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Inequality of Nordhaus-Gaddum Type for Total Outer-connected Domination in Graphs

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Acta Mathematica Sinica,English Series 2011年第3期27卷 607-616页

作者： Hong Xing JIANG li ying kang College of Mathematics and Information Science Wenzhou University Wenzhou 325000 P. R. China Department of Mathematics Shanghai University Shanghai 200444 P. R. China

A set S of vertices in a graph G = （V, E） without isolated vertices is a total outer-connected dominating set （TCDS） of G if S is a total dominating set of G and G[V - S] is connected. The total outer-connected domination number of G, denoted by γtc（G）, is the minimum cardinality of a TCDS of G. For an arbitrary graph without isolated vertices, we obtain the upper and lower bounds on γtc（G）＋ γytc（G）, and characterize the extremal graphs achieving these bounds.

关键词： Graph domination number total outer-connected domination Nordhaus-Gaddum inequality

The Pos/neg-weighted 2-medians in Balanced Trees with Subtree-shaped Customers

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Acta Mathematicae Applicatae Sinica 2016年第4期32卷 891-898页

作者： Chun-song BAI li-ying kang Department of Mathematics Fuyang Normal College Department of Mathematics Shanghai University

This paper deals with the pos/neg-weighted p-median problem on tree graphs where all customers are modeled as subtrees. We present a polynomial algorithm for the 2-median problem on an arbitrary tree. Then we improve the time complexity to O（n logn） for the problem on a balanced tree, where n is the number of the vertices in the tree.

关键词： Location problems subtree-shaped customers obnoxious facilities

The General Facility Location Problem with Connectivity on Trees

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Acta Mathematica Sinica,English Series 2016年第9期32卷 1106-1112页

作者： Er Fang SHAN li ying kang School of Management Shanghai University Shanghai 200444 P. R. China Department of Mathematics Shanghai University Shanghai 200444 P. R. China

In this note we study the general facility location problem with connectivity. We present an O（np2）-time algorithm for the general facility location problem with connectivity on trees. Furthermore,we present an O（n... 详细信息

关键词： Connected p-center connected p-median tree equivalent binary tree

Clique-Transversal Sets in 4-Regular Claw-Free Graphs

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Acta Mathematica Sinica,English Series 2011年第5期27卷 883-890页

作者： Er Fang SHAN li ying kang Department of Mathematics Shanghai University Shanghai 200444 P. R. China

A clique-transversal set D of a graph C is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted by To（G）, is the minimum cardinality of a clique- transversal set in G. In this paper we give the exact value of the clique-transversal number for the line graph of a complete graph. Also, we give a lower bound on the clique-transversal number for 4-regular claw-free graphs and characterize the extremal graphs achieving the lower bound.

关键词： Clique-transversal set claw-free graph line graph regular graph

The Maximum α-spectral Radius of Unicyclic Hypergraphs with Fixed Diameter

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Acta Mathematica Sinica,English Series 2022年第5期38卷 924-936页

作者： li ying kang Jing WANG Er Fang SHAN Department of Mathematics Shanghai UniversityShanghai 200444P.R.China School of Management Shanghai UniversityShanghai 200444P.R.China

For 0≤α<1,theα-spectral radius of an r-uniform hypergraph G is the spectral radius of A_(α)(G)=αD(G)+(1-α)A(G),where D(G)and A(G)are the diagonal tensor of degrees and adjacency tensor of G,*** this paper,we sho... 详细信息

For 0≤αlic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with fixed *** also determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with given number of pendant edges.

关键词： Unicyclic hypergraph α-spectral radius principal eigenvector diameter pendant edge

The Backup 2-Median Problem on Block Graphs

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 309-320页

作者： Yu-kun CHENG li-ying kang Hong YAN Zhejiang University of Finance and Economics Department of Mathematics Shanghai University Department of Logistics and Maritime Studies The Hong Kong Polytechnic University

The backup 2-median problem is a location problem to locate two facilities at vertices with the minimum expected cost where each facility may fail with a given probability. Once a facility fails, the other one takes full responsibility for the services. Here we assume that the facilities do not fail simultaneously. In this paper, we consider the backup 2-median problem on block graphs where any two edges in one block have the same length and the lengths of edges on different blocks may be different. By constructing a tree-shaped skeleton of a block graph, we devise an O（n log n q- m）-time algorithm to solve this problem where n and m are the number of vertices and edges, respectively, in the given block graph.

关键词： location theory backup median block graph

Preface:Special Issue on Combinatorial Optimization

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Journal of the Operations Research Society of China 2019年第3期7卷 395-397页

作者： Xiao-Dong Hu Guo-Hui lin li-ying kang Guo-Chuan Zhang Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China Department of Computer Science University of AlbertaEdmontonAB T6G 2R3Canada Department of Mathematics Shanghai UniversityShanghai 200444China College of Computer Science and Technology Zhengjiang UniversityHouzhou 310027China

Combinatorics is,as defined by MathWorld,the branch of mathematics that studies the enumeration,combination and permutation of sets of elements and the mathemat-ical relations that characterize their *** optimization not only enumerates the sets studied,but also has the goal of finding the member of the set in an efficient manner that optimizes an objective *** optimization is an emerging field at the forefront of combinatorics,theoretical computer science and operations research that has various applications in many disciplines of science,engineering,industry,economy,military and so on.

关键词： properties. function. optimization

Preparation of silver nanoparticles through the reduction of straw-extracted lignin and its antibacterial hydrogel

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International Journal of Minerals,Metallurgy and Materials 2025年第2期32卷 504-514页

作者： Lou Zhang Shuo li Fu Tang Jingkai Zhang Yuetong kang Hean Zhang lidong li State Key Laboratory for Advanced Metals and Materials School of Materials Science and EngineeringUniversity of Science and Technology BeijingBeijing 100083China

Silver nanoparticles(Ag NPs)have attracted attention in the field of biomaterials due to their excellent antibacterial ***,the reducing and stabilizing agents used for the chemical reduction of Ag NPs are usually toxic and may cause water *** this work,Ag NPs(31.2 nm in diameter)were prepared using the extract of straw,an agricultural waste,as the reducing and stabilizing *** analysis revealed that the straw extract contained lignin,the structure of which possesses phenolic hydroxyl and methoxy groups that facilitate the reduction of silver salts into Ag *** surfaces of Ag NPs were negatively charged due to the encapsulation of a thin layer of lignin molecules that prevented their *** the prepared Ag NPs were added to the precursor solution of acrylamide,free radical polymerization was triggered without the need for extra heating or light irradiation,resulting in the rapid formation of an Ag NP-polyacrylamide composite *** inhibition zone test proved that the composite hydrogel possessed excellent antibacterial ability due to the presence of Ag *** prepared hydrogel may have potential applications in the fabrication of biomedical materials,such as antibacterial dressings.

关键词： silver nanoparticles hydrogel straw extraction antibacterial

Nanostructured ZnO/BiVO_(4)I-scheme heterojunctions for piezocatalytic degradation of organic dyes via harvesting ultrasonic vibration energy

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International Journal of Minerals,Metallurgy and Materials 2025年第2期32卷 488-497页

作者： Yiling li Xiaoyao Yu yingjie Zhou Yao lin ying Wu Key Laboratory of the Ministry of Education for Advanced Catalysis Materials College of Chemistry and Materials ScienceZhejiang Normal UniversityJinhua 321004China

BiVO_(4)porous spheres modified by ZnO were designed and synthesized using a facile two-step *** resulting ZnO/BiVO_(4)composite catalysts have shown remarkable efficiency as piezoelectric catalysts for degrading Rhodamine B(RhB)unde mechanical vibrations,they exhibit superior activity compared to pure *** 40wt%ZnO/BiVO_(4)heterojunction composite displayed the highest activity,along with good stability and *** enhanced piezoelectric catalytic activity can be attributed to the form ation of an I-scheme heterojunction structure,which can effectively inhibit the electron-hole ***,hole(h+)and superoxide radical(·O_(2)^(-))are proved to be the primary active ***,ZnO/BiVO_(4)stands as an efficient and stable piezoelectric catalyst with broad potential application in the field of environmental water pollution treatment.

关键词： piezoelectric catalytic heterojunction dye degradation ultrasonic vibration