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Ramsey Numbers of Trees Versus Multiple Copies of Books

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 600-612页

作者： Xiao-bing GUO Si-nan HU yue-jian peng School of Mathematical Sciences Luoyang Normal UniversityLuoyang 471934China School of Mathematics Hunan UniversityChangsha 410082China

Given two graphs G and H,the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of K_(N) in red or blue yields a red G or a blue *** v(G) be the number of vertices of G and χ(G) be the chromatic number of *** s(G) denote the chromatic surplus of G,the number of vertices in a minimum color class among all proper χ(G)-colorings of *** showed that R(G,H)≥(v(G)-1)(χ(H)-1)+s(H) if G is connected and v(G)≥s(H).A connected graph G is H-good if R(G,H)=(v(G)-1)(χ(H)-1)+s(H).Let tH denote the disjoint union of t copies of graph H,and let G∨H denote the join of G and *** a complete graph on n vertices by K_(n),and a tree on n vertices by T_(n).Denote a book with n pages by B_(n),i.e.,the join K_(2) ∨■.Erd?s,Faudree,Rousseau and Schelp proved that T_(n) is B_(m)-good if n≥*** this paper,we obtain the exact Ramsey number of T_(n) versus 2B_(2).Our result implies that T_(n) is 2B_(2)-good if n≥5.

关键词： ramsey number ramsey goodness tree book

The Maximum Lagrangian of 5-uniform Hypergraphs without Containing Two Edges Intersecting at a Vertex

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Acta Mathematica Sinica,English Series 2022年第5期38卷 877-889页

作者： Biao WU yue jian peng MOE-LCSM School of Mathematics and StatisticsHu’nan Normal UniversityChangsha 410081P.R.China School of Mathematics Hu’nan UniversityChangsha 410082P.R.China

Obtaining Turán densities of hypergraph through determining Lagrangian densities have been studied *** showed that the Lagrangian density of an r-uniform hypergraph equals the Turán density of the extension of this ***,Lagrangian density and Turán density are the same for a large class of hypergraphs such as hypergraphs covering *** Pr,sbe the r-uniform hypergraph with two edges intersecting at s *** determined the Lagrangian densities of Pr,sfor r=3 and s=1 or 2,or r=4 and s=2 or *** and Keevash determined for r=3 and s=0,and Bene Watts,Norin and Yepremyan determined for r≥4 and s=*** cases r=5 and s=4 or r=6 and s=5 were determined by Norin and *** showed for r=5,6 or 7,and s=3,4 or 5 *** cases r=4 and s=1 or r=5 and s=2 were determined by jiang,peng and Wu,and Hu,peng and Wu *** r=5,the only remaining case is s=*** this paper,we determine for this case.

关键词： Hypergraph Lagrangian Turán number

Connection Between Continuous Optimization and Turán Densities of Non-uniform Hypergraphs

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Acta Mathematicae Applicatae Sinica 2021年第4期37卷 858-866页

作者： Xiao-bing GUO yue-jian peng School of Mathematics Hunan UniversityChangsha410082China

A classical result of Motzkin and Straus established the connection between the Lagrangian of a graph and its maximum *** it,they gave a new proof of Turán’s *** aroused the interests in studying the connection between continuous optimization and extremal problems in *** 2009,*** Bulòand *** extended the result of Motzkin-Straus to r-uniform ***,Johnston and Lu initiated the study of the Turán density of a non-uniform *** optimization problems related to several types of non-uniform hypergraphs and its applications on Turán densities have also been *** this paper,we obtain a Motzkin-Straus type of results for all non-uniform *** it,we give an upper bound of the Turán density of a complete non-uniform hypergraph.

关键词： hypergrapli maximum clique polynomial optimization

Maximum Cliques of Hypergraphs and Polynomial Optimization

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Acta Mathematicae Applicatae Sinica 2018年第4期34卷 842-855页

作者： Yan-ming CHANG yue-jian peng College of Mathematics Hunan University Changsha 410082 China Institute of Mathematics Hunan University Changsha 410082 China

A remarkable connection between the clique number and the Lagrangian of a graph was established by Motzkin and Straus. Later, Rota Bul′o and Pelillo extended the theorem of Motzkin-Straus to r-uniform hypergraphs by studying the relation of local（global） minimizers of a homogeneous polynomial function of degree r and the maximal（maximum） cliques of an r-uniform hypergraph. In this paper, we study polynomial optimization problems for non-uniform hypergraphs with four different types of edges and apply it to get an upper bound of Tur′an densities of complete non-uniform hypergraphs.

关键词： hypergraph maximum clique polynomial optimization

On Graph-Lagrangians and Clique Numbers of 3-Uniform Hypergraphs

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Acta Mathematica Sinica,English Series 2016年第8期32卷 943-960页

作者： Yan Ping SUN yue jian peng Biao WU College of Mathematics and Econometrics Hu'nan University Institute of Mathematics Hu'nan University

The paper explores the connection of Graph-Lagrangians and its maximum cliques for 3-uniform hypergraphs. Motzkin and Straus showed that the Graph-Lagrangian of a graph is the Graph-Lagrangian of its maximum cliques. This connection provided a new proof of Turin classical result on the Turan density of complete graphs. Since then, Graph-Lagrangian has become a useful tool in extremal problems for hypergraphs. peng and Zhao attempted to explore the relationship between the Graph-Lagrangian of a hypergraph and the order of its maximum cliques for hypergraphs when the number of edges is in certain range. They showed that if G is a 3-uniform graph with m edges containing a clique of order t - 1, then A（G） = A（[t- 1]（3）） provided （t31） ≤ m ≤ （3^t1）＋（2^rt-2）. They also conjectured： If G is an r-uniform graph with m edges not containing a clique of order t - 1, then A（G）〈 A（[t - 1]（r）） provided （r^t-1） ≤ m ≤ （r^t-1）＋（r-1^t-2）. It has been shown that to verify this conjecture for 3-uniform graphs, it is sufficient to verify the conjecture for left-compressed 3-uniform graphs with m = （3^t-1）＋（2^t-2）. Regarding this conjecture, we show： If G is a left-compressed 3-uniform graph on the vertex set It] with m edges and lit - 1]（3）／ E（G）｜=- p, then A（G）〈 A（[t - 1]（3）） provided m = （3^t-1）＋（2^t-2） and t ≥ 17p/2 ＋ 11.

关键词： Lagrangians of hypergraphs extremal problems in hypergraphs

On Frankl and Fredi's Conjecture for 3-uniform Hypergraphs

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Acta Mathematicae Applicatae Sinica 2016年第1期32卷 95-112页

作者： Qing-song TANG Hao peng Cai-ling WANG yue-jian peng College of Sciences Northeastern University School of Mathematics Jilin University College of Mathematics Hunan University

Frankl and Füredi in [1] conjectured that the r-graph with m edges formed by taking the first m sets in the colex ordering of N^（r） has the largest Lagrangian of all r-graphs with m *** this r-graph by Cr,m and the Lagrangian of a hypergraph by λ（G）.In this paper,we first show that if（3^t-1） ≤m〈（3^t）,G is a left-compressed 3-graph with m edges and on vertex set[t],the triple with minimum colex ordering in G^c is（t — 2 — i）（t — 2）t,then λ（G） ≤λ（C3,m）.As an implication,the conjecture of Frankl and Fiiredi is true for（3^t）-6≤m≤（3^t）.

关键词： Colex ordering Lagrangians of r-graphs extremal problems in combinatorics

Knittable and washable aerogel fiber inspired by polar bear hair

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Science China Materials 2024年第2期67卷 705-706页

作者： yue Liu Huisheng peng State Key Laboratory of Molecular Engineering of Polymers Department of Macromolecular Scienceand Institute of Fiber Materials and DevicesFudan UniversityShanghai 200438China

The advances in chemistry and materials have boosted the development of smart textiles,which are poised to revolutionize human lifestyles through multifunctional integration,such as heating,cooling,sensing and supplying energy^([1,2]).Among them,thermal insulation is an essential function of textiles to protect humans from complex and extreme environments and realize personal thermal management without energy con-sumption^([3]).

关键词： textiles insulation extreme

Semi-quantitative analysis of the structural evolution of mesophase pitch-based carbon foams by Raman and FTIR spectroscopy

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新型炭材料（中英文） 2024年第4期39卷 668-680页

作者： LIU yue CHANG Sheng-kai SU Zhan-peng HUANG Zu-jian QIN Ji YANG jian-xiao Hunan Province Key Laboratory for Advanced Carbon Materials and Applied Technology College of Materials Science and EngineeringHunan UniversityChangsha410082China

Graphitized carbon foams(GFms)were prepared using mesophase pitch(MP)as a raw material by foaming(450℃),pre-oxidation(320℃),carbonization(1000℃)and graphitization(2800℃).The differences in structure and properties of GFms prepared from different MP precursors pretreated by ball milling or liquid phase extraction were investigated and compared,and semi-quantitative calculations were conducted on the Raman and FTIR spectra of samples at each preparation ***-quantitat-ive spectroscopic analysis provided detailed information on the structure and chemical composition changes of the MP and GFm de-rived from *** with microscopic observations,the change from precursor to GFm was *** results showed that ball milling concentrated the distribution of aromatic molecules in the pitch,which contributed to uniform foaming to give a GFm with a uniform pore distribution and good *** phase extraction helped remove light components while retaining large aromatics to form graphitic planes with the largest average size during post-treatment to produce a GFm with the highest degree of graphitization and the fewest open pores,giving the best compression resistance(2.47 MPa),the highest thermal conductivity(64.47 W/(m·K))and the lowest electrical resistance(13.02μΩ·m).Characterization combining semi-quantitative spectroscopic ana-lysis with microscopic observations allowed us to control the preparation of the MP-derived GFms.

关键词： Mesophase pitch Carbon foams Raman FTIR Graphitization

Microfacies and diagenetic alteration in a semi-deep to deep lacustrine shale: The Yanchang Formation in the Ordos Basin, China

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Petroleum Science 2024年第3期21卷 1524-1538页

作者： Bin Bai Jing-yue Hao Ling Fu Yu-Xi Liu jian-peng Wang Lan Wang Kevin GTaylor Lin Ma PetroChina Research Institute of Petroleum Exploration and Development Beijing100083China Department of Earth and Environmental Sciences University of ManchesterM139PLUK College of Earth Sciences Jilin UniversityChangchun130061jilinChina Department of Chemical Engineering University of ManchesterM139PLUK

The mineralogical development and diagenetic sequence of lacustrine shales in the Chang 7 Member of the Yanchang Formation in the Ordos Basin are detailed studied.A model of their depositional system and a diagenetic diagram are proposed in this *** detailed petrographic,mineralogical,and elemental analyses,four distinct shale types are identified:argillaceous shale,siliceous shale,calcareous shale,and carbonate,clay,and silt-bearing *** main diagenetic process in argillaceous shale is the transformation of illite to smectite,negatively impacting shale *** shale undergoes carbonate cementation and quartz dissolution,contributing to increased porosity,particularly in *** shale experiences diagenesis characterised by carbonate formation and dissolution,with a prevalence of *** carbonate,clay,and silt-bearing shale,the dissolution of K-feldspar contributes to illitization of *** shale,characterised by more clay minerals and lower mesopore volume,is identified as a potential hydrocarbon *** shale,with the highest pore volume and abundant inter-mineral pores,emerges as a promising shale oil *** findings contribute to a comprehensive understanding of shale properties,aiding in the prediction of shale oil exploration potential in the studied area.

关键词： Ordos Basin Yanchang Formation Chang 7 Member Diagenesis Microfacies