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A Note on Upper Convex Density

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Communications in Mathematical Research 2010年第4期26卷 361-368页

作者： YIN JIAN-DONG zhou zuo-ling Department of Mathematics Nanchang University Nanchang 330031 lingnan College Zhongshan University Guangzhou 510275

For a self-similar set E satisfying the open set condition,upper convex density is an important concept for the computation of its Hausdorff measure,and it is well known that the set of relative interior points with upper convex density 1 has a full Hausdorff *** whether the upper convex densities of E at all the relative interior points are equal to 1？ In other words,whether there exists a relative interior point of E such that the upper convex density of E at this point is less than 1？ In this paper,the authors construct a self-similar set satisfying the open set condition,which has a relative interior point with upper convex density less than ***,the above problem is sufficiently answered.

关键词： self-similar set open set condition upper convex density

The Hausdorff Dimension and Hausdorff Measure of Full Parry Measure Subset of Finite Type

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Northeastern Mathematical Journal 2006年第1期22卷 114-118页

作者：尹建东周作领 Mathematics and Computing Science College Zhongshan University Guangzhou 510275 lingnan College Zhongshan University Guangzhou 510275

All the full Parry measure subsets of a given subshift of finite type determined by an irreducible 0-1 matrix have the same Hausdorrf dimension and Hausdorff measure which coincide with those of the set of finite type.

关键词： chaotic set set of finite type Hausdorff dimension Hausdorff measure

Comparative Analysis of Diagonal and Centrifugal Compressors with Synergy Theory in Compressed Air Energy Storage System

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Journal of Thermal Science 2024年第4期33卷 1325-1339页

作者： ZHANG Yuxin zuo Zhitao zhou Xin GUO Wenbin CHEN Haisheng Institute of Engineering Thermophysics Chinese Academy of SciencesBeijing100190China University of Chinese Academy of Sciences Beijing100049China National Energy Large Scale Physical Energy Storage Technologies R&D Center of Bijie Bijie551700China Nanjing Institute of Future Energy System IETCASNanjing211135China

Energy storage technology is an essential part of the efficient energy *** air energy storage(CAES)is considered to be one of the most promising large-scale physical energy storage *** is favored because of its low-cost,long-life,environmentally friendly and low-carbon *** compressor is the core component of CAES,and the performance is critical to the overall system *** importance is not only reflected in the design point,but also in the continuous efficient operation under variable working *** diagonal compressor is currently the focus of the developing large-scale CAES because of its stronger flow capacity compared with traditional centrifugal *** the diagonal compressor has the higher single stage pressure ratio compared with axial *** this paper,the full three dimensional numerical simulation technologies with synergy theory are used to compare and analyze the internal flow *** performance of the centrifugal and diagonal impellers that are optimized under the same requirements for large-scale CAES has been *** relationship between the internal flow characteristics and performance of the centrifugal and diagonal impellers with the change of mass flow rates and total inlet temperature is given qualitatively and *** the cosine value of the synergy angle is high,the local flow loss is *** smaller proportion of the positive area is the pursuit of *** comparative analysis,it is concluded that the internal flow and performance changes of centrifugal and diagonal impellers are *** results confirm the superiority and feasibility of the off-design performance of the diagonal compressor applied to the developing large-scale CAES.

关键词： compressed air energy storage synergy theory diagonal compressor centrifugal compressor comparative analysis

Neural-field-assisted transport-of-intensity phase microscopy: partially coherent quantitative phase imaging under unknown defocus distance

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Photonics Research 2024年第7期12卷 1494-1501页

作者： YANBO JIN LINPENG LU SHUN zhou JIE zhou YAO FAN CHAO zuo Smart Computational Imaging Laboratory(SCILab) School of Electronic and Optical EngineeringNanjing University of Science and TechnologyNanjing 210094China Smart Computational Imaging Research Institute(SCIRI)of Nanjing University of Science and Technology Nanjing 210019China Jiangsu Key Laboratory of Spectral Imaging&Intelligent Sense Nanjing 210094China

The transport-of-intensity equation(TIE) enables quantitative phase imaging(QPI) under partially coherent illumination by measuring the through-focus intensities combined with a linearized inverse reconstruction algorithm. However, overcoming its sensitivity to imaging settings remains a challenging problem because of the difficulty in tuning the optical parameters of the imaging system accurately and because of the instability to long-time measurements. To address these limitations, we propose and experimentally validate a solution called neural-field-assisted transport-of-intensity phase microscopy(NFTPM) by introducing a tunable defocus parameter into neural field. Without weak object approximation, NFTPM incorporates the physical prior of partially coherent image formation to constrain the neural field and learns the continuous representation of phase object without the need for training. Simulation and experimental results of He La cells demonstrate that NFTPM can achieve accurate, partially coherent QPI under unknown defocus distances, providing new possibilities for extending applications in live cell biology.

关键词： field coherent phase

A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 695-707页

作者： Song-bai GUO Yu-ling XUE Xi-liang LI zuo-huan ZHENG School of Science Beijing University of Civil Engineering and ArchitectureBeijing 102616China School of Mathematics and Statistics Hainan Normal UniversityHaikou 571158China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematics and Information Science Shandong Technology and Business UniversityYantai 264005China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>*** approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using *** addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)1.

关键词： uniform persistence epidemic model control reproduction number quarantine standard incidence rate

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分形几何和动力系统中的一些问题

工程数学学报 2006年第5期23卷 761-766页

作者：周作领乐军中山大学岭南学院广州510275 广东广播电视大学广州510275

本文是zhou与Feng,Nonlinearity,2004的续篇,对自相似集的结构和动力系统提出一些较为深入的问题。

关键词：分形几何动力系统

Experimental and numerical investigation of two blended blade and endwall configurations

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CHINESE JOURNAL OF AERONAUTICS 2024年第9期37卷 150-163页

作者： Meng, Tongtong Li, Xin zhou, ling Ji, Lucheng Tsinghua Univ Inst Aero Engine Beijing 100084 Peoples R China Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China

The Blended Blade and Endwall (BBEW) technique has proven to be effective in controlling the intersection of boundary layer in corner region of the compressor endwall. In this study, the experiment and analysis of two different BBEW designs are emphasized. First, based on a linear cascade with 0.7 Mach number inflow, two different configurations, BBEW 1 and BBEW 2, are well conducted. Then, according to the experimental result, control effects of these two BBEW configurations are validated and compared subsequently under various working conditions. The results demonstrate a reduction in total pressure loss of 12.8% and 29% at the design point for BBEW 1 and BBEW 2, respectively. Consequently, the BBEW technique proves effective in suppressing the development of the boundary layer and preventing corner separation. Followed by detailed numerical analysis, improvements around the corner region, especially for the boundary layer, are extracted to show the mechanisms and distinctions between the two configurations. The results indicate that BBEW 1 significantly restrains the development of boundary layer before separation occurs, while BBEW 2 directly controls the strength and scale of the corner separation. (c) 2024 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics.

关键词： Aerodynamic Computational fluid dynamic Experiment Corner separation Blended Blade and Endwall (BBEW) COMPRESSOR DESIGN SUCTION FLOW

关于满足强分离开集条件的自相似集的Hausdorff测度

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数学进展 2005年第5期34卷 545-552页

作者：许绍元周作领中山大学数学与计算科学学院中山大学岭南学院广州广东510275

设E是Rn中由相似压缩S1,S2,…,Sm所确定的满足开集条件的自相似集,其Hausdorff维数为s,其s-维Hausdorff测度记为Hs(E).利用部分估计原理得到了本文的主要结果:若E满足强分离开集条件,则在E中存在一个压缩拷贝串序列{Ui}和紧集U(|U|>0),... 详细信息

设E是Rn中由相似压缩S1,S2,…,Sm所确定的满足开集条件的自相似集,其Hausdorff维数为s,其s-维Hausdorff测度记为Hs(E).利用部分估计原理得到了本文的主要结果:若E满足强分离开集条件,则在E中存在一个压缩拷贝串序列{Ui}和紧集U(|U|>0),使得Hs(U)等于|U|s,并且{Ui}按Hausdorff度量收敛到U,进而证明了由U可以构造一个数列,使得该数列正好收敛到Hs(E);另外,引入了自相似集的相似压缩不动点,得到了等式Hs(E∩U)=|U|s 成立的一个必要条件.

关键词：自相似集 Hausdorff测度与维数强分离开集条件 Hausdorff度量相似压缩不动点

Tomographic particle image velocimetry measurement on three-dimensional swirling flow in dual-stage counter-rotating swirler

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Chinese Journal of Aeronautics 2024年第3期37卷 7-20页

作者： Yuyang zhou ling DONG Mingtao SHANG Jibao LI Akira RINOSHIKA Key Laboratory of Fluid Mechanics of Ministry of Education Beihang UniversityBeijing 100191China School of Mechanical and Automotive Engineering Shanghai University of Engineering ScienceShanghai 201620China AECC Commercial Aircraft Engine Co. Ltd.Shanghai 200241China Department of Mechanical Systems Engineering Yamagata UniversityYamagata 992-8510Japan

Three-Dimensional(3D)swirling flow structures,generated by a counter-rotating dualstage swirler in a confined chamber with a confinement ratio of 1.53,were experimentally investigated at Re=2.3×10^(5)using Tomographic Particle Image Velocimetry(Tomo-PIV)and planar Particle Image Velocimetry(PIV).Based on the analysis of the 3D time-averaged swirling flow structures and 3D Proper Orthogonal Decomposition(POD)of the Tomo-PIV data,typical coherent flow structures,including the Corner Recirculation Zone(CRZ),Central Recirculation Zone(CTRZ),and Lip Recirculation Zone(LRZ),were *** counter-rotating dual-stage swirler with a Venturi flare generates the independence process of vortex breakdown from the main stage and pilot stage,leading to the formation of an LRZ and a smaller CTRZ near the nozzle *** confinement squeezes the CRZ to the corner and causes a reverse rotation flow to limit the shape of the CTRZ.A large-scale flow structure caused by the main stage features an explosive breakup,flapping,and Precessing Vortex Core(PVC).The explosive breakup mode dominates the swirling flow structures owing to the expansion and construction of the main jet,whereas the flapping mode is related to the wake *** limits the expansion of PVC and causes it to contract after the impacting area.

关键词： Coherent structures Dual-stage counter-rotating swirler cup Precessing vortex core Proper orthogonal decomposition Swirling flow Tomographic particle image velocimetry