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探究微积分——让知识成为智慧
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作者 韩云瑞 唐烁 +1 位作者 周友洲 张莉 《大学数学》 2024年第5期1-7,共7页
沿着历史脉络,准确把握微积分概念,领悟微积分蕴含的丰富智慧.数学智慧可以充实读者的精神世界,促进学生的心智成长,对他们的思维方式和世界观产生积极影响.在培养逻辑思维能力的同时,重视直觉思维能力,促进创新能力的培养.
关键词 无穷小 极限 微分 定积分 不定积分 微元法 拉格朗日乘子 直觉思维
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Small-time sampling behavior of a Fleming-Viot process
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作者 zhou youzhou 《Science China Mathematics》 SCIE CSCD 2017年第3期529-550,共22页
The Fleming-Viot process with parent-independent mutation process is one particular neutral pop- ulation genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population... The Fleming-Viot process with parent-independent mutation process is one particular neutral pop- ulation genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high, mutated species will elbow out all the initial species very quickly. Small-time behavior in thls case seems to be the key to understand this fast transition. The small-time asymptotic results related to time scale t and a(O)t, where lim0→∞θ θa(θ) = O, are obtained by Dawson and Shni (1998, 2001), Shui and Xiong (2002), and Xiang and Zhang (2005), respectively. Only the behavior under the scale t(θ), where limθ→∞θt(θ) = 0 and limθ→∞(O) =∞ was left untouched. In this paper, the weak limits under various small-time scales are obtained. Of particular interest is the large deviations for the small-time transient sam- pling distributions, which reveal interesting phase transition. Interestingly, such a phase transition is uniquely determined by some species diversity indices. 展开更多
关键词 Fleming-Viot process transient sampling distributions large deviations phase transition
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