WAVELET TRANSFORM ASSOCIATED TO THE AFFINE GROUP AGS,

This paper considers wavelet transforms associated to the affine group, which is more general than the paper given by R. Murenzi, and it seems more important in mathematical theory and more natural to be used to analyze signals in more than 1-dimension.     

NOTE ON THE PAPER “ AN NEGATIVE ANSWER TO A CONJECTURE ON THE SELF-SIMILAR SETS SATISFYING THE OPEN SET CONDITION”

In this paper,we present a more simple and much shorter proof for the main result in the paper " An negative answer to a conjecture on the self-similar sets satisfying the open set condition",which was published in the journal Analysis in Theory and Applications in 2009.     

RESEARCH ANNOUNCEMENTS ON “THE LIMIT FROM VLASOV-MAXWELL-BOLTZMANN SYSTEM TO NAVIER-STOKES-MAXWELL SYSTEM WITH OHM'S LAW”

正1 Introduction and Main Results Two-species Vlasov-Maxwell-Boltzmann system (in brief,VMB) describes the evolution of a gas of two species of oppositely charged particles (the positively charged ions,i.e.,cations of charge q~+ 0 and mass m~+ 0,and the negatively charged ions,i.e.anions of charge-q~-0 and mass m~- 0),subject to auto-induced electromagnetic forces.Such a gas of charged particles,under a global neutrality condition,is called a plasma.The particle number densities F~+(t,x,v)≥0 and F~-(t,x,v)≥0 represent the distributions of cations,     

SIMILARITY TRANSFORMATION, THE STRUCTURE OF THE TRAVELING WAVES SOLUTION AND THE EXISTENCE OF A GLOBAL SMOOTH SOLUTION TO GENERALIZED KURAMOTO SIVASHINSKY TYPE EQUATIONS

The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.     

CORRECTION TO “ON THE PROBLEM OF BEST CONVERGENCE RATES OF DENSITY ESTIMATES

The assertion of Th.1 in[1]should be replaced bylimsup n→∞ a_nn~(k/(2k m)=∞.(A)Since the proof of Th.1 in[1]is somewhat in error,we give here a sketch ofproof of(A).Choose f∈C_ka with f(x)≥a>0 for ‖x‖≤ε>0,and define h_δ(x)=f(x) e_(kδ)(x),where e_(kδ)(x),as well as d and C_(kα)~(n)(d) to appear in the following,are thesame as in[1].Choose ■>0 so that h_δ∈C_(kα) for δ∈(0,■).For each δ in(0,■),thereexists an integer n such that h_δ∈C_(kα)~(n)(d).Hence an integer N can be found such that     

SUPPLEMENT TO “PASSAGE, BLOCKADE, SINK AND SOURCE OF A PLANAR DYNAMICAL SYSTEM”

A Theorem is given on the number of passages passing throgh a multiply-connected region,which corrects a wrong conjecture in a former paper of the author.     

ADDENDUM TO“THE STRUCTURES OF GROUPS OF ORDER 2~3p~2n

The present paper is a complement to the paper[1].It is proved that groups oforder 2~37~2 have 44 types.     

THE C~(1,α) REGULARITY OF SOLUTIONS TO DOUBLE OBSTACLE PROBLEM OF VARIATIONAL INEQUALITY

In this paper, a double obstacle problem of variational inequalities is considered and its solutions is obtained. The results of one-sided obstacle problem are not required in the analysis of our main results, which is different from the previous works.     

CORRECTION TO“CHROMATIC SUM EQUATIONS FOR ROOTFD CUBIC PLANAR MAPS”

Mistakes in the paper "Chromatic sum equations for rooted cubic planar maps" have been corrected.     

经历“山穷水尽”,喜获“柳暗花明”

<正>在日常解数学题时,我们经常会对一道题产生困惑,并且尝试了很多方法,可以说是"山穷水尽"了.怎样突破思维阻碍,如何产生新的想法使解题过程出现转机,并且顺利地解决问题,给我们一种"柳暗花明"的喜悦?下面列举三个案例,希望对各位读者有所帮助!案例1:两组对角相等的四边形是平行四边形的证明如图1,     

预设“错误”,成就“精彩”

在数学认知活动中,"错误"是难以回避的.因为错误来自于教与学的"前沿",所以无论是学生无意生成的错误,还是教师有意预设的错误,都应成为宝贵的教学资源.在教学过程中,我们应充分挖掘这些"错误"的教学价值,为学生知识的增长、技能的形成、经验的积淀及"良习"的养成服务.在近期的"因式分解"教学中,笔者就预设了一道"错误"的例题,让学生展开探索,取得了较好的教学成效.现呈现这则片断及教学的感悟,希望     

引导“发散”,注意“收敛”

在教学过程中,为了开拓学生智力,培养和训练学生的思维能力,有时我们有意识地注意选择那些结合日常教学学生力所能及的问题进行一题多解,培养和训练学生的发散思维。