微分差分KdV方程新的类多孤子解

This article is concerned with the Hirota direct method for studying novel multisoliton solutions of the discrete KdV equation.First the Hirota method was introduced,then the novel multisoliton solutions were obtained.Simultaneously the figures of the novel one-soliton solution and two-solton solution were given and the singularity of the novel multisoliton solutions was discussed.Finally it was pointed out that the multisoliton solutions with sigularity can be called soliton-like solutions.     

一类五阶KdV方程行波解

拟用双曲函数法求得非线性五阶KDV方程的行波解。     

耦合KdV方程的微扰孤子解

对于两个具有任意非零色散系数的弱耦合Ｋｏｒｔｅｗｅｇ－ｄｅＶｒｉｅｓ（ＫｄＶ）方程，得到一类微扰孤子解及其存在性条件，数值结果表明，弱耦合相互作用仅给未扰孤子对以小的修正，不改变孤子的特性。     

变系数KdV方程的孤子解

利用特殊的截断展开方法求出了变系数KdV方程的孤子解．其基本思想是假定该方程的形式解具有截断展开形式，以致可把变系数KdV方程转化为一组待定函数的方程组．进而给出待定函数容易积分的常微分方程。     

含修正项的KdV方程是否一定存在孤子尾

含修正项的KdV方程是否一定存在孤子尾是最近孤子理论中争论的中心问题之一。给出几类含修正项的KdV方程的精确解，证明含修正项的KdV方程不一定存在孤子尾。     

KdV方程的新Wronskian解

The novel Wronskian solutions of the KdV equation were obtained as limits of the soliton solutions in the Wronskian form. These solutions were verified by direct substitution to satisfy the bilinear derivative form of the KdV equadon and its Backlund transformation.     

Caudrey-Dodd-Gibbon-Kaeada方程的Hirota双线性形式和多孤子解

通过变换求出Caudrey-Dodd-Gibbon-Kaeada(CDGK)方程的Hirota双线性形式,进而得CDGK出方程多孤子解的解析表达式,并用三维图形展示出CDGK方程多孤子解的主要相互作用过程的特征.     

用试探函数法求KdV方程的孤子解

通过引入一个新的变换，利用试探函数法，并选取准确的试探函数形式，将一个难于求解的非线性偏微分方程化成了一组易于求解的非线性代数方程，从而简洁地求得了KdV方程的孤子解，所得结果与已有结果完全吻合。这种方法可望进一步推广用于求解其它非线性偏微分方程。     

耦合KdV方程的微扰孤子解

对于两个具有任意非零色散系数的弱耦合Korteweg-deVries（KdV）方程,得到一类微扰孤子解及其存在性条件．数值结果表明,弱耦合相互作用仅给未扰孤子对以小的修正,不改变孤子的特性．     

KdV方程的Darboux变换

分析了标准Ｄａｒｂｏｕｘ变换方法用于ＫｄＶ方程时遇到的困难,然后利用同一个ＫｄＶ方程的两个不同的Ｌａｘ表示,导出了ＫｄＶ方程Ｄａｒｂｏｕｘ变换。利用该变换就可以递推导出所有孤子解。     

New N-Soliton Solutions for the Sawada-Kotera Equation

1　Introduction　Inthedevelopmentofsolitontheory ,thebilineartransformationsmethodinitiatedbyHirotaisapower fultoolforfindingexactsolutionstotheunderlyingnonlinearevolutionequations[1,2 ] .Thistechniquehastheadvantageofbeingapplicabledirectlyuponthenonlinearevolutionequations .Byusingthetransfor mationofdependentvariables,theequationunderconsiderationcanbetransformedintothebilinearderivativeequation .　Recently ,thebilineartransformedmethodhasbeensuccessfullyextendedandthenewmulti solitonsolu…     

A note on the Marcinkiewicz integral operators on Fp^a,q

In this paper, we shall prove that the Marcinkiewicz integral operator #n, when its kernel Ω satisfies the L^1-Dini condition, is bounded on the Triehel-Lizorkin spaces. It is well known that the Triehel-Lizorkin spaces are generalizations of many familiar spaces such as the Lehesgue spaces and the Soholev spaces. Therefore, our result extends many known theorems on the Marcinkiewicz integral operator. Our method is to regard the Marcinkiewicz integral operator as a vector valued singular integral. We also use another characterization of the Triehel-Lizorkin space which makes our approach more clear.     

On some projectively flat polynomial （α,β）-metrics

In this paper, we consider some polynomial (α,β)-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α a1β a2β2/α a4β4/α3 to be projectively flat, where ai (i=1,2,4) are constants with a1≠0, α is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.     

两个Ramsey数R(m,n,l)和R(m,n,l,s)的含参数的上界

Ｉｎ 1935 ,Ｐ .Ｅｒｄ¨ｏｓａｎｄＧＳｚｅｋｅｒｅｓｏｂｔａｉｎｅｄｔｈｅｃｌａｓｓｉｃａｌｉｎｅｑｕａｌｉｔｙＲ (ｍ ,ｎ)≤Ｒ (ｍ - 1,ｎ) Ｒ(ｍ ,ｎ - 1) .　Ｉｎ 196 8,Ｋ .ＷａｌｋｅｒｐｒｏｖｅｄｔｈａｔＲ(ｎ ,ｎ)≤ 4Ｒ(ｎ- 2 ,ｎ) 2 .　Ｉｎ 1998,ＨｕａｎｇＹ .Ｒ .ａｎｄＺｈａｎｇＫ .Ｍ .[1,2 ] ｐｒｏｖｅｄｔｈａｔＲ(ｍ ,ｎ)≤ 12 (β 3γ 5 ) 　　12 γ(4α 2 β - 3γ 6 ) (β 1) 2　Ｉｎｔｈｉｓｐａｐｅｒ ,ｗｅｏｂｔａｉｎｓｏｍｅｎｅｗｕｐｐｅｒｂｏｕｎｄｓｆｏｒＲ(ｍ ,ｎ ,ｌ)ａｎｄＲ(ｍ …     

<Emphasis Type="Italic">Negativity</Emphasis> and the <Emphasis Type="Italic">new</Emphasis> in John Dewey’s theory of learning and democracy

Zusammenfassung Negativit?t und das Neue in John Deweys Theorie vom Lernen und der Demokratie — Für einen erneuten Blick auf Lernkulturen Die Rolle des Neuen in Lernprozessen bezieht sich auf die grundlegende Frage, wie Lernen überhaupt m?glich ist und wo es beginnt. In diesem Beitrag wird zun?chst John Deweys Lernkonzeption als Basis für die Analyse entwickelt. Dann wird die Beziehung zwischen Negativit?t und dem Neuen erarbeitet. Beim übergang vom Alten zum Neuen und vom Gewussten zum Ungewussten entstehen Verwirrungen und Schwierigkeiten, die in diesem Papier als Negativit?t im Lernprozess untersucht werden. Au?erdem vermittelt der Beitrag Einsichten in praktische p?dagogische Probleme, etwa bezüglich der Frage, wie Lehrer und andere Erzieher Lernprozesse f?rdern und wie Lernkulturen als besondere Lernumwelten Lehr-Lern-Prozesse unterstützen k?nnen.

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Negativity and the new in John Dewey’s theory of learning and democracy Toward a renewed look at learning cultures

Summary The role of the New in learning processes relates to basic questions of how learning is possible, and where learning begins. Using John Dewey’s concept of learning as the basis for analysis, this inquiry looks into the relation between Negativity and the New and seeks to uncover the negativity in learning processes associated with the perplexities and difficulties which arise in the transitions from Old to New and Known to Unknown. Furthermore, it offers insight into practical pedagogical issues, such as how teachers and educators can support learning processes and how learning cultures, as particular environments for learning, can assist processes of teaching and learning.

     

Software Development for Digital Control of WDW Series Testing Machine and Measurement of KIC

Software has been developed for digital control of WDW series testing machine and the measurement of fracture toughness by modularized design. Development of the software makes use of multi-thread and serial communication techniques, which can accurately control the testing machine and measure the fracture toughness in real-time. Three-point bending specimens were used in the measurement. The software operates stably and reliably, expanding the function of WDW series testing machine.