An Efficient Control Strategy of Epidemic Spreading on Scale-Free Networks

We present a novel and effective method for controlling epidemic spreading on complex networks, especially on scale-free networks. The proposed strategy is performed by deleting edges according to their significances （the significance of an edge is defined as the product of the degrees of two nodes of this edge）. In contrast to other methods, e.g., random immunization, proportional immunization, targeted immunization, acquaintance immunization and so on, which mainly focus on how to delete nodes to realize the control of epidemic spreading on complex networks, our method is more effective in realizing the control of epidemic spreading on complex networks, moreover, such a method can better retain the integrity of complex networks.

Generalizations of Euler Inequality in the n-dimensional Euclidean Space

The relation between the circum-radius and the in-radius of an n-dimensional simplex in E^n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.

Generalization of the linguistic aggregation operator and its application in decision making

A generalization of the linguistic aggregation functions （or operators） is presented by using generalized and quasiarithmetic means. Firstly, the linguistic weighted generalized mean （LWGM） and the linguistic generalized ordered weighted averaging （LGOWA） operator are introduced. These aggregation functions use linguistic information and generalized means in the weighted average （WA） and in the ordered weighted averaging （OWA） function. They are very useful for uncertain situations where the available information cannot be assessed with numerical values but it is possible to use linguistic assessments. These aggregation operators generalize a wide range of aggregation operators that use linguistic information such as the linguistic generalized mean （LGM）, the linguistic OWA （LOWA） operator and the linguistic or- dered weighted quadratic averaging （LOWQA） operator. We also introduce a further generalization by using quasi-arithmetic means instead of generalized means obtaining the quasi-LWA and the quasi-LOWA operator. Finally, we develop an application of the new approach where we analyze a decision making problem regarding the selection of strategies.

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.

CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence

In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.

Some Convergence Results for Sequences of -mixing Random Variables

In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.

Existence of Positive Solutions of Three-point Boundary Value Problem for Higher Order Nonlinear Fractional Differential Equations

In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.

Positive Solutions for Fourth-order Delay Differential Equation of Boundary Value Problem with p-Laplacian

In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian（Φp（u000））0（t）＋a（t）f（t, u（t？τ）, u0（t））=0, 0〈t〈1;u000 （0）=u00 （0）=0, u0 （1）=αu0 （η）;u（t）=0, ？τ ≤t≤0. By using Schauder fixed-point theorem, some su？cient conditions are obtained which guar-antee the fourth-order delay differential equation of boundary value problem with p-Laplacian has at least one positive solution. Some corresponding examples are presented to illustrate the application of our main results.

On the strong convergence properties for weighted sums of negatively orthant dependent random variables

In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.

The CUSUM statistic of change point under NA sequences

In this paper,we investigate the CUSUM statistic of change point under the neg-atively associated(NA)sequences.By establishing the consistency estimators for mean and covariance functions respectively,the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge,which extends the results obtained under the case of an indepen-dent normal sample and the moving average processes.Finally,the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.

ON THE REGULARITY CRITERIA OF THE 3D NAVIER-STOKES EQUATIONS IN CRITICAL SPACES

Regularity criteria of Leray-Hopf weak solutions to the three-dimensional Navier-Stokes equations in some critical spaces such as Lorentz space, Morrey space and multiplier space are derived in terms of two partial derivatives, θ1u1, θ2u2, of velocity fields.

Dynamical behaviour of an epidemic on complex networks with population mobility

In this paper, we study the dynamical behaviour of an epidemic on complex networks with population mobility. In our model, the number of people on each node is unrestricted as the nodes of the network are considered as cities, communities, and so on. Because people can travel between different cities, we study the effect of a population＇s mobility on the epidemic spreading. In view of the population＇s mobility, we suppose that the susceptible individual can be infected by an infected individual in the same city or other connected cities. Simulations are presented to verify our analysis.

On the Strong Rates of Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables

A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively dependent random variables can be easily extended to the case of arrays of rowwise extended negatively dependent random variables.

The Strong Convergence Properties for Partial Sums of m-NA Random Variables

In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.

On Complete Convergence for Arrays of Rowwise Strong Mixing Random Variables

In this paper, we present a general method to prove the complete conver- gence for arrays of rowwise strong mixing random variables, and give some results on complete convergence under some suitable conditions. Some Marcinkiewicz-Zygmund type strong laws of large numbers are also obtained.

NONLINEAR STABILITY OF PLANAR SHOCK PROFILES FOR THE GENERALIZED KdV-BURGERS EQUATION IN SEVERAL DIMENSIONS

This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation.

Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and Discrete Delays

Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.

Some notes on the spectral perturbations of the signless Laplacian of a graph

Let G be a simple graph and let Q（G） be the signless Laplacian matrix of G. In this paper we obtain some results on the spectral perturbation of the matrix Q（G） under an edge addition or an edge contraction.

Strong Law of Large Numbers for Array of Rowwise AANA Random Variables

In this article, the strong laws of large numbers for array of rowwise asymptotically almost negatively associated(AANA) random variables are studied. Some sufficient conditions for strong laws of large numbers for array of rowwise AANA random variables are presented without assumption of identical distribution. Our results extend the corresponding ones for independent random variables to case of AANA random variables.