谋定而后动无往而不胜 ——构建小学英语拓展性微课堂

随着教学改革的进一步深入,'微课'已悄然成为拓展性课程的重要内容之一.本文从'微课堂'教学模式的构建、完善'微课堂'教学策略二方面进行深入探讨;并进行富有特色的亮点操作,从而激发学生学习英语的兴趣,提高学生的英语综合语用能力.

Some Fixed Point Results on a Class of Contractive Mappings in Cone Metric Spaces

In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and generalize some fixed point results in metric soaces and some previous results in cone metric spaces.

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.

Fuzzy MP-filters Lattice on a Given FI-algebra

In this paper, the properties of fuzzy MP-filters are discussed by using methods of Domain theory in FI-algebras. It is proved that all fuzzy MP-filters of a given FI-algebra form a distributive algebraic lattice, particularly form a frame.

On Reverses of the Blaschke-Santalo Inequality for Convex Bodies

Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal5 inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty＇s conjecture for projection bodies, respectively.

Complete Moment Convergence for Arrays of Rowwise Negatively Associated Random Variables

In this paper, the authors present some new results on complete moment convergence for arrays of rowwise negatively associated random variables. These results improve some previous known theorems.

Simplicities and Automorphisms of a Special Infinite Dimensional Lie Algebra

In this paper, a special infinite dimensional Lie algebra is studied. The infinite dimensional Lie algebra appears in the fields of conformal theory, mathematical physics, statistic mechanics and Hamilton operator. The infinite dimensional Lie algebras is pop ularized Virasoro-like Lie algebra. Isomorphisms, homomorphisms, ideals of the infinite dimensional Lie algebra are studied.

The Relations between Discrete Frames and Continuous Frames with Respect to （N, μ）

The discrete frame and the continuous frame in a Hilbert space are discussed. By the tool excess of a sequence, a sufficient and necessary condition is presented under which a discrete frame is equivalent to a continuous frame with respect to the whole natural numbers with a positive Borel measure. And some examples are given to illuminate the condition.

Existence of Periodic Solutions to a Class of Third-order p-Laplacian Equations with Delays

By using the continuation theorem of coincidence degree theory due to Mawhin and the new analytical method, we study the T-periodic solutions to a class of third order p-Laplacian equations with distributed delays as follows . Some new results for existence of T-periodic solutions to such equations are obtained.

Anti-control of Hopf Bifurcation in a Delayed Predator-prey Gompertz Model

A delayed predator-prey Gompertz model is investigated. The stability is analyzed. Anti-control of Hopf bifurcation for the model is presented. Numerical simulations are performed to confirm that the new feedback controller using time delay is efficient in creating Hopf bifurcation. Finally, main conclusions are included.

On Pseudo Small Injective Modules

The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.

The Completeness of Cone Metric Spaces

Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.

Oscillation of a Second-order Impulsive Neutral Differential Equation

Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equation with impuls[es. J Comput Appl Math 197（2006）： 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.

Global Stability in a Model for CTL Response to HTLV-I Infection

In this paper, a mathematical model for HTLV-I infection of CD4＋ T cells that incorporates the CD8＋ cytotoxic T-cell（CTL） response is studied. We establish two threshold parameters Ro and R1, the basic reproduction numbers for viral persistence and for CTL response, respectively. We also show that the parameter R1 can be used to distinguish asymptomatic carriers from HAM/TSP patients and as an important control parameter for preventing the development of HAM/TSP.

Periodic Solutions for p-Laplacian Neutral Functional Differential Equation with a Deviating Argument

In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating argument,some new results on the existence of periodic solutions is obtained.

Some Alternating Double Binomial Sums

We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.

Complete Convergence for Arrays of Rowwise Ч-mixing Random Variables

In the paper, the complete convergence for arrays of rowwise Q-mixing random variables is studied. Some sufficient conditions for complete convergence for an array of row wise Q-mixing random variables without assumptions of identical distribution and stochastic domination are presented.

Fuzzy Rough Ring and Its Properties

This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binarv operation of ring was discussed.

Energy Decay of Solution to a Nonlinear Wave Equation of Kirchhoff Type

The paper studies the asymptotic behavior of solution to the initial boundary value problem for a nonlinear hyperbolic equation of Kirchhoff type It proves the global existence of solution by constructing a stable set and the energy exponential decayestimate by applying a lemma of V Komornik.