (Mw). The dynamic interfacial rheological properties showed that the interfacial pressure and modulus (E) decreased significantly with the decrease of functional groups (especially proteins), which also led to the bimodal distribution of particle size. These results indicated that the superior emulsification property of SBP is mainly determined by proteins, followed by ferulic acid, and the existence of other functional groups also promotes the emulsification property of SBP.     

Syntheses,crystal structures and properties of Cd(II) and Ag(I) complexes based on 2-p-methylphenyl-5-(2-pyridyl)-1,3,4-thiadiazole

Abstract

Complexes of [CdL₂(NO₃)₂]·1.5H₂O and [Ag₂(μ-L)₂(NO₃)₂] were synthesized by the reactions of 2-p-methylphenyl-5-(2-pyridyl)-1,3,4-thiadiazole (L) with Cd(NO₃)₂·4H₂O and AgNO₃, respectively. Their structures were determined by single crystal X-ray diffraction. The photophysical property and thermal stability were characterized by FT???IR, UV???Vis absorption, fluorescence, and thermogravimetric analysis (TGA). Both complexes belong to the triclinic system with space group p???1. The central metal of [CdL₂(NO₃)₂]·1.5H₂O has a distorted octahedral geometry [CdN₄O₂], while two central Ag(I) atoms of [Ag₂(μ-L)₂(NO₃)₂] exhibit distorted tetrahedral geometries [AgN₃O].     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

Characterization and linear-time detection of minimal obstructions to concave-round graphs and the circular-ones property

A graph is concave-round if its vertices can be circularly enumerated so that the closed neighborhood of each vertex is an interval in the enumeration. In this study, we give a minimal forbidden induced subgraph characterization for the class of concave-round graphs, solving a problem posed by Bang-Jensen, Huang, and Yeo [SIAM J. Discrete Math., 13 (2000), pp. 179–193]. In addition, we show that it is possible to find one such forbidden induced subgraph in linear time in any given graph that is not concave-round. As part of the analysis, we obtain characterizations by minimal forbidden submatrices for the circular-ones property for rows and for the circular-ones property for rows and columns and show that, also for both variants of the property, one of the corresponding forbidden submatrices can be found (if present) in any given matrix in linear time. We make some final remarks regarding connections to some classes of circular-arc graphs.