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A Note on the Existence of a Specified Number of interior points

Chinese Quarterly Journal of Mathematics 2012年第4期27卷 606-614页

作者：魏祥林丁仁 College of Science Hebei University of Science and Technology College of Mathematics Hebei Normal University

An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set. For any integer k ≥ 1, let h（κ） be the smallest integer such that every set of points in the plane, no three collinear, with at least h（κ） interior points, has a subset of points with exactly κ or κ ＋ 1 interior points of P. We prove that h（5）=11.

关键词： interior points empty triangle deficient point set (χ, У)-splitters

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Code constructions for multi-node exact repair in distributed storage

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Science China(Information Sciences) 2018年第10期61卷 80-97页

作者： Marwen ZORGUI Zhiying WANG Center for Pervasive Communications and Computing(CPCC) Department of Electrical Engineering and Computer Science University of California at Irvine

We study the problem of centralized exact repair of multiple failures in distributed *** present constructions that achieve a new set of interior points under exact repair. The constructions build upon the layered code construction by Tian et al., designed for exact repair of single failure. We firstly improve upon the layered construction for general system parameters. Then, we extend the improved construction to support the repair of multiple failures, with varying number of helpers. In particular, for some parameters, we prove the optimality of one point in terms of the storage size and the repair bandwidth for multiple erasures. Finally, considering minimum bandwidth cooperative repair(MBCR) codes as centralized repair codes, we determine explicitly the best achievable region obtained by space-sharing among all known points, including the MBCR point.

关键词： regenerating codes exact repair multiple failures interior points Steiner systems

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AN AFFINE SCALING interior ALGORITHM VIA CONJUGATE GRADIENT PATH FOR SOLVING BOUND-CONSTRAINED NONLINEAR SYSTEMS

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Journal of Computational Mathematics 2008年第4期26卷 578-597页

作者： Chunxia Jia Detong Zhu Mathematics and Sciences College Shanghai Normal University Shanghai 200234 China Business College Shanghai Normal University Shanghai 200234 China

In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective func- tion nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective.

关键词： Conjugate gradient path interior points Affine scaling.

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