模度量空间下的不动点定理

推广了模度量空间，针对一类被称之为Chatterjea映射，在适当的条件下，建立了映射T具有不动点的存在性和唯一性结果．     

Common Fixed Points for Mappings with Quasi-Lipschitz Conditions on TVS-valued Cone Metric Spaces

A new unique common fixed point result for a pair of mappings satisfying certain quasi-Lipschitz type conditions on a topological vector space-valued cone metric space is obtained, and its particular forms and a more general form are given. Our main results generalize and improve some well-known recent results in the literature.     

R6中的Laguerre等参超曲面的分类

若超曲面的Laguerre形式为零且Laguerre第二基本形式的特征值(称为Laguerre主曲率)为常数,则称超曲面为Laguerre等参超曲面. 对$\mathbb{R}^{6}$中的Laguerre等参超曲面进行了研究,得到了分类定理.     

Multi-dimensional smoothing transformations: Existence,regularity and stability of fixed points

We analyze a class of smoothing transformations on probability measures in multiple space dimensions. Applying a synthesis of probabilistic methods and Fourier analysis, we prove existence and uniqueness of a fixed point inside the class of probability measures of finite second moment, characterize it as a scale mixture of Gaussians, and discuss its regularity. We also classify its tail, which might be of Pareto type. As an application, we study the stability of stationary solutions in a Kac-type kinetic model. In particular, we prove that the domain of attraction is precisely the probability measures of finite second moment.     

Halpern Iteration in CAT（k） Spaces

In this paper we show that an iterative sequence generated by the Halpern algorithm converges to a fixed point in the case of complete CAT(κ) spaces. Similar results for Hadamard manifolds were obtained in [Li, C., López, G., Martín-Márquez, V.: Iterative algorithms for nonexpansive mappings on Hadamard manifolds. Taiwanese J. Math., 14, 541–559 (2010)], but we study a much more general case. Moreover, we discuss the Halpern iteration procedure for set-valued mappings.     

Energy aware proactive optimized link state routing in mobile ad-hoc networks

In this paper we develop a novel energy aware routing approach for mobile ad hoc network (MANET) problems. The approach is based on using Optimized Link State Routing Protocol. Our Energy Aware OLSR labeled as OLSR_EA measures and predicts per-interval energy consumptions using the well-known Auto-Regressive Integrated Moving Average time series method. We develop a composite energy cost, by considering transmission power consumption and residual energy of each node, and use this composite energy index as the routing metric. Our extensive ns2 simulation experiments show that OLSR_EA substantially prolongs the network lifetime and saves total energy used in MANET. In our experiments we considered different scenarios considering a variety of traffic loads, node mobilities, homogeneous power consumption, and heterogeneous power consumption. Simulation results also confirm that OLSR_EA improves the traffic balance between nodes, and packet delivery ratio in higher node speed. We further develop characteristics of OLSR_EA in power-wise heterogeneous MANET to achieve efficient energy preserving performance.     

A classification of unitary invariant weakly complex Berwald metrics of constant holomorphic curvature

In this paper, we give a characterization of strongly pseudoconvex complex Finsler metric F which is unitary invariant. A necessary and sufficient condition for F to be a weakly complex Berwald metric and a necessary and sufficient condition for F to be a weakly Kähler Finsler metric are given, respectively. We also give a classification of unitary invariant weakly complex Berwald metrics which are of constant holomorphic curvatures.     

On a problem of iteration invariants for distributional chaos

We show that if f is a DC3 continuous map of a compact metric space then also f^N is DC3, for every N > 0. This solves a problem given by [Li R. A note on the three versions of distributional chaos. Commun Nonlinear Sci Numer Simulat 2011;16:1993-1997].