Spherical basis functions and uniform distribution of points on spheres

The main purpose of the present paper is to employ spherical basis functions (SBFs) to study uniform distribution of points on spheres. We extend Weyl's criterion for uniform distribution of points on spheres to include a characterization in terms of an SBF. We show that every set of minimal energy points associated with an SBF is uniformly distributed on the spheres. We give an error estimate for numerical integration based on the minimal energy points. We also estimate the separation of the minimal energy points.     

凝聚态炸药爆轰测试技术研究进展

爆轰物理学科仍然是以实验为主的一门科学,爆轰测试技术的不断进步仍然是爆轰物理学科发展的主要推动力.本文在阐述凝聚态炸药爆轰性能主要几个研究方面的基础上,从光学测试技术和电学测试技术两个方面系统介绍了凝聚态炸药爆轰测试技术及其应用.通过对现代爆轰测试技术进展的阐述,分析了凝聚态炸药爆轰测试研究面临的问题,展望了爆轰测试技术的发展前景.      

A Particle Swarm Algorithm Based on a Multi-Stage Search Strategy

Particle swarm optimization (PSO) has the disadvantages of easily getting trapped in local optima and a low search accuracy. Scores of approaches have been used to improve the diversity, search accuracy, and results of PSO, but the balance between exploration and exploitation remains sub-optimal. Many scholars have divided the population into multiple sub-populations with the aim of managing it in space. In this paper, a multi-stage search strategy that is dominated by mutual repulsion among particles and supplemented by attraction was proposed to control the traits of the population. From the angle of iteration time, the algorithm was able to adequately enhance the entropy of the population under the premise of satisfying the convergence, creating a more balanced search process. The study acquired satisfactory results from the CEC2017 test function by improving the standard PSO and improved PSO.     

Design,synthesis, insecticidal,and acaricidal activities of novel pyrimidinamine derivatives containing a biphenyl ether

A series of original pyrimidinamine derivatives containing a biphenyl ether moiety were designed and synthesized. Their structures were confirmed by ¹H NMR, MS, and elemental analyses. Their insecticidal activities against lepidopteran and hemiptera insects and acaricidal activities were tested. The results of bioassay demonstrated that 9k showed the best activity (LC₅₀ = 2.08 mg/L) against Tetranychus urticae, which is comparable with the positive control, spirotetramat (LC₅₀ = 2.27 mg/L), and 9g showed better activity (LC₅₀ = 0.52 mg/L) against Aphis fabae than the positive control, imidacloprid (LC₅₀ = 1.02 mg/L), and relatively good activity (LC₅₀ = 2.49 mg/L) against T urticae. Their structure‐activity relationships indicated that both an ethyl group on the 4‐position of the pyrimidine ring and alkyl chain as a para‐substituent group of the benzene ring showed good biological activity.     

一致仿缩矩阵无穷乘积的收敛性及在Vicsek模型同步问题中的应用

研究仿缩矩阵无穷乘积的收敛问题.将文献中的仿缩矩阵概念推广,提出一致仿缩集合概念,并推导出一致仿缩集的若干的有用的性质.基于这些性质,利用Rn空间的紧致性质证明了如下结论:取自一致仿缩集的任意无穷矩阵乘积都是收敛的,并给出了极限矩阵的构造.这一结果改进了现有的结论.应用得到的结论,研究了Vicsek模型的同步问题,用新的方法证明了一个基于最近邻居规则的粒子运动方位同步的结论.     

Sampling scattered data with Bernstein polynomials: stochastic and deterministic error estimates

Viewing the classical Bernstein polynomials as sampling operators, we study a generalization by allowing the sampling operation to take place at scattered sites. We utilize both stochastic and deterministic approaches. On the stochastic side, we consider the sampling sites as random variables that obey some naturally derived probabilistic distributions, and obtain Chebyshev type estimates. On the deterministic side, we incorporate the theory of uniform distribution of point sets (within the framework of Weyl’s criterion) and the discrepancy method. We establish convergence results and error estimates under practical assumptions on the distribution of the sampling sites.     

The generalized weighted Moore-Penrose inverse

In this paper, we definite a generalized weighted Moore-Penrose inverse A _M,N ⁺ of a given matrixA, and give the necessary and sufficient conditions for its existence. We also prove its uniqueness and give a representation of it. In the end we point out this generalized inverse is also a prescribed rangT and null spaceS of {2}-(or outer) inverse ofA.     

Self‐assembly of Functionalized Gold Nanoparticles with Rigid and Flexible Multifunctional Linkers

The interparticle spacing of carboxyl functionalized gold nanoparticles (Au‐COOH) were mediated by rigid crosslinkers, octa(3‐aminopropyl)octasilsesquioxane (POSS‐NH₃ ⁺) and poly(amidoamine) dendrimer terminated with hydroxyl groups (PAMAM‐OH), and a flexible polymeric linker, poly(hexanul viologen) (6‐VP). Regular interparticle spacing was achieved by utilizing POSS‐NH₃ ⁺ and PAMAM‐OH dendrimer as cross linkers, whereas size growth of Au‐COOH was observed featuring no interparticle spacing by utilizing 6‐VP as the crosslinker.     

Formation and properties of hydrophobic CeO2 nanoparticles

Uniform hydrophobic cerium oxide (CeO₂) nanoparticles in a cubic structure with an average size of 4.6 nm were obtained by a novel oil-water interface method in the presence of 0.40 M NaOH. Effects of reactants concentration, oxidation reaction temperature, and the type of surfactants on the final products were investigated. The products were characterized by X-ray diffraction, transmission electron microscopy, UV-visible spectroscopy, room-temperature photoluminescence spectroscopy and contact angle measurements. The products exhibited high luminescence and strong hydrophobicity. The data suggest that Ce(OH) _x ^4?x (x < 4) is a precursor complex for the formation of CeO₂ nanoparticles in liquid phase and its concentration controls the size of CeO₂ particles. The adsorption of the surfactant influences the formation of the hydrophobic particles of CeO₂ by the oil-water interface method.