ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Q to (F(x,u,Du))+integral from n=■Q to (G(x,u))

In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.

Beyond Reading Comprehension--Cultivating Critical Readers through Critical Press News Reading

English newspapers, which have already been widely used as supplementary readings in an input-poor Chinese EFL context, are chosen and modified as needed for the proficiency levels of the class and used with suitable activities and exercises that engage students in an active and purposeful construction of the meaning of the text in extensive reading instruction. However, critical reading of the press news, which requires readers moving beyond comprehension, is rarely involved. This article, using Fairclough＇s critical discourse analysis （henceforth, CDA） as the theoretical framework, and Halliday＇s systemic functional grammar （henceforth, SFG） as the analytical tool in the analysis of the news texts, makes a sample analysis of the critical news reading from China Daily on China＇s response to the US-led campaign against terrorism after the September 11 events, 2001. The analysis made is undertaken in three stages： （1） the Transitivity analysis of the headlines, （2） the textual meaning of the clauses in terms of Themes, and （3） the explanations made to give grounding for the preceding analysis. The paper concludes with the hypothesis that integrating critical news reading into extensive reading instruction will not only improve students＇ reading skills, but also increase their adequate comprehension to the reading materials, as well as cultivate their critical reading competence.

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.

Periodic Solutions to a Kind of Second Order Neutral Functional Differential Equation in the Critical Case

In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows：（x（t） - cx（t -τ）＂ = g（t, x（t - μ（t））） ＋ e（t）,in the critical case ｜c｜ = 1. By employing Mawhin＇s continuation theorem and some analysis techniques, some new results are obtained.

Maintenance Management Research of a Large-span Continuous Rigid Frame Bridge Based on Reliability Assessment by Using Strain Monitored Data

When the bridge components needing maintenance are the world problem at present,and the health monitoring system is considered to be a very help­ful tool for solving this problem.In this paper,a large number of strain data acquired from the structural health monitoring system(SHMS)installed on a continuous rigid frame bridge are adopted to do reliability assessment.Firstly,a calculation method of punctiform time-dependent reliability is proposed based on the basic reliability theory,and introduced how to cal­culate reliability of the bridge by using the stress data transformed from the strain data.Secondly,combined with“Three Sigma”principle and the basic pressure safety reserve requirement,the critical load effects distribu­tion function of the bridge is defined,and then the maintenance reliability threshold for controlling the unfavorable load state which appears in the early operation stage of this type bridge is suggested,and then the combi­nation of bridge maintenance management and health monitoring system is realized.Finally,the transformed stress distribution certifies that the load effects of concrete bridges practically have a normal distribution;as for the concrete continuous rigid frame bridge with C50 strength grade concrete,the retrofit reliability threshold should be valued at 6.13.The methodology suggested in this article can help bridge engineers do effective maintenance of bridges,which can effectively extend the service life of the bridge and bring better economic and social benefits.