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Some Ore-type Results for Matching and Perfect Matching in k-uniform Hypergraphs

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Acta Mathematica Sinica,English Series 2018年第12期34卷 1795-1803页

作者： Yi ZHANG mei lu Department of Mathematical Sciences Tsinghua University

Let SI and S2 be two （k- 1）-subsets in a k-uniform hypergraph H. We call S1 and S2 strongly or middle or weakly independent if H does not contain an edge e ∈ E（H） such that S1 ∩ e≠ 0 and S2 ∩ e ≠0 or e S1 ∪ S2 or e S1 ∪ S2, respectively. In this paper, we obtain the following results concerning these three independence. （1） For any n ≥ 2k2 - k and k ≥ 3, there exists an n-vertex k-uniform hypergraph, which has degree sum of any two strongly independent （k - 1）-sets equal to 2n - 4（k - 1）, contains no perfect matching; （2） Let d ≥ 1 be an integer and H be a k-uniform hypergraph of order n ≥ kd＋（k- 2）k. If the degree sum of any two middle independent （k- 1）-subsets is larger than 2（d- 1）, then H contains a d-matching; （3） For all k ≥ 3 and sufficiently large n divisible by k, we completely determine the minimum degree sum of two weakly independent （k - 1）-subsets that ensures a perfect matching in a k-uniform hypergraph H of order n.

关键词： Ore-type condition matching perfect matching hypergraph

Lower Bounds on the(Laplacian) Spectral Radius of Weighted Graphs

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Chinese Annals of Mathematics,Series B 2014年第4期35卷 669-678页

作者： Aimei YU mei lu Department of Mathematics Beijing Jiaotong University Department of Mathematical Sciences Tsinghua University

The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds.

关键词： Weighted graphs Adjacency matrix Laplacian matrix Spectral radius Lower bounds

Perfect Matching in k-partite k-graphs and 3-uniform HM-bipartite Hypergraphs

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Acta Mathematicae Applicatae Sinica 2020年第3期36卷 636-641页

作者： Chun-qiu FANG mei lu Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China

Let H=(V,E)be an n-balanced k-partite k-graph with partition classes V1,...,*** for every legal(k-1)-tuple f contained in V\V1 and for every legal(k-1)-tuple g contained in V\Vk such that f∪g■E(H),we have d(f)+d(g)≥n+*** this paper,we prove that under this condition H must have a perfect *** result of this paper is about the perfect matching in 3-uniform hm-bipartite *** G be a 3-uniform hm-bipartite hypergraph with one of whose sides V1 has the size n,the another side V2 has size 2 *** for all the legal 2-tuple f with|f∩V1|=1 and for all the legal 2-tuple g with|g∩V1|=0,we have d(f)≥n-2 and d(g)>n/2,then G has a perfect matching.

关键词： Perfect matching k-partite k-graph hm-bipartite hypergraph

The Game of Cops and Robbers on Directed Graphs with Forbidden Subgraphs

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Acta Mathematicae Applicatae Sinica 2022年第3期38卷 684-689页

作者： Ming-rui LIU mei lu Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China

The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of the corresponding class of graphs. In this paper, we analyze the game of cops and robbers on H^(-)-free digraphs. However, it is not the same as the case of undirected graph. So we give a new concept(H^(-)^(*)-free digraph) to get a similar conclusion about the case of undirected graph.

关键词： cops and robbers directed graph induced subgraphs

Receding horizon H_∞ control for constrained time-delay systems

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Journal of Systems Engineering and Electronics 2009年第2期20卷 363-370页

作者： lu mei Jin Chengbo Shao Huihe Inst. of Automation Shanghai Jiaotong Univ. Shanghai 200240 P. R. China Dept. of Fieldbus Shanghai Automation Instrument Co. Ltd. Shanghai 200233 P. R. China Dept. of Product Design Shanghai Gaoke Valve Manufactory Co. Ltd. Shanghai 200092 P. R. China

A receding horizon Hoo control algorithm is presented for linear discrete time-delay system in the presence of constrained input and disturbances. Disturbance attenuation level is optimized at each time instant, and the receding optimization problem includes several linear matrix inequality constraints. When the convex hull is applied to denote the saturating input, the algorithm has better performance. The numerical example can verify this result.

关键词： receding horizon control Hoo control time-delay constrained input

NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL CONTROLLABILITY OF A CLASS OF AFFINE NONLINEAR SYSTEMS

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Journal of Systems Science & Complexity 2007年第4期20卷 492-500页

作者： Yimin SUN Shengwei mei Qiang lu Department of Electrical Engineering Tsinghua University Beijing 100084 China

In this paper, we investigate the global controllability of a class of n-dimensional affine nonlinear systems with n- 1 controls and constant control matrix. A necessary and sufficient condition for its global controllability has been obtained by using the methods recently developed. Furthermore, we generalize the above result to a class of affine nonlinear systems with a block-triangular-like structure. Finally, we will give three examples to show the applications of our results.

关键词： Affine nonlinear systems block-triangular-like structure global controllability vector field

Study on carbon emission calculation method and carbon reduction indexes of urban building stock

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Science China(Technological Sciences) 2024年第9期67卷 2706-2726页

作者： YANG Liu ZHANG Nan lu mei luO ZhiXing DOU mei State Key Laboratory of Green Building Xi’an University of Architecture and TechnologyXi’an 710055China School of Architecture Xi’an University of Architecture and TechnologyXi’an 710055China School of Language Literature and LawXi’an University of Architecture and TechnologyXi’an 710055China School of Management Xi’an University of Architecture and TechnologyXi’an 710055China China Southwest Architectural Design and Research Institute Corp.Ltd. Chengdu 610041China

Carbon emissions associated with buildings are a major source of urban emissions. To put forward the methods and strategies to curb carbon emissions from urban building stock, it is not only necessary to establish a carbon emission calculation method for fine statistical analysis, but also to evaluate carbon emissions of urban planning schemes with applicable indexes. Currently,researches mainly focus on carbon emissions of individual buildings. When expanded to urban building stock, the calculation faces the lack of basic data, inadequate spatial analysis and unspecific carbon reduction indexes. Therefore, this study proposes a bottom-up calculation method for urban building stock, conducts spatial analysis based on carbon balance of urban grids, reveals the coupling mechanism between urban carbon reduction indexes and grid carbon emissions, and systematically establishes a carbon-reduction-oriented urban planning method that comprises calculation, analysis and evaluation, which is applied to Xi'an,China. This study provides a theoretical reference for cities to formulate carbon reduction targets and implement planning strategies by evaluating and predicting carbon emissions from urban building stock.

关键词： carbon emissions urban building stock calculation method carbon reduction index

Survey on Lie Group Machine Learning

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Big Data Mining and Analytics 2020年第4期3卷 235-258页

作者： mei lu Fanzhang Li the School of Software Engineering Jinling Institute of TechnologyNanjing 211169China the School of Computer Science and Technology Jiangsu Normal UniversityXuzhou 221000China the School of Computer Science and Technology Soochow UniversitySuzhou 215006China

Lie group machine learning is recognized as the theoretical basis of brain intelligence,brain learning,higher machine learning,and higher artificial *** sets of Lie group matrices are widely available in practical *** group learning is a vibrant field of increasing importance and extraordinary potential and thus needs to be developed *** study aims to provide a comprehensive survey on recent advances in Lie group machine *** introduce Lie group machine learning techniques in three major categories:supervised Lie group machine learning,semisupervised Lie group machine learning,and unsupervised Lie group machine *** addition,we introduce the special application of Lie group machine learning in image *** work covers the following techniques:Lie group machine learning model,Lie group subspace orbit generation learning,symplectic group learning,quantum group learning,Lie group fiber bundle learning,Lie group cover learning,Lie group deep structure learning,Lie group semisupervised learning,Lie group kernel learning,tensor learning,frame bundle connection learning,spectral estimation learning,Finsler geometric learning,homology boundary learning,category representation learning,and neuromorphic synergy ***,this survey aims to provide an insightful overview of state-of-the-art development in the field of Lie group machine *** will enable researchers to comprehensively understand the state of the field,identify the most appropriate tools for particular applications,and identify directions for future research.

关键词： Lie group machine learning Lie group subspace orbit generation learning quantum group learning symplectic group learning Lie group fiber bundle learning

Panconnectivity for Interconnection Networks with Faulty Elements

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Acta Mathematica Sinica,English Series 2010年第4期26卷 647-652页

作者： mei lu Hui Qing LIU Department of Mathematical Sciences Tsinghua University Beijing 100084 P. R. China School of Mathematics and Computer Science Hubei University Wuhan 430062 P. R. China

Let Go and G1 be two graphs with the same vertices. The new graph G（G0, G1; M） is a graph with the vertex set V（0o） ∪）V（G1） and the edge set E（Go） UE（G1） UM, where M is an arbitrary perfect matching between the vertices of Go and G1, i.e., a set of cross edges with one endvertex in Go and the other endvertex in G1. In this paper, we will show that if Go and G1 are f-fault q-panconnected, then for any f 〉 2, G（G0, G1; M） is （f ＋ 1）-fault （q ＋ 2）-panconnected.

关键词： fault vertex fault edge fault panconnected interconnection networks