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THE GENERALIZED LOCAL HERMITIAN AND SKEW-HERMITIAN SPLITTING ITERATION METHODS FOR THE NON-HERMITIAN GENERALIZED SADDLE POINT PROBLEMS

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Journal of Computational Mathematics 2014年第3期32卷 312-331页

作者： Hongtao fan Bing zheng School of Mathematics and Statistics Lanzhou University Lanzhou 730000 China

For large and sparse saddle point problems, Zhu studied a class of generalized local Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian saddle point problem [M.-Z. Zhu, Appl. Math. Comput. 218 （2012） 8816-8824 ]. In this paper, we further investigate the generalized local Hermitian and skew-Hermitian splitting （GLHSS） iteration methods for solving non-Hermitian generalized saddle point problems. With different choices of the parameter matrices, we derive conditions for guaranteeing the con- vergence of these iterative methods. Numerical experiments are presented to illustrate the effectiveness of our GLHSS iteration methods as well as the preconditioners.

关键词： Generalized saddle point problems Hermitian and skew-Hermitian matrixsplitting Iteration method Convergence.

Investigation of high power laser coatings

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光学精密工程 2005年第4期13卷 471-479页

作者： SHAO Jian-da fan zheng-xiu R＆D Center for Optical Thin Film Coating Technology Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences Shanghai 201800 China

High laser-induced damage threshold and large aperture were focuses on the studies of high power laser coatings. This paper reports the research activities at our center. Several measures were developed for evaluating characters of laser damage, including determination of laser induced damage threshold and detection of absorption based on surface thermal lensing technique. Defect was deemed to be the initial source of laser damage, and was the main factor restricting the laser damage resistance of optical coatings. The contribution of several kinds of typical defects to laser damage was analyzed, and some deposition measures were adopted to control and eliminate the origin of defect. Furthermore, some post-treatment methods were also employed to alleviate the influence of the defect and to improve the laser damage resistance. Correction mask was introduced to improve the thickness uniformity, and the thickness uniformity can be amended to less than 1% in the range of Φ650 mm. Preliminary investigation related to surface deformation was also conducted.

关键词：激光涂覆技术 LIDT 吸收能力激光器

Bowel preparation before colonoscopy: Consequences, mechanisms, and treatment of intestinal dysbiosis

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World Journal of Gastroenterology 2025年第2期31卷 13-26页

作者： Ze-Long zheng Qing-fan zheng Li-Qiang Wang Yi Liu Department of Gastroenterology(Endoscopy Center) China-Japan Union Hospital of Jilin UniversityChangchun 130033Jilin ProvinceChina

The term“gut microbiota”primarily refers to the ecological community of various microorganisms in the gut,which constitutes the largest microbial community in the human *** adequate bowel preparation can improve the results of colonoscopy,it may interfere with the gut *** preparation for colonoscopy can lead to transient changes in the gut microbiota,potentially affecting an individual’s health,especially in vulnerable populations,such as patients with inflammatory bowel ***,measures such as oral pro-biotics may ameliorate these adverse *** focused on the bowel prepa-ration-induced changes in the gut microbiota and host health status,hypothesized the factors influencing these changes,and attempted to identify measures that may reduce dysbiosis,thereby providing more information for individualized bowel preparation for colonoscopy in the future.

关键词： Bowel preparation Colonoscopy Microbiota Inflammatory bowel disease Probiotics

A Lower Bound for the Algebraic Connectivity of a Graph in Terms of the Domination Number

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Acta Mathematicae Applicatae Sinica 2018年第4期34卷 752-760页

作者： Yi-zheng fan Ying-Ying TAN School of Mathematical Sciences Anhui University Hefei 230601 P. R. China School of Mathematics and Physics Anhui Jianzhu University Hefei 230601 China

We investigate how the algebraic connectivity of a graph changes by relocating a connected branch from one vertex to another vertex, and then minimize the algebraic connectivity among all connected graphs of order n with fixed domination number γ≤（n＋2）/3, and finally present a lower bound for the algebraic connectivity in terms of the domination number. We also characterize the minimum algebraic connectivity of graphs with domination number half their order.

关键词： graph algebraic connectivity domination number

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 concerted actions of Tipl/CLIP-170, Klp5/Kinesin-8, and Alpl4/XMAP215 regulate microtubule catastrophe at the cell end

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Journal of Molecular Cell Biology 2019年第11期11卷 956-966页

作者： Xiaojia Niu fan zheng Chuanhai Fu Division of Molecular&Cell Biophysics Hefei National Science Center for Physical SciencesUniversity of Science and Technology of ChinaHefeiAnhuiChina Chinese Academy of Sciences Center for Excellence in Molecular Cell Sciences School of Life SciencesUniversity of Science and Technology of ChinaHefeiAnhuiChina Anhui Key Laboratory for Cellular Dynamics&Chemical Biology University of Science and Technology of ChinaHefeiChina

Spatial regulation of microtubule catastrophe is important for controlling microtubule length and consequently contributes to the proper establishment of cell polarity and cell ***+TIP proteins including Tipl/CLIP-170,Klp5/Kinesin-8,and Alpl4/XMAP215 reside at microtubule plus ends to regulate microtubule *** the fission yeast Schizosaccharomyces pombe,Tipi and Alpl4 serve as microtubule-stabilizing factors,while Klp5 functions oppositely as a catastrophe-promoting *** that Tipi has been shown to play a key role in restricting microtubule catastrophe to the cell end,how Tipi fulfills the role remains to be *** live-cell microscopy,we showed that the absence of Tip i impairs the localization of both Klp5 and Alpl4 at microtubule plus ends,but the absence of Klp5 prolongs the residence time of Tipi at microtubule plus *** further revealed that Klp5 accumulates behind Tip i at microtubule plus ends in a Tipl-dependent *** addition,artificially tethering Klp5 to microtubule plus ends promotes premature microtubule catastrophe,while tethering Alpl4 to microtubule plus ends in the cells lacking Tipi rescues the phenotype of short *** findings establish that Tipi restricts microtubule catastrophe to the cell end likely by spatially restricting the microtubule catastrophe activity of Klp5 and stabilizing Alpl4 at microtubule plus ***,the work demonstrates the orchestration of Tipi,Alpl4,and Klp5 in ensuring microtubule catastrophe at the cell end.

关键词： microtubule microtubule catastrophe kinesin-8 Tipi Alpl4

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

Group-based user pairing for virtual MIMO in LTE

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The Journal of China Universities of Posts and Telecommunications 2007年第3期14卷 38-42页

作者： QIAN Yu fan Bin zheng Kan Wireless Signal Processing and Network Laboratory Beijing University ofPosts and Telecommunications Beijing 100876 China

A user pairing method is proposed to improve the throughput gain of virtual multiple input multiple output （virtual MIMO） in 3G long-term evolution（LTE）. The approach taken in this study separated the user pairing into four steps： 1） the users are divided into two groups according to their signal-to-noise ratio （SNR）, and different user pairing metrics are proposed for each group; 2） the scheduler chooses a user for transmitting by a given rule; 3） the scheduler searches the pairing candidate for the selected user in each group; 4） the scheduler chooses the final pairing user from the co-group and crossover-group candidates by using a marginal utility function, to balance fairness and efficiency. The method can improve the throughput of users with high SNR, and guarantee fairness for users with low SNR, so it can be used in 3G LTE systems. The article provides both theoretical analysis and simulation results to support the idea.

关键词： virtual MIMO user pairing 3G LTE space division multiple access (SDMA)

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