共查询到19条相似文献,搜索用时 109 毫秒
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通过建立命题、构造反例,论述了反函数求导定理中,函数y=f(x)在点x0的某邻域连续这一条件不能减弱为f在点x0连续,即使有附加条件:f在点x0可导且导数不为零,也不足以保证结论成立 相似文献
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就可微函数的导函数的连续性归纳出一个命题:↓Af(x)∈D(a,b),f′(x)∈C(a,b)<=>f′(x)在(a,b)中不存在第二类间断点。 相似文献
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积分型Cauchy中值函数若干分析性质 总被引:1,自引:0,他引:1
樊守芳 《数学的实践与认识》2014,(3)
给出"积分型Cauchy中值函数"的定义,对"积分型Cauchy中值函数"的分析性质进行了系统讨论,证明了"积分型Cauchy中值函数"的单调性、可积性、连续性、可微性等分析性质.作为"积分型Cauchy中值函数"的特例,给出了"第一积分中值函数"的定义及"第一积分中值函数"相应的分析性质. 相似文献
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樊守芳 《数学的实践与认识》2009,39(5)
给出了"Taylor中值函数"的定义,对Taylor中值函数的分析性质进行了系统的综合讨论,证明了Taylor中值函数的单调性、可积性、连续性、可微性等分析性质. 相似文献
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Vladimir I. Koltchinskii 《Journal of Theoretical Probability》1998,11(3):645-699
Let H be a map from a set SR
d
to R
d
. For tR
d
let
H
(t) denote the distance from t to the set H(S). Consider sequences {s
n}
n1 in S such that
. Any limit point of any such sequence (finite or infinite) is considered as a possible value of the inverse H
–1(t). Any map
defined in such a way will be called an SC-inverse (a selected closest inverse) to H. In the paper we study differentiability of the nonlinear operator
at H=G, where G is a one-to-one map from S onto a set TR
d
with good analytic properties (specifically, a diffeomorphism). We establish compact differentiability of this operator tangentially to continuous functions and introduce a family of norms such that it is Fréchet differentiable with respect to them. We also obtain optimal bounds for the remainder of the differentiation, extending to the multivariate case recent results of Dudley. These differentiability results are applied to random maps
, which could be statistical estimators of an unknown map G. For a function J on R
d
, let (J)
T
be its restriction to T. It is shown that for a diffeomorphism G and for an increasing sequence of positive numbers {a
n
}
n1 weak convergence of the sequence {a
n
(G
n
– G)}
n1 (locally in S) is equivalent to weak convergence of the sequence
(locally in T) along with the convergence of the sequence
to 0 in probability (locally uniformly in S). The equivalence holds for all SC-inverses
and all double SC-inverses
and it extends to the multivariate case a theorem of Vervaat. Moreover, each of these equivalent statements implies a kind of Taylor expansion of the SC-inverse
at G (locally uniformly in T)
where inv(A) denotes the inverse of a nonsingular linear transformation A in R
d
. Such limit theorems for functional inverses can be used to study asymptotic behavior of statistical estimators defined implicitly (as solutions of equations involving the empirical distribution P
n
). We show how to apply this approach to get asymptotic normality of M-estimators in the multivariate case under minimal assumptions. We consider an extension of the quantile function to the multivariate case related to M-parameters of a distribution P in R
d
(an M-quantile function)and use limit theorems for functional inverses to study limit behavior of the empirical M-quantile process. We also show how to use these theorems to study asymptotics of regression quantiles. 相似文献
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This article describes a practical procedure to compute, for any Fuchsian group of genus 2 acting on the unit disc, a uniformizing
function for the corresponding algebraic curve. 相似文献
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复函数微分中值公式的注记 总被引:2,自引:0,他引:2
周永正 《数学的实践与认识》1998,(4)
本文给出了复函数的一个一般性的微分中值公式,获得了该公式的“中间值”的渐近性质,给出了该性质的简洁证明. 相似文献
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This paper provides new results on pseudotrees. First, it is shown that pseudotrees are precisely those posets for which consistent
sets, directed sets, and nonempty chains coincide. Second, we show that chain-complete pseudotrees yield complete meet-semilattices.
Third, we prove that pseudotrees are precisely those posets that admit a set representation by sets of appropriate chains.
This latter result generalizes results needed for applications in game theory and economics. 相似文献