共查询到20条相似文献,搜索用时 78 毫秒
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本文介绍几种常用的定积分估值的方法:一、直接用定积分的性质①用估值性质:若M,m分别是连续函数f(x)在[a,b]上的最大值与最小值,则.这是我们常用的一种估值方法.例呈估计积分的值.解由于在单调减少,故:②放大或缩小积分区间:若[a,b」Th[c,d],f(x)>0,则f(x)dx>f(x)dx二、用变形来估值若f(x)在[a,b]上可积,有时可以通过各种变形来对f(x)dx估计.例如,简单不等式,变量替换,分部积分等将积分变成易于估计的形式.三、利用Darboux和估计积分值若s一乙。凸J;S一乙从西J;表示积分I一D人S)ds的小和和… 相似文献
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通过变量代换,将被积函数推广为[2,+∞)上的连续函数,构造出一类积分等式,并利用偶函数在对称区间上的积分性质,化简定积分计算. 相似文献
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给出了一个积分型Cauchy中值定理的推广,并讨论了连续函数的积分型Cauchy中值定理的逆问题. 相似文献
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该文使用分析技巧和数学归纳法给出了一类非连续函数积分不等式中未知函数的估计.该文用所得结果研究文献[8]中的非连续函数不等式.最后,该文把所得结果用于研究脉冲积分-微分方程解的估计. 相似文献
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分段函数、函数的可积性与原函数存在性 总被引:2,自引:0,他引:2
论述了分段函数在数学分析中的作用,并以分段函数为工具,给出了函数的原函数存在和黎曼可积之间的关系,有助于全面掌握原函数和定积分这两个重要概念. 相似文献
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下面的定理肯定了一致连续函数的积分体系唯一性.
命题 5(一致连续函数的积分体系唯一性) 设f(x)在区间I的任一个闭子区间上一致连续,S(u,v)和R(u,v)都是f(x)在I上的积分体系,则恒有S(u,v)=R(u,v). 相似文献
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主要研究了具有两个独立变量的不连续函数(有跳跃间断点)的一类更为广泛的新型积分不等式(Wendroff型),得出了一些新的结论,从而推广了前人的工作. 相似文献
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对连续分段函数的不定积分进行比较深入的研究,通过构造例子,阐述连续分段函数不定积分的四种求法,即狭义上限函数法、广义上限函数法、方程(组)法和差分方程法. 相似文献
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本文利用多元样条函数来定义分片代数集合,讨论了分片代数集合的不可约性和同构问题,给出了分片代数集合不可约的两个等价条件,并把分片代数集合的同构分类问题转化为交换代数的同构分类问题。 相似文献
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迭代运算下,函数值可以交叉于不同的子区间,使得逐段单调函数的高度异常复杂.本文考虑一个非单调点的连续函数类.首先给出高度的充分必要条件,以此获得此类函数的一种划分.其次针对函数类的一个非空子集,给出判定拓扑共轭的充分必要条件和构造拓扑共轭的新方法.进一步地,我们阐明这样的事实:两个逐段单调函数拓扑共轭是其高度相等的充分不必要条件,最后举例说明. 相似文献
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B Tomas Johansson 《International Journal of Mathematical Education in Science & Technology》2016,47(1):144-148
Exercises involving the calculation of the derivative of piecewise defined functions are common in calculus, with the aim of consolidating beginners’ knowledge of applying the definition of the derivative. In such exercises, the piecewise function is commonly made up of two smooth pieces joined together at one point. A strategy which avoids using the definition of the derivative is to find the derivative function of each smooth piece and check whether these functions agree at the chosen point. Showing that this strategy works together with investigating discontinuities of the derivative is usually beyond a calculus course. However, we shall show that elementary arguments can be used to clarify the calculation and behaviour of the derivative for piecewise functions. 相似文献
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《Optimization》2012,61(7):879-893
We extend the work of Ioffe and Lewis [A. Ioffe and A. Lewis, Critical points of simple functions, Optimization, 57 (2008), pp. 3–16] and relate it to the previous work of Morse [M. Morse, Topologically non-degenerate functions in a compact n-manifold, J. Anal. Math. 7 (1959), p. 243]. We show that the concept of regularity for piecewise linear functions can be explained in geometric topological terms and this explanation leads to a unified view of several concepts of regularity for such functions. 相似文献
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《Optimization》2012,61(3):209-221
In this paper we present a number of characterizations of piecewise affine and piecewise linear functions defined on finite dimesional normed vector spaces. In particular we prove that a real-valued function is piecewise affine [resp. piecewise linear] if both its epigraph and its hypograph are (nonconvex) polyhedral sets[resp..Polyhedral cones]. Also,We show that the collection of all piecewise affine[resp.piecewise linear] functions. Furthermore, we prove that a function is piecewise affine[resp.piecewise linear] if it can be represented as a difference of two convex [resp.,sublinear] polyhedral fucntions. 相似文献
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In the univariate case there are certain equivalences between the
nonlinear approximation methods that use piecewise polynomials and
those that use rational functions. It is known that for certain
parameters the respective approximation spaces are identical and
may be described as Besov spaces. The characterization of the
approximation spaces of the multivariate nonlinear approximation
by piecewise polynomials and by rational functions is not known.
In this work we compare between the two methods in the bivariate
case. We show some relations between the approximation spaces of
piecewise polynomials defined on n triangles and those of
bivariate rational functions of total degree n which are
described by n parameters. Thus we compare two classes of
approximants with the same number Cn of parameters. We consider
this the proper comparison between the two methods. 相似文献
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对分片 C2凸函数的 Moreau-Yosida逼近研究了它的梯度性质,引进了序列常秩约束条件,在此条件下证明了梯度函数具有分片光滑性质. 相似文献