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	1. The Calculation of Discriminating Kernel Base on Viability Kernel
	Han Yanli,Gao Yan
	Mathematics 20 January 2016
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	Abstract:In this paper, an application of the computation of kernel in differential game is given. Firstly, an under-approximation of the viability kernel is computed by the backward reachable set from a closed target. Secondly, using the relationship of discriminating kernel and viability kernel, an algorithm of discriminating kernel is proposed. Finally, using the alternative theorem, victory domain can be computed.
	TO cite this article:Han Yanli,Gao Yan. The Calculation of Discriminating Kernel Base on Viability Kernel[OL].[20 January 2016] http://en.paper.edu.cn/en_releasepaper/content/4676768


	2. Nodal domain count and vertex bipartiteness
	LUO Zuo-juan, ZHOU Bo
	Mathematics 28 November 2015
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	Abstract:We establish a novel relation between the nodal domain count and the vertex bipartiteness of a graph, give upper and/or lower bound for the nodal domain count of a graph in terms ofthe independent number, and the diameter, and the chromatic number, and characterize the (connected) graphs $G$ withnodal domain count $4$.
	TO cite this article:LUO Zuo-juan, ZHOU Bo. Nodal domain count and vertex bipartiteness[OL].[28 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4666784

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	3. The convergence analysis of Carroll function method for nonlinear SOC programming
	GU Jian, XIAO Xian-Tao
	Mathematics 26 November 2015
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	Abstract:This paper focuses on the study of the rate of convergence for thenonlinear Lagrangian method based on Carroll function for nonconvexnonlinear second-order cone programming. A set of conditions,including the componentwise strict complementarity condition, theconstraint nondegeneracy condition and the second order sufficientcondition, are used to guarantee the convergence of the nonlinearLagrangian method. The convergence theorem shows that under aboveconditions the dual algorithm based on Carroll function is locallyconvergent when the penalty parameter is less than a threshold andthe error bound of solution is proportional to the penaltyparameter.
	TO cite this article:GU Jian, XIAO Xian-Tao. The convergence analysis of Carroll function method for nonlinear SOC programming[OL].[26 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4661202


	4. On solving nonlinear least squares problems with approximate Jacobian matrix
	XIAO Xian-Tao
	Mathematics 19 November 2015
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	Abstract:Gauss-Newton method is a classical method for solving nonlinear least square problems. However, in many applications, the Jacobian matrix is usually impossible or expensive to compute exactly. In this paper, we consider the Gauss-Newton methods based on approximate Jacobian matrix. Under some mild conditions, we show that the methods are convergent.
	TO cite this article:XIAO Xian-Tao. On solving nonlinear least squares problems with approximate Jacobian matrix[OL].[19 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4661220


	5. On the existence of Pareto efficient Nash equilibria in discontinuous games
	LIU Zhi-Gang, Hou Ji-Cheng
	Mathematics 10 November 2015
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	Abstract:In this paper, we give a new existence theorem on Pareto efficient Nash equilibrium for discontinuous N-person noncooperative games in the framework of topological spaces without any linear structures. Moreover, we provide some examples where it is straightforward to verify our conditions and the previous conditions do not apply.
	TO cite this article:LIU Zhi-Gang, Hou Ji-Cheng. On the existence of Pareto efficient Nash equilibria in discontinuous games[OL].[10 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4660949


	6. A Note on NE Approximate Strong Equilibria in Load Balancing Games
	MIAO Cui-xia
	Mathematics 06 November 2015
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	Abstract:This note discusses the stability of NE against coalitionaldeviation in the load balancing games. We use an approach to get all the structures of theminimal deviation graph for the case of 5-servers, and show that anyNE assignment is a $rac{19}{16}pprox 1.1875-$approximate SE.
	TO cite this article:MIAO Cui-xia. A Note on NE Approximate Strong Equilibria in Load Balancing Games[OL].[ 6 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4660499


	7. Characterizing the nonemptiness andboundedness of the solution set forequilibrium problem with set valued mapping
	Wang Gang
	Mathematics 03 November 2015
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	Abstract:This paper is devoted to characterizing the nonemptiness and boundedness of the solution set for equilibrium problem with set-valued mapping in reflexive Banach space. By asymptotic cone technology, the equivalent characterizationson the nonemptiness and boundedness of the solution set for equilibrium problemwith set valued mapping are proposed. Furthermore, under suitable conditions, theequilibrium problem with set valued mapping has a nonempty and bounded solutionset if and only if it is generalized strictly feasible.
	TO cite this article:Wang Gang. Characterizing the nonemptiness andboundedness of the solution set forequilibrium problem with set valued mapping[OL].[ 3 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4660095


	8. Extremal Graphs with Maximum Edge-Neighbor-Connectivity
	BAI Yan-Ru, ZHANG Zhao, LIU Qing-Hai
	Mathematics 26 August 2015
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	Abstract:An edge is subverted if the two ends of the edge aredeleted from the graph. The edge-neighbor-connectivity$lambda_{NB}(G)$ is the minimum number of edges the subversion ofwhich results in an empty, or trivial, or disconnected graph. It isknown that $lambda_{NB}(G)leqlfloor n/2 floor$, where$n=\|V(G)\|$. In this paper, we characterize all extremal graphs whoseedge-neighbor-connectivity reaches this upper bound: for even $n$,an extremal graph can only be the complete graph $K_n$ or thecomplete bipartite graph $K_{rac{n}{2},rac{n}{2}}$; for odd $n$,an extremal graph can only be the 5-cycle $C_5$, or $K_n-M_0$ (thecomplete graph with a matching $M_0$ removed, where $M_0$ is anarbitrary matching of $K_n$ containing $i$ edges for $iin{0,1,ldots,lfloor n/2 floor}$), or a graph $G$ spanned by a$K_{lfloor rac{n}{2} floor,lceil rac{n}{2} ceil}$ such thatthe $lfloor n/2 floor$-part is independent in $G$ and the subgraphinduced by the $lceil n/2 ceil$-part has matching number at mostone.
	TO cite this article:BAI Yan-Ru, ZHANG Zhao, LIU Qing-Hai. Extremal Graphs with Maximum Edge-Neighbor-Connectivity[OL].[26 August 2015] http://en.paper.edu.cn/en_releasepaper/content/4653169


	9. Diameter variation of directed cycles and directed tori
	MA Xiao-Yan, Huang Xiao-Hui, ZHANG Zhao
	Mathematics 26 August 2015
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	Abstract:In this paper, we study two parameters concerningwith the diameter variation under the addition or deletion of arcsin a digraph $G$: $D^{-0}(G)$ is the maximum number of arcs theaddition of which dose not change the diameter of $G$; $D^{+k}(G)$is the minimum number of arcs the deletion of which increases thediameter of $G$ by at least $k$. We give a formula for $D^{-0}(G)$if $G$ is vertex transitive and every vertex has a unique vertexwhich is farthest from it. As consequences, the values of $D^{-0}$for the directed cycle and the directed torus can be determined. Thevalues of $D^{+k}$ for these two digraphs are also determined.
	TO cite this article:MA Xiao-Yan, Huang Xiao-Hui, ZHANG Zhao. Diameter variation of directed cycles and directed tori[OL].[26 August 2015] http://en.paper.edu.cn/en_releasepaper/content/4653178


	10. Mean Value Inequalities with respect to Intuitionistic Fuzzy Calculus
	Ai Zhenghai
	Mathematics 25 August 2015
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	Abstract:Atanassov introduced intuitionistic fuzzy set (A-IFS), whose basic elements are intuitionistic fuzzy numbers (IFNs). The IFN is an ordered pair, which is described by a membership degree, a non-membership degree, based on which the intuitionistic fuzzy calculus (IFC) has been put forward recently. To further develop the theory of IFCs, in this paper, we first review the basic concepts and properties, then we present the mean value inequalities which are similar to the ones in the classical calculus and offer the proofs in detail, finally, we simplify integrand function under intuitionistic fuzzy environment.
	TO cite this article:Ai Zhenghai. Mean Value Inequalities with respect to Intuitionistic Fuzzy Calculus[OL].[25 August 2015] http://en.paper.edu.cn/en_releasepaper/content/4653129

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