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共查询到20条相似文献，搜索用时 153 毫秒
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<正> 微分中值定理在高等数学中具有重要的理论意义。其中Taylor中值定理更具有一般性。文[1]给出了两个广义Taylor公式,文[2]对其中一个公式给出一个简单证明方法。本文对文[1]的两个公式再给出三个简单的证明方法。  相似文献

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<正> 在现行《复变函数论》教材中,Cauchy 型积分的高阶导数公式一般都不证明,最多仅仅指出证明的方法——数学归纳法.而用数学归纳法证明比较繁.下面介绍一个较简单的证明方法(主要取材于 J.B.Conway,Function of One Complex variable).这个方法不仅使 Cauchy 型积分的高阶导数公式得到圆满的证明,而且使 Cauchy 积分的高阶导数公式作为它的特殊情形而得到证明.下面就来证明这个公式.  相似文献

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Green公式给出了平面图形面积与曲线积分的关系,利用这种关系给出了平面曲线等周不等式的一个简捷证明,并给出了平面图形面积的一个近似计算公式以及两个教学计算实例.  相似文献

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Wolfe线搜索下一类混合共轭梯度法的全局收敛性   总被引：3，自引：0，他引：3

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The best quadrature formula has been found in the following sense: for a function whose norm of the second derivative is bounded by a given constant and the best quadrature formula for the approximate evaluation of integration of that function can minimize the worst possible error if the values of the function and its derivative at certain nodes are known. The best interpolation formula used to get the quadrature formula above is also found. Moreover, we compare the best quadrature formula with the open compound corrected trapezoidal formula by theoretical analysis and stochastic experiments.  相似文献

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A new Newton-like iterative formula for the solution of non-linear equations is proposed. To derive the formula, the convergence criteria of the one-parameter iteration formula, and also the quasilinearization in the derivation of Newton's formula are reviewed. The result is a new formula which eliminates the limitations of other methods. There is now no need to first ensure a good initial approximation to the root, complex roots are found without necessarily starting from a complex formulation of the iteration formula, and the convergence is faster. The rate of convergence is discussed, and examples given.  相似文献

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The paper is devoted to the problem of finding explicit combinatorial formulae for the Pontryagin classes. We discuss two formulae, the classical Gabrielov-Gelfand-Losik formula based on investigation of configuration spaces and the local combinatorial formula obtained by the author in 2004. The latter formula is based on the notion of a universal local formula introduced by the author and on the usage of bistellar moves. We give a brief sketch for the first formula and a rather detailed exposition for the second one. For the second formula, we also succeed to simplify it by providing a new simpler algorithm for decomposing a cycle in the graph of bistellar moves of two-dimensional combinatorial spheres into a linear combination of elementary cycles.  相似文献

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We develop a formula for enumerating the partitions of a set up to the action of a group. We give some special cases of this formula and illustrate its use with an example. Some comments are made relating the formula to an earlier formula.This work was supported in part by NSF Contract GP-43010.  相似文献

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In the framework of the Mermin approach, we obtain formulas for the longitudinal electric conductivity in a quantum collisional plasma with a collision frequency depending on the momentum. We use a kinetic equation in the momentum space in the relaxation approximation. We show that as the Planck constant tends to zero, the derived formula transforms into the corresponding formula for a classical plasma. We also show that as the frequency of collisions between plasma particles tends to zero (the plasma transforms into a collisionless plasma), the derived formula transforms into the well-known Klimontovich-Silin formula for the collisionless plasma. We show that if the collision frequency is constant, then the derived formula for the permittivity transforms into the well-known Mermin formula.  相似文献

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The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments.  相似文献

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