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1)  higher derivative
高阶导数
1.
Several theories on the higher derivative;
关于高阶导数的几个定理
2.
Author presented a concise gradual derivation about higher derivative whose function defined by paramtric eguation.
求由参数方程所确定的函数的高阶导数,提出了一种较为直观、简便的逐次求导方法。
3.
A recurrence formula of higher derivatives for the integral of universal Cauchy type is given,by making use of the formula,it is proved that analytic functions are infinitely differentiable.
给出了泛Cauchy型积分高阶导数的一个递推公式,并由此证明了解析函数的无限次可微性定理。
2)  higher order derivative
高阶导数
1.
In this paper, through analyzing the structural features of a kind of ralatively complicated functions derivative and of this kind function itself, we deduce quickly and accurately the consequences of some kinds of functions primary functions and their higher order derivatives, without any analysis and opreation.
通过分析一类较为复杂函数的导数与其自身的结构特征 ,获得了由该类函数的一阶导数及其自身的结构特征 ,在不需要任何分析运算条件下 ,即可快速准确推知该类函数的原函数及其高阶导数的结果 研究结果表明 :高阶导数与原函数这对互逆运算在该类函数中可实现统一 利用该结果可给实际运算带来许多简化与方
2.
In this paper, the higher order derivative and the primary function of several special kinds of function are investigated, we then obtain the characteristic of those functions and it s primary function.
本文通过研究几种特殊类型函数的高阶导数与原函数的求法 ,获得了由该类函数自身及其一阶导数的特征 ,即可快速写出该类函数的 n阶导数 y( n) 与原函数 y( - 1 ) 的统一公式 y( n) ( n=-1 ,1 ,2 ,3 ,… ) 。
3.
We make use of the existence of the H2 solution of Hasegawa-Mima equation and a prioris estimates of the higher order derivative to derive the higher order solution,and show the regularity of the solution.
给出带扰动项的Hase-gawa—Mima方程的解的存在性及解的正则性,主要利用了带扰动项的Hasegawa—Mima方程的H2解的存在性和高阶导数的先验估计来得到高阶解的存在性,并给出了解的正则性。
3)  Derivatives of higher order
高阶导数
1.
This paper studies derivatives of higher order about product of three functions,and obtains a group dependent derivative formulas.
研究了三个函数乘积的高阶导数,得到了一组相应的导数公式。
2.
We use the method of generating functions to study the derivatives of higher order of a kind functions,some computational formulas are given,extend and improve the results of Carlitz,Zeitlin.
利用生成函数的方法研究了一类函数的高阶导数,建立了一些计算公式,推广和改进了C arlitz,Ze itlin的结果。
4)  higher-order derivative
高阶导数
1.
The results show that the higher-order derivative and its primary function,the two-way transformer counterparts,can be practically unified in a kind of complicated special functions,and that only through analyzing the structural featur.
把文献[1]中所研究的高阶导数与原函数的统一性公式,利用数学归纳法推广到了结构更为复杂的特型函数中,获得了比文献[1]应用更为广泛的结果。
5)  derivative of higher order
高阶导数
1.
At first, this paper introduces the wavelet function, scaling function of Daubechies wavelet and the modified solving methods of derivative of higher order for scaling functions are given.
本文首先介绍了Daubechies小波函数、尺度函数,给出了尺度函数高阶导数的改进求解方法。
6)  higher order derivatives
高阶导数
1.
Using the DitzianTotik moduli of smothness,the authors give the characterization of higher order derivatives for the generalized Baskakov operators.
讨论广义Baskakov算子借助Ditian Totik光滑模给出的高阶导数的特征刻画,统一了点态和整体的2种结果。
2.
A varying limit of integration and several higher order derivatives are appeared in these inequalities.
讨论具变动积分限并含有高阶导数的积分微分不等式,适当选取变积分限的值,可由它们导出包含许多已知结果的新Opial型不等
补充资料:七阶──藏教七阶
【七阶──藏教七阶】
  ﹝出天台四教仪集注﹞
  藏教者,即小乘经律论三藏教也。阶者,阶级次第也。谓藏教菩萨修行之次第也。(菩萨,梵语具云菩提萨埵,华言觉有情。)
  [一、四弘誓愿],弘者,大也。誓者,要制其心也。愿者,志求满足也。谓菩萨从初发心,观四谛境,发四弘誓,一、未度者令度,即众生无边誓愿度,此观苦谛境。二、未解者令解,即烦恼无数誓愿断,此观集谛境。三、未安者令安,即法门无量誓愿学,此观道谛境。四、未得涅槃者令得涅槃,即佛道无上誓愿成,此观灭谛境也。(梵语涅槃,华言灭度。)
  [二、三祇修六度],三祇者,三阿僧祇劫也。六度者,布施、持戒、忍辱、精进、禅定、智慧也。度,越也,越生死流,到涅槃岸也。谓菩萨既发心已,必须行六度行,填满本愿,是为三祇修六度。(梵语阿僧祇劫,华言无数时。)
  [三、百劫种相好],劫,梵语具云劫波,华言分别时节。百劫种相好者,一增一减为一小劫;凡历二十番增减,为一中劫;八十番增减,为一大劫。谓菩萨于百劫中,种诸相好。用百福德成一相好,如是至三十二相具足,而身清净也。(人寿从十岁增至八万四千岁,名增劫。从八万四千岁减至十岁,名减劫。如是一增一减,名一小劫。三十二相者,足下安平相,千辐轮相,手指纤长相,手足柔软相,手足缦网相,足跟满足相,足趺高好相,端如鹿王相,手过膝相,马阴藏相,身纵广相,毛孔生青色相,身毛上靡相,身金色相,身光面各一丈相,皮肤细滑相,七处平满相,两腋满相,身如师子相,身端直相,肩圆满相,四十齿相,齿白齐密相,四牙白净相,颊车如师子相,咽中津液得上味相,广长舌相,梵音深远相,眼色如金精相,眼睫如牛王相,眉间白毫相,顶肉髻成相也。)
  [四、六度相满],六度相满者,谓菩萨修行六度之相圆满也。如尸毗王代鸽,即檀度满也。普明王舍国,即戒度满也。羼提仙人被歌利王割截身体,慈忍不动,血变为乳,即忍度满也。大施太子抒海,即精进度满也。尚阇黎鹊巢顶上,即禅度满也。劬嫔大臣分阎浮提为七分,城邑山川均等,故能息诤,即智度满也。如上六人,皆释迦往昔所修之行,是为六度相满。(梵语尸毗,华言与。代鸽者,遍割身肉与鹰以代鸽命,身肉俱尽,不恼不死,自誓真实,感身平复也。梵语羼提,华言忍辱。梵语歌利,华言恶世无道。大施太子求如意珠济贫,得珠堕海,抒海取之,言欲酌海干而取之也。筋骨断坏,终不解废,诸天见而问之,答曰:吾生生不休。诸天愍之,助其抒海,海水减半,龙恐海干,令夜叉送珠还之。尚阇黎者,螺髻仙人,名此人得四禅定,出入息断,鸟谓为木,于髻生卵。定起欲行,恐鸟母不来,即更入定,待鸟飞去,方始出定。梵语阎浮提,华言胜金洲。梵语释迦,华言能仁。)
  [五、兜率降生],梵语兜率,华言知足。降生者,谓菩萨将补佛处,出世度生,即从兜率天降生人间,以补其处,是为兜率降生。(菩萨即释迦佛也。补佛处者,前佛既灭,而此菩萨即补其处也。)
  [六、降神出家],谓菩萨既降神出胎,厌生老病死之苦,而欲脱离,故求出家,入山修道,是为降神出家。
  [七、菩提树下成道],梵语菩提,华言道。谓菩萨自知成道时至,于菩提树下,破诸魔众。魔王败绩,鬼兵退散,菩萨安坐不动,即成佛道,是为菩提树下成道。(菩提树者,谓佛于此树下成道,故名菩提树也。)
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