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	1. Research on a second-order cone reformulating problem of CDT problem
	QU Yanming
	Mathematics 12 March 2019
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	Abstract:In this paper, we study a class of CDT problem with two quadratic constraints, one of which is the unit ball constraint and the other is the ellipsoid constraint. Select the appropriate hyperplane through the optimal line segment, without dividing the feasible region. In the case of the second-order cone recombination technique and the SDP relaxation method, the necessary and sufficient conditions for the existence of the dual gap in the second-order cone reformulating problem of the CDT problem are obtained, and the theoretical proof is given which is paved to reduce or even eliminate the dual gap of the CDT problem.
	TO cite this article:QU Yanming. Research on a second-order cone reformulating problem of CDT problem[OL].[12 March 2019] http://en.paper.edu.cn/en_releasepaper/content/4747715


	2. Scalarization and Optimality Conditions for Vector Equilibrium Problems via Improvement Sets in Real Linear Spaces
	LIU Jia,CHEN Chun-Rong
	Mathematics 19 September 2018
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	Abstract:In this paper, we study vector equilibrium problems with the ordering relations defined via improvementsets in real linear spaces without assuming any topology. We deal with efficient solutions, weak efficient solutions, Benson and Henig proper efficient solutions. The linear scalarization characterizations of these solutions are established, moreover, optimization conditions via Lagrange multiplier rulers for vector equilibrium problems with constraints are also obtained. Our results generalized the corresponding ones in the literature.
	TO cite this article:LIU Jia,CHEN Chun-Rong. Scalarization and Optimality Conditions for Vector Equilibrium Problems via Improvement Sets in Real Linear Spaces[OL].[19 September 2018] http://en.paper.edu.cn/en_releasepaper/content/4746010

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	3. $Z_3$-connectivity for power graphs
	LI Xiangwen
	Mathematics 13 June 2017
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	Abstract:Let $G$ be a connected graph. For an integer $kgeq 2$, $G^k$ isdefined to be a graph obtained from $G$ by adding new edge $uv$where $2leq d(u, v)leq k$. Let $A$ be an Abelian group with$\|A\|geq 3$. In this note, we prove that for any connected graph$G$, $G^l$ is $Z_3$-connected if and only if $\|V(G)\|geq 5$ or$Gcong K_1$, where $lgeq 3$.
	TO cite this article:LI Xiangwen. $Z_3$-connectivity for power graphs[OL].[13 June 2017] http://en.paper.edu.cn/en_releasepaper/content/4736426


	4. Non Interior Point Supporting Hyperplane method for solving Mixed Integer Nonlinear Programming
	Dalin,Chen Aruna
	Mathematics 15 May 2017
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	Abstract:In 1995 Westerlund and Pettersson proposed extended cutting plane (ECP) method for solving MINLP problems which is extended from Kelley's Cutting Plane (CP) method. The advantage of ECP method is simplicity and robustness of the solution and ECP method is suitable for solving large convex MINLP problems with moderate degree nonlinearity. In 1967 Veinott introduced a supporting hyperplane (SHP) method for solving NLP problems. Following the idea of ECP method, SHP method can be extended to solve MINLP problems. When SHP method is applied for solving MINLP problems, an interior point or a feasible solution must be gotten at first. However, finding a good feasible solution to a MINLP problem is difficult. So in this paper a new kind of SHP method, non interior point based SHP (NISHP) method，is introduced. A feasible solution is not required at the beginning in this method, and this method is more efficient than ECP method.
	TO cite this article:Dalin,Chen Aruna. Non Interior Point Supporting Hyperplane method for solving Mixed Integer Nonlinear Programming[OL].[15 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4734001


	5. Distributed fuzzy adaptive iterative learning control with initial-state learning for consensus of multi-agent systems with uncertain communication topology structure
	WU Hui,LI Junmin
	Mathematics 26 April 2017
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	Abstract:Distributed consensus problem is addressed in this paper for linearly parameterized multi-agent systems with uncertain communication topology structure under initial-state learning condition. T-S fuzzy models are presented to describe the uncertain communication topology structure, and a distributed iterative learning control protocol is proposed without using any global information for the consensus problem. The AILC protocols are designed with distributed initial-learning and it is not essential to fix the initial value at the start of each iteration. It is proved that the proposed protocol ensures all the internal signals in the multi-agnt system are bounded and the follower agents track the leader exactly on [0,T]. Sufficient conditions of perfectly consensus for multi-agent systems are obtained by appropriately constructing Lyapunov function. The formation control problem is also studied by converting to the consensus problem. Finally, the simulation examples are given to verify the efficacy of the theoretical analysis.
	TO cite this article:WU Hui,LI Junmin. Distributed fuzzy adaptive iterative learning control with initial-state learning for consensus of multi-agent systems with uncertain communication topology structure[OL].[26 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4726586


	6. The linear programming approach to the harmonic index of a graph
	ZHU Yan,CHANG Ren-ying
	Mathematics 17 April 2017
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	Abstract:The harmonic index $H(G)$ of a graph $G$ is the sum of $rac{2}{d(u)+d(upsilon)}$ over all edges $uupsilon$ of $G$, where $d(u)$ denotes the degree of a vertex $u$ in $G$. In this paper, we give the minimum value of $H(G)$ for graphs $G$ with given minimum degree $delta(G) geq 3$ and characterize the corresponding extremal graph.
	TO cite this article:ZHU Yan,CHANG Ren-ying. The linear programming approach to the harmonic index of a graph[OL].[17 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4725178


	7. On Robust Solutions To Uncertain Variational Inequality Problem
	LIU Jian-Xun,YAO Bin
	Mathematics 12 April 2017
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	Abstract:This paper considers a class of uncertain variational inequality problems(UVI).An robust counterpart to the UVI was defined by minimizing the worst-case of the gapfunction, and the definition of robust solution to the UVI was given, also, some optimalityconditions of a class of special UVI was derived.
	TO cite this article:LIU Jian-Xun,YAO Bin. On Robust Solutions To Uncertain Variational Inequality Problem[OL].[12 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4724778


	8. Successive Rank-One Decomposition of Higher-Order Symmetric Complex Tensors
	ZHANG Zhanghui,BAI Minru
	Mathematics 12 April 2017
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	Abstract:In order to get the symmetric canonical decomposition of the higher-order symmetric complex tensors, this paper extends the successive decomposition method to the tensor case, and proposes a successive symmetric rank-one complex approximation method to decompose the higher-order symmetric complex tensors. It notes that the successive decomposition of real tensors may actually be different over the real field and the complex field. We further show that a symmetric canonical decomposition could be obtained when the method is applied to a unitary diagonalizable tensor. Numerical part analyzes the solving method of solving the sub-problem. Numerical results verify the efficiency of the proposed method.
	TO cite this article:ZHANG Zhanghui,BAI Minru. Successive Rank-One Decomposition of Higher-Order Symmetric Complex Tensors[OL].[12 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4724791


	9. Unicyclic graphs with the fourth extremal Wiener indices
	YANG Yu-Jun,CAO Yu-Liang,Wang Guang-Fu
	Mathematics 22 March 2017
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	Abstract:Unicyclic graphs with the fourth extremal Wiener indices are characterized. It is shown that among all unicyclic graphs with $ngeq 8$ vertices,$C_5(S_{n-4})$ and $C_2^{u_1,u_2}(S_3,S_{n-4})$ have the fourth minimum Wiener indices, whereas $C^{u_1,u_2}_3(P_{3},P_{n-4})$ has the fourth maximum Wiener index.
	TO cite this article:YANG Yu-Jun,CAO Yu-Liang,Wang Guang-Fu. Unicyclic graphs with the fourth extremal Wiener indices[OL].[22 March 2017] http://en.paper.edu.cn/en_releasepaper/content/4722647


	10. The thickness of the complete bipartite graph $K_{n,n+4}$
	HU Si-Wei,CHEN Yi-Chao
	Mathematics 10 March 2017
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	Abstract:The thickness t(G) of a graph G is the minimum number of planar spanning subgraphsinto which G can be decomposed. Determining the thickness of a graphis NP-hard, thus it is very difficult to obtain the exact number of thickness forarbitrary graphs. Compared with other classical topological invariant, the results about thickness are few. For the thickness of complete bipartite graph $K_{m,n}$, Beineke, Harary and Moon obtained the following formula in 1964 ,$$t(K_{m,n})=leftlceilrac{mn}{2(m+n-2)} ight ceil,$$ except possibly when $m$ and $n$ are both odd and there exists an integer $k$ satisfying $n=leftlfloorrac{2k(m-2)}{(m-2k)} ight floor$.According to the above formula, the thickness of the complete bipartite graph is not completely determined. In 1980, two famous graph theorist Gross and Harary posed the following problem in the paper 《 Some problems in topological graph theory》： Find the thickness of $K_{m,n}$ for all $m,n?$ In this paper, we obtain the thickness for the complete bipartite graph $K_{n,n+4} .$
	TO cite this article:HU Si-Wei,CHEN Yi-Chao. The thickness of the complete bipartite graph $K_{n,n+4}$[OL].[10 March 2017] http://en.paper.edu.cn/en_releasepaper/content/4721674

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