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鉴于 L agrange插值多项式并非对任何的连续函数都能一致收敛 ,本文以 ( 1-x) Wn( x)的零点作为插值节点 ,对 L agrange插值多项式中的被插值函数进行线性组合 (也称函数平均 ) ,构造了算子 An,r( f;x) ,它对于有任意阶导数的连续函数 f ( x )∈ Cl[-1,1] ,( 0≤ l≤ r)都一致收敛 ,收敛阶为 |An,r( f ;x ) -f ( x ) |=O En( f ) 1nl ω( f (l) ,1n) 1nl 1且收敛阶达到了最佳 .( r是奇自然数 ) 相似文献
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Anna Svensson 《Annals of science》2013,70(2):157-183
Abel Evans's poem Vertumnus (1713) celebrates Jacob Bobart the Younger, second keeper of the Oxford Physick Garden (now the Oxford University Botanic Garden), as a model monarch to his botanical subjects. This paper takes Vertumnus as a point of departure from which to explore the early history of the Physick Garden (founded 1621), situating botanical collections and collecting spaces within utopian visions and projects as well as debates about order more widely in the turbulent seventeenth-century. Three perspectives on the Physick Garden as an ordered collection are explored: the architecture of the quadripartite Garden, with particular attention to the iconography of the Danby Gate; the particular challenges involved in managing living collections, whose survival depends on the spatial order regulating the microclimates in which they grow; and the taxonomic ordering associated with the hortus siccus collections. A final section on the ideal ‘Botanick throne’ focuses on the metaphor of the state as a garden in the period, as human and botanical subjects resist being order and can rebel, but also respond to right rule and wise cultivation. However, the political metaphor is Evans’s; there is little to suggest that Bobart himself was driven by utopian, theological and political visions. 相似文献
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曹瑞 《兰州大学学报(自然科学版)》2007,43(6):112-116
改进了最近提出的F-展开方法,并且利用改进的F-展开方法构造了一类非线性藕合Klein-Gordon方程的精确解.当Jacobi椭圆函数的模m趋向于1时,得到孤立波解.与F-展开方法相比,此方法求得的解更为丰富. 相似文献
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This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing—the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. 相似文献
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