A local-world heterogeneous model of wireless sensor networks with node and link diversity

In this paper, we present a novel local-world model of wireless sensor networks (WSN) with two kinds of nodes: sensor nodes and sink nodes, which is different from other models with identical nodes and links. The model balances energy consumption by limiting the connectivity of sink nodes to prolong the life of the network. How the proportion of sink nodes, different energy distribution and the local-world scale would affect the topological structure and network performance are investigated. We find that, using mean-field theory, the degree distribution is obtained as an integral with respect to the proportion of sink nodes and energy distribution. We also show that, the model exhibits a mixed connectivity correlation which is greatly distinct from general networks. Moreover, from the perspective of the efficiency and the average hops for data processing, we find some suitable range of the proportion p of sink nodes would make the network model have optimal performance for data processing.     

Detecting communities in clustered networks based on group action on set

In this paper, we propose a well targeted algorithm (GAS algorithm) for detecting communities in high clustered networks by presenting group action technology on community division. During the processing of this algorithm, the underlying community structure of a clustered network emerges simultaneously as the corresponding partition of orbits by the permutation groups acting on the node set are achieved. As the derivation of the orbit partition, an algebraic structure r-cycle can be considered as the origin of the community. To be a priori estimation for the community structure of the algorithm, the community separability is introduced to indicate whether a network has distinct community structure. By executing the algorithm on several typical networks and the LFR benchmark, it shows that this GAS algorithm can detect communities accurately and effectively in high clustered networks. Furthermore, we compare the GAS algorithm and the clique percolation algorithm on the LFR benchmark. It is shown that the GAS algorithm is more accurate at detecting non-overlapping communities in clustered networks. It is suggested that algebraic techniques can uncover fresh light on detecting communities in complex networks.     

光速在相对论中的核心地位

介绍了关于真空中光速的假定的重要作用,它不仅是相对论理论的基础,而且使人们能够定义同时性并测量空间距离.     

静态球对称黑洞热力学与爱因斯坦场方程

建立在广义相对论基础上的黑洞理论与热力学定律之间有着深刻的内在联系.具体考虑球对称黑洞,研究表明通过史瓦西黑洞和Reissner-Nordstrom黑洞在其视界附近的爱因斯坦场方程可以直接得到对应的黑洞热力学第一定律.这揭示了爱因斯坦引力场方程与黑洞热力学的关系,表明了在广义相对论理论框架下黑洞热力学规律的必然性.     

Spectral asymptotics and basis properties of fourth order differential operators with regular boundary conditions

In this paper, we consider the problem where λ is a spectral parameter; q(x) ∈ L₁(0,1) is complex‐valued function; α_s, s = 1,2,3, are arbitrary complex constants that satisfy α₂ = α₁ + α₃ and σ = 0,1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established. It is proved that all the eigenvalues, except for finite number, are simple and the system of root functions of this spectral problem forms a basis in the space L_p(0,1), 1 < p < ∞ , when ; moreover, this basis is unconditional for p = 2. We note that the considered problem was previously investigated in the condition of α₂ ≠ α₁ + α₃. Copyright © 2013 John Wiley & Sons, Ltd.     

Existence of solutions for a damped nonlinear impulsive problem with Dirichlet boundary conditions

In this paper, we consider the existence of solutions for second‐order nonlinear damped impulsive differential equations with Dirichlet boundary condition. By critical point theory, we obtain some existence theorems of solutions for the nonlinear problem. We extend and improve some recent results. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytic invariant curves for an iterative equation related to mosquito model

In this paper, we study the existence of analytic invariant curves of a iterative equation which from mosquito model. By constructing an invertible analytic solution g(x) of an auxiliary equation of the form invertible analytic solutions of the form g(αg ^{? 1}(x)) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < | α | < 1, we focus on those α on the unit circle S¹, that is, | α | = 1. We discuss not only those α at resonance, that is at a root of the unity, but also those α near resonance under the Brjuno condition. Copyright © 2013 John Wiley & Sons, Ltd.     

The fekete-szegö problem for close-to-convex functions with respect to the koebe function

An analytic function f   in the unit disk D :={z ∈ ? : |z| < 1}$\mathbb{D}\hspace{0.17em}:=\left\{z\hspace{0.17em}\in \hspace{0.17em}?\hspace{0.17em}:\hspace{0.17em}\left|z\right|\hspace{0.17em}<\hspace{0.17em}1\right\}$, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1−z)², z ∈ D$k\left(z\right)\hspace{0.17em}:=\hspace{0.17em}z/{\left(1-z\right)}^2,\hspace{0.17em}z\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$ if there exists δ∈(-π/2,π/2) such that Re{eiδ(1−z)²f^′(z)} > 0, ∈ D$\text{Re}\left\{{\text{e}}^{\text{i}\delta }{\left(1-z\right)}^2{f}^{\prime }\left(z\right)\right\}\hspace{0.17em}>\hspace{0.17em}0,\hspace{0.17em}\in \hspace{0.17em}\mathbb{D}$. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szegö problem is studied.     

ERROR ESTIMATION FOR NUMERICAL METHODS USING THE ULTRA WEAK VARIATIONAL FORMULATION IN MODEL OF NEAR FIELD SCATTERING PROBLEM

In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.     

∣x∣在调整的第二类Chebyshev结点组的有理插值

本文研究了Newman型有理算子逼近|x|的收敛速度,插值结点组X取调整的第二类Chebyshev结点组.利用上界估计得到确切的逼近阶为O 1n2.这个结果优于结点组取作第一、二类Chebyshev结点组、等距结点组和正切结点组.