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Ergodic Retraction Theorem and Weak Convergence Theorem for Reversible Semigroups of Non-Lipschitzian Mappings

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Acta Mathematica Sinica,English Series 2006年第2期22卷 407-416页

作者： Liu chuan zeng Department of Mathematics Shanghai Normal University

Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banaeh space E with a Frechet differentiable norm, and T = {Tt ： t ∈ G} be a continuous representation of G as nearly asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F（T） of T in C is nonempty. It is shown that if G is right reversible, then for each almost-orbit u（.） of T, ∩s∈G ^-CO{u（t）： t ≥ s} ∩ F（T） consists of at most one point. Furthermore, ∩s∈G ^-CO{Ttx ： t ≥ s} ∩ F（T） is nonempty for each x ∈ C if and only if there exists a nonlinear ergodic retraction P of C onto F（T） such that PTs - TsP = P for all s ∈ G and Px ∈^-CO{Ttx ： s ∈ G} for each x ∈ C. This result is applied to study the problem of weak convergence of the net {u（t）： t ∈ G} to a common fixed point of T.

关键词： Non Lipschitzian mapping Reversible semigroup Ergodic retraction Weak convergence

Cystine-assisted accumulation of gold nanoparticles on ZnO to construct a sensitive surface-enhanced Raman spectroscopy substrate

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Frontiers of Chemical Science and Engineering 2023年第1期17卷 15-23页

作者： Qi Qu chuan zeng Jing Huang Mengfan Wang Wei Qi Zhimin He School of Chemical Engineering and Technology State Key Laboratory of Chemical EngineeringTianjin UniversityTianjin 300072China School of Life Sciences Tianjin UniversityTianjin 300072China Co-Innovation Centre of Chemistry and Chemical Engineering of Tianjin Tianjin 300072China Tianjin Key Laboratory of Membrane Science and Desalination Technology Tianjin 300350China Technical Centre of Gongbei Customs District of China Zhuhai 519000China

Recently,various semiconductor/metal composites have been developed to fabricate surfaceenhanced Raman spectroscopy ***,low metal loading on semiconductors is still a *** this study,cystine was introduced to increase the accumulation of gold nanoparticles on zinc oxide,owing to the biomineralization_property of_*** analysis revealed that the obtained ZnO/Au/cystine composite not only had a higher metal loading but also formed a porous structure,which is beneficial for Raman *** with ZnO/Au,the ZnO/Au/cystine substrate displayed a 40-fold enhancement in the Raman signal and a lower limit of detection(10^(-11) mol·L^(-1))in the detection of rhodamine ***,the substrate has favorable homogeneity and ***,ZnO/Au/cystine displayed excellent performance toward crystal violet and methylene blue in a test based on river water *** study provided a promising method to fabricate sensitive semiconductor/noblemetal-based surface-enhanced Ramans spectroscopy substrates for Raman detection.

关键词： biomineralization cystine semiconductor/metal composite SERS detection Raman detection

Convergence Analysis of Iterative Sequences for a Pair of Mappings in Banach Spaces

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Acta Mathematica Sinica,English Series 2008年第3期24卷 463-470页

作者： Liu chuan zeng N.C.WONG J.C.YAO Department of Mathematics Shanghai Normal University Shanghai 200234 P. R. China Department of Applied Mathematics National Sun Yat-Sen University Kaohsiung Taiwan 80424

Let C be a nonempty closed convex subset of a real Banach space E. Let S ： C→ C be a quasi-nonexpansive mapping, let T ： C→C be an asymptotically demicontractive and uniformly Lipschitzian mapping, and let F ：= {x ∈C ： Sx = x and Tx = x}≠Ф Let {xn}n≥0 be the sequence generated irom an arbitrary x0∈Cby xn＋i=（1-cn）Sxn＋cnT^nxn, n≥*** prove the necessary and sufficient conditions for the strong convergence of the iterative sequence {xn} to an element of F. These extend and improve the recent results of Moore and Nnoli.

关键词： quasi-nonexpansive mapping asymptotically demicontractive type mapping iterative sequence convergence analysis

Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map

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Acta Mechanica Sinica 2012年第4期28卷 1143-1153页

作者： Ni Zhen Feng-Lian Li Yue-Sheng Wang chuan-zeng Zhang Institute of Engineering Mechanics Beijing Jiaotong University100044 BeijingChina Department of Civil Engineering University of SiegenSiegenD-57068Germany

In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.

关键词： Phononic crystal Band structure Cylindrical wave expansion Dirichlet-to-Neumann (DtN) map Bloch theorem

Convergence of Hybrid Steepest-Descent Methods for Generalized Variational Inequalities

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Acta Mathematica Sinica,English Series 2006年第1期22卷 1-12页

作者： Liu chuan zeng N. C. Wong J. C. YAO Department of Mathematics Shanghai Normal University Shanghai 200234 P. R. China Department of Applied Mathematics National Sun Yat-sen University Kaohsiung Taiwan 804

In this paper, we consider the generalized variational inequality GVI（F, g, C）, where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We propose two iterative algorithms to find approximate solutions of the GVI（F,g, C）. Strong convergence results are established and applications to constrained generalized pseudo-inverse are included.

关键词： iterative algorithms hybrid steepest-descent methods nonexpansive mappings Hilbert space Constrained generalized pseudo-inverse

Improved PSO algorithm based on chaos theory and its application to design flood hydrograph

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Water Science and Engineering 2010年第2期3卷 156-165页

作者： Si-fang DONG zeng-chuan DONG Jun-jian MA Kang-ning CHEN State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Hohai University Nanjing 210098 P. R. China Department of Remote Sensing Center China Institute of Water Resources and Hydropower Research Beijing 100044 P. R. China

The deficiencies of basic particle swarm optimization （bPSO） are its ubiquitous prematurity and its inability to seek the global optimal solution when optimizing complex high-dimensional functions. To overcome such deficiencies, the chaos-PSO （COSPSO） algorithm was established by introducing the chaos optimization mechanism and a global particle stagnation-disturbance strategy into bPSO. In the improved algorithm, chaotic movement was adopted for the particles＇ initial movement trajectories to replace the former stochastic movement, and the chaos factor was used to guide the particles＇ path. When the global particles were stagnant, the disturbance strategy was used to keep the particles in motion. Five benchmark optimizations were introduced to test COSPSO, and they proved that COSPSO can remarkably improve efficiency in optimizing complex functions. Finally, a case study of COSPSO in calculating design flood hydrographs demonstrated the applicability of the improved algorithm.

关键词： particle swarm optimization chaos theory initialization strategy of chaos factor global particle stagnation-disturbance strategy design flood hydrograph

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

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Water Science and Engineering 2024年第1期17卷 13-20页

作者： Wen-zhuo Wang zeng-chuan Dong Tian-yan Zhang Li Ren Lian-qing Xue Teng Wu College of Water Resources and Hydrology Hohai UniversityNanjing 210098China Yellow River Research Center Hohai UniversityNanjing 210098China

Copula functions have been widely used in stochastic simulation and prediction of ***,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all *** address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal *** model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine *** up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine *** developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River *** results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of *** model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

关键词： Stochastic monthly streamflow simulation Mixed D-vine copula Conditional quantile model Up-to-down sequential method Tangnaihai hydrological station

Involvement of unusual noncovalent interactions in the self-assembly of cucurbit[6]uril with [CdCl_4]^(2-) anions

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Chinese Chemical Letters 2016年第1期27卷 173-177页

作者： Xiao-Wei Cui Shi-Yan Chen chuan-zeng Wang Wen-Xuan Zhao Tao Sun Xin-Long Ni Yun-Qian Zhang Zhu Tao Key Laboratory of Macrocyclic and Supramolecular Chemistry of Guizhou Province Guizhou University Key Laboratory of Guizhou High Performance Computational Chemistry Guizhou University

The [CdCl_4]^（2-） anion as a structure inducer has proved to be useful in the construction of cucurbit[n]urilmetal coordination architectures and materials. In order to better understand the role and influence of the structure inducer in Q[n] systems, we report herein the self-assembly of Q[6] solely in the presence of[CdCl_4]^（2-）anions and in the presence of both a linear cationic organic guest and [CdCl_4]^（2-）anions. X-ray diffraction analysis revealed that 1D Q[6] porous channels were formed by the noncovalent interactions between Q[6] and [CdCl_4]^（2-）anions, but the ＇＇honeycomb effect＇＇ was not observed in the present ***, it seems that the ＇＇honeycomb effect＇＇ and the self-assembly of Q[6] with [CdCl_4]^（2-）anions can be significantly modified and switched in the presence of a linear cationic dibutylamine guest through some unusual noncovalent interactions.

关键词： Cucurbituril [CdCl_4]^(2-) anions Cationic guest Honeycomb effect Assembly

超重力场反应熔铸合成TiB_2基复相陶瓷刀具材料

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中国有色金属学报 2015年第12期25卷 3439-3444页

作者：潘传增张靖张龙军械工程学院先进材料研究所石家庄050003

通过超重力场反应熔铸合成TiB_2基复相陶瓷刀具材料,研究材料的物相组成、组织结构及力学性能,探讨材料中典型组织的形成过程。结果表明:反应产物由TiB_2与TiC两相构成,尺寸约为2μm的TiB_2柱状晶构成陶瓷基体,TiC晶粒不规则地分布于Ti... 详细信息

通过超重力场反应熔铸合成TiB_2基复相陶瓷刀具材料,研究材料的物相组成、组织结构及力学性能,探讨材料中典型组织的形成过程。结果表明:反应产物由TiB_2与TiC两相构成,尺寸约为2μm的TiB_2柱状晶构成陶瓷基体,TiC晶粒不规则地分布于TiB_2晶粒之间,二者结合紧密,呈现出典型的凝固组织特征。所得反应产物的相对密度为93.2%,维氏显微硬度值为21.4 GPa,抗弯强度为258 MPa,断裂韧性为4.6 MPa·m^(0.5)。分析认为超重力场促进Ti-B-C中间熔体的生成,是合成TiB_2基复相陶瓷的关键。

关键词： TiB2 超重力场反应熔铸刀具