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On Edge Singularity and Eigenvectors of Mixed Graphs

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Acta Mathematica Sinica,English Series 2008年第1期24卷 139-146页

作者： ying ying TAN yi zheng fan School of Mathematics and Computation Sciences Anhui UniversityHefei 230039 P. R. China Department of Mathematics and Physics Anhui Institute of Architecture and Industry Hefei 230022 Po R. China

Let G be a mixed glaph which is obtained from an undirected graph by orienting some of its edges. The eigenvalues and eigenvectors of G are, respectively, defined to be those of the Laplacian matrix L（G） of G. As L（G） is positive semidefinite, the singularity of L（G） is determined by its least eigenvalue λ1 （G）. This paper introduces a new parameter edge singularity εs（G） that reflects the singularity of L（G）, which is the minimum number of edges of G whose deletion yields that all the components of the resulting graph are singular. We give some inequalities between εs（G） and λ1 （G）（and other parameters） of G. In the case of εs（G） = 1, we obtain a property on the structure of the eigenvectors of G corresponding to λ1 （G）, which is similar to the property of Fiedler vectors of a simple graph given by Fiedler.

关键词： mixed graphs edge singularity Laplacian eigenvectors

The Distance Coloring of Graphs

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Acta Mathematica Sinica,English Series 2014年第9期30卷 1579-1587页

作者： Lian ying MIAO yi zheng fan Institute of Mathematics China University of Mining and Technology School of Mathematical Sciences Anhui University

Let G be a connected graph with maximum degree △≥ 3. We investigate the upper bound for the chromatic number Xr（G） of the power graph Gr. It was proved that Xr（G） ≤ △ （△-1）r-1/△-2 ＋1 =M ＋ 1, where the equality holds if and only if G is a Moore graph. If G is not a Moore graph, and G satisfies one of the following conditions：（1） G is non-regular, （2） the girth g（G）≤2r - 1, （3） g（G） ≥ 2r＋ 2, and the connectivity k（G） ≥ 3 if r ≥ 3, k（G）≥4 but g（G）〉 6 if r= 2, （4） A is sufficiently larger than a given number only depending on % then Xr（G） ≤ M - 1. By means of the spectral radius λ1（G） of the adjacency matrix of G, it was shown that X2（G） ≤λ1（G）2＋ 1, where the equality holds if and only if G is a star or a Moore graph with diameter 2 and girth 5, and Xr（G）〈 λ1（G）r＋ 1 if ≥ 3.

关键词： Distance coloring power graph spectral radius

The Linear Unicyclic Hypergraph with the Second or Third Largest Spectral Radius

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Acta Mathematica Sinica,English Series 2020年第10期36卷 1140-1150页

作者： Chao DING yi zheng fan Jiang Chao WAN School of Mathematics and Physics Anqing Normal UniversityAnqing 246133P.R.China School of Mathematical Sciences Anhui UniversityHefei 230601P.R.China

The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the *** is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,and the unique linear unicyclic hypergraph with the largest spectral radius is a power *** this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius,where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.

关键词： Linear unicyclic hypergraph adjacency tensor spectral radius weighted incident matrix

Flow-restricted Etching Method on Isotropic Substrates and Its Mechanism

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Chinese Journal of Mechanical Engineering 2010年第5期23卷 560-567页

作者： XIE Haibo zheng yi fan Yurun FU Xin YANG Huayong The State Key Lab of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

With the development of analytical instrumentation to minimization,integration and automation,the microfluidic chips,which are more integrated,complex and diversified,have been applied widely on the manufacturing of analytical ***,the present photolithography-based microfabrication technology,which is only able to pattern microchannels with simple inside structures,can not follow the rapid development of *** solving the problem,a fabrication method based on the restricting effect of laminar flow is proposed for the micro etching on isotropic *** were conducted inside glass-based microchannels,in which certain etchant was used to form complicated *** flow parameters＇ effects on the aspect ratio,side wall profile and etching rate were revealed by the *** experimental results reveal that the topography of micro structures patterned with the restricted flow etching method is mainly determined by the flowrates of separator and *** computational fluid dynamics（CFD） model on the interface between multiple streams was established for the etching process,and analysis on the causes of various micro topographies was conducted based on the CFD simulation *** experimental data consisted with the simulation results very *** investigation depicted in this paper indicate that the flow restricted etching method provides sufficient references for the research and understanding on the mass transport at the liquid-liquid surface in the microchannel and can be used to pattern complex micro structures with high aspect ratios,meantime,it greatly enriches the microfabrication technology for microfluidic chips.

关键词： microfluidics etching computational fluid dynamics(CFD) laminar

Synthesis of Cu_2O nanobelts via surfactant-assisted polyol method

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Chinese Chemical Letters 2011年第7期22卷 879-882页

作者： Xin Wen Huang Zong Jian Liu yi fan zheng College of Biological and Environmental Engineering Zhejiang University of Technology Hangzhou 310014 China Resource & Environment Catalysis Institute College of Chemical Engineering and Materials Science Zhejiang University of Technology Hangzhou 310014 China

The synthesis of nanostructured Cu2O was conducted in a non-aqueous solution via polyol method at a temperature of 130 ℃. It was found that the formation of Cu2O nanobelts was heavily dependent on the presence of surfactant cetyltrimethylammonium bromide （CTAB）. Cu2O nanobelts with 100400 nm in width and several micrometers in length were only observed when CTAB was used, whereas in other cases where CTAB was absent or CTAB was replaced with polyvinylpyrrolidone （PVP K-30）, only spherical or cube-like particles were formed. The formation mechanism of Cu2O nanobelts was discussed.

关键词： Cuprous oxide Nanobelts Surfactant Polyol method

Synthesis of SnO_2 nanorods from aqueous solution:The effect of preparation conditions on the formed patterns

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Chinese Chemical Letters 2010年第8期21卷 999-1002页

作者： Xin Wen Huang Zong Jian Liu yi fan zheng Qiu Lin Nie Resource & Environment Catalysis Institute College of Chemical Engineering and Materials Science Zhejiang University of Technology Hangzhou 310014 China College of Biological and Environmental Engineering Zhejiang University of Technology Hangzhou 310014 China College of Mechanical & Electrical Engineering Hangzhou Dianzi University Hangzhou 300018 China

SnO2 nanorods were deposited on the Si substrates in an aqueous solution containing both SnCl4 and CO（NH2）*** is found that different self-assembled patterns of SnO2 nanorods can be obtained by changing the deposition conditions such as the molar ratio of CO（NH2）2 to SnCl4 and the pretreatment of the *** SnO2 nanorods,for example,can be changed into flower-like patterns when the molar ratio of CO（NH2）2 to SnCl4 is raised,and well-aligned nanorod arrays can be formed when the pretreatment of the substrate is *** addition,some interesting patterns,***-like patterns,can also be observed.

关键词： Tin dioxide Nanorods Heterogeneous nucleation

On the Least Eigenvalue of Graphs with Cut Vertices

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Journal of Mathematical Research and Exposition 2010年第6期30卷 951-956页

作者： yi WANG Yun QIAO yi zheng fan School of Mathematical Sciences Anhui UniversityAnhui 230039P.R.China

Let ψ be a certain set of graphs.A graph is called a minimizing graph in the set ψ if its least eigenvalue attains the minimum among all graphs in ψ.In this paper,we determine the unique minimizing graph in ψn,whe... 详细信息

关键词： adjacency matrix least eigenvalue minimizing graph cut vertex.

Experimental validation of material discrimination ability of muon scattering tomography at the TUMUTY facility

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Nuclear Science and Techniques 2019年第8期30卷 26-34页

作者： Xing-Yu Pan yi-fan zheng Zhi Zeng Xue-Wu Wang Jian-Ping Cheng Key Laboratory of Particle and Radiation Imaging(Ministry of Education) and Department of Engineering Physics Tsinghua UniversityBeijing 100084China Department of Nuclear Engineering University of CaliforniaBerkeleyCA 94709USA Department of Radiology and Biomedical Imaging University of CaliforniaSan FranciscoCA 94143USA College of Nuclear Science and Technology Beijing Normal UniversityBeijing 100875China

Muon scattering tomography is believed to be a promising technique for cargo container inspection, owing to the ability of natural muons to penetrate into dense materials and the absence of artificial radiation. In this work, the material discrimination ability of muon scattering tomography is evaluated based on experiments at the Tsinghua University cosmic ray muon tomography facility,with four materials: flour(as drugs substitute), aluminum,steel, and lead. The features of the different materials could be discriminated with cluster analysis and classifiers based on support vector machine. The overall discrimination precisions for these four materials could reach 70, 95, and 99% with 1-, 5-, and 10-min-long measurement,respectively.

关键词： Muon tomography Cargo containerinspection Material discrimination SVM classifier

BiIO4 Nanoflakes for the Degradation of Phenol under Simulated Solar Light Irradiation

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Chinese Journal of Structural Chemistry 2019年第8期38卷 1404-1413页

作者： LIU Min-yi LIU Qing-ying zheng yi-fan LIN Guo-Liang SONG Xu-Chun Department of Chemistry Fujian Normal UniversityFuzhou350007China College of Ecological Environment and Urban Construction Fujian University of TechnologyFuzhou350118China Research Center of Analysis and Measurement Zhejiang University of TechnologyHangzhou310014China Fujian Provincial Key Laboratory of Advanced Technologyand Information in Civil Engineering Fuzhou350118China

BiIO4 nanoflakes were successfully prepared through a facile hydrothermal method. The as-prepared BiIO4 was characterized by scanning electron microscope(SEM), high-resolution transmission electron microscopy(HRTEM), X-ray diffraction(XRD), energy-dispersive spectroscopy(EDS) and ultraviolet visible diffuse reflectance spectroscopy. BiIO4 nanoflakes showed excellent photocatalytic activity for the degradation of phenol solution under simulated solar irradiation. The influence of synthesis temperature on the morphology, size and photocatalytic performance of BiIO4 was investigated. BiIO4 prepared under 140 ℃ exhibited the highest removal rate of phenol under simulated solar light irradiation. In addition, the parametric studies such as the effect of catalyst loading and phenol solution pH were carried out to optimize the reaction conditions. The active species trapping experiment demonstrated that h+ and ·OH are the major active species during the photocatalytic process.

关键词： BiIO4 nanoflakes photocatalytic