共查询到20条相似文献,搜索用时 218 毫秒
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借助复变函数、积分变换、数学物理方程等数学方法和工具,可通过多种途径证明Dirichlet积分的结果. 相似文献
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王於平 《应用泛函分析学报》2013,15(1):47-52
研究Dirichlet边界条件下的积分-微分算子逆结点问题.证明了积分-微分算子稠定的结点子集能够唯一确定[0,π]上的势函数q(x)和区域Do上的积分扰动核M(x-t)且给出了这个逆结点问题的解的重构算法. 相似文献
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再谈关于Dirichlet积分的处理 总被引:1,自引:0,他引:1
《数学通报》1987年第10期发表的《关于Dirichlet积分的处理》一文,提供了针对不同知识水平处理Dirichlet积分integra from n=0 to +∞((sinx/x)dx)的六种方法。由于教学中经常考虑教材体系的顺序性,笔者觉得下面三种处理方法也是可取的。 相似文献
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(M, g)是黎曼曲面,该文给出了M上函数的Φ- Dirichlet积分的定义,并在此基础上得到了一个关于具有有限的Φ - Dirichlet积分的Φ -次调和函数的有界性定理. 相似文献
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冯小高 《纯粹数学与应用数学》2016,32(2):119-126
分别借助解析函数与调和函数两类函数的Dirichlet积分,利用相关文献给定边界值的拟共形映射极值伸缩商的估计方法,通过有限偏差函数和拟共形映射的关系估计了具有给定边界值的有限偏差函数的极值伸缩商.得到了解析函数的Dirichlet积分在有限偏差函数下具有拟不变性,同时给出有限偏差函数极值伸缩商的下界估计. 相似文献
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本文举例说明 ,如何通过构造递推序列的方法 ,对被积函数是与自然数 n有关的一些定积分进行计算 .读者从中可以看出此方法的简捷和优越 ,用以抛砖引玉 .1 计算问题上的应用在某些定积分计算问题中 ,若被积函数是与自然数 n有关 ,则可把整个积分看成一个序列的一般项 ,然后根据其积分的结构特点 ,恰当地找出它的递推公式 .通常首先考虑 In± In- 1,In± In- 2 ,In/In- 1等型 ,这样再经过递推 ,问题往往就可简捷而巧妙地得到解决 .例 1 计算著名的狄利克莱 (Dirichlet)积分∫π0sin(n 12 ) xsin x2dx,n =0 ,1 ,2 ,…解 令 In =∫π0s… 相似文献
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姚祖喜 《数学的实践与认识》2002,32(3):523-528
把复超球 Bn看作多复变典型域 RI(m,n)当 m=1时的特例 ,本文给出复超球上 Poisson-华积分边界性质的不同于文献 [3 ]的一个新证明 ,并研究了 Cauchy积分的边界性质及 Bn上的 Dirichlet问题 相似文献
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研究了Dirichlet除数问题的余项Δ(x)在小区间上的k次积分均值(k≥3), 并得到了其渐近公式.特别在k=3和k=4时,进一步改进了Ivic和Sargos的结果. 相似文献
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研究了Dirichlet除数问题的余项Δ(x)在小区间上的k次积分均值(k≥3), 并得到了其渐近公式.特别在k=3和k=4时,进一步改进了Ivic和Sargos的结果. 相似文献
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对振荡函数数值积分方法的进一步探讨 总被引:5,自引:0,他引:5
李毅夫 《数学的实践与认识》2002,32(1):91-93
本文在 [1 ]等成果的基础上 ,对振荡函数数值积分的方法做了进一步的探讨 ,给出了一种代数精确度更高、具有函数振荡越剧烈求积结果越精确的特点的、优于 [1 ]的新的对振荡函数的 Gauss型积分 . 相似文献
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B. A. Kats 《Mathematical Notes》1998,64(4):476-482
A definition of integration, i.e., a generalization of a functional of the form
to the case where is a fractal curve on the complex plane andƒ(z) (integration density) is a function defined on this curve is given. The existence and uniqueness of the integral with given density are examined.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 549–557, October, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-00674. 相似文献
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P. Sablonnière 《BIT Numerical Mathematics》2007,47(4):825-837
We study a new simple quadrature rule based on integrating a C
1 quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions.
We also give error estimates for smooth functions and we show that our formula is a useful companion to Simpson’s rule.
AMS subject classification (2000) 41A15, 65D07, 65D25, 65D32 相似文献
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E.L. Radzhabov 《Applicable analysis》2013,92(1-4):229-242
Some general fractional integral operators are studied including those of RIEMANN-LIOUVILLE, HADAMARD and others. They are used to solve a generalized ABEL equation. 相似文献
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Richard D. Sauerheber 《International Journal of Mathematical Education in Science & Technology》2013,44(3):420-425
The anatomic features of filaments, drawn through graphs of an integral F(x) and its derivative f(x), clarify why integrals automatically calculate area swept out by derivatives. Each miniscule elevation change dF on an integral, as a linear measure, equals the magnitude of square area of a corresponding vertical filament through its derivative. The sum of all dF increments combine to produce a range ΔF on the integral that equals the exact summed area swept out by the derivative over that domain. The sum of filament areas is symbolized ∫f(x)dx, where dx is the width of any filament and f(x) is the ordinal value of the derivative and thus, the intrinsic slope of the integral point dF/dx. dx displacement widths, and corresponding dF displacement heights, along the integral are not uniform and are determined by the intrinsic slope of the function at each point. Among many methods that demonstrate why integrals calculate area traced out by derivatives, this presents the physical meaning of differentials dx and dF, and how the variation in each along an integral curve explicitly computes area at any point traced by the derivative. This area is the filament width dx times its height, the ordinal value of the derivative function f(x), which is the tangent slope dF/dx on the integral. This explains thoroughly but succinctly the precise mechanism of integral calculus. 相似文献
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Absolute continuity for functionals is studied in the context of proper and abstract Riemann integration examining the relation
to absolute continuity for finitely additive measures and giving results in both directions: integrals coming from measures
and measures induced by integrals.
To this end, we look for relations between the corresponding integrable functions of absolutely continuous integrals and we
deal with the possibility of preserving absolute continuity when extending the elemental integrals. 相似文献
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Jack Grahl 《Journal of Mathematical Analysis and Applications》2008,340(1):358-365
We construct an integral of a measurable real function using randomly chosen Riemann sums and show that it converges in probability to the Lebesgue integral where this exists. We then prove some conditions for the almost sure convergence of this integral. 相似文献