共查询到20条相似文献,搜索用时 203 毫秒
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定积分是新课标教材的新增内容,它为我们解答数学问题提供了新视角,一些数学问题可以借助定积分概念来灵活、高效地解决,请看几例:1.基于定积分内部结构是积式的特征,寻求解题思路由定积分的概念知,定积分是利用小矩形的面积去无限逼近曲边三角形的面积,而矩形的面积正是长与宽的积. 相似文献
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关于九参数拟协调板元 总被引:5,自引:2,他引:3
1980年以来,唐立民等提出一种拟协调元法,用来构造椭圆型方程的离散格式.粗略地讲,该法将每个单元上的能量表达式所含导数项的面积分(假设问题二维的),用格林公式转化为单元边界上的线积分,然后采用某种数值积分,将线积分进行离散.对只含函数项的面积分,也用相应的数值积分进行离散.用此法计算单元刚度阵,比较简单、灵活. 相似文献
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本文提到的特殊函数定积分,是指被积函数的原函数不能用初等函数表达,但其积分值存在的函数的定积分。Euler积分就是一例。计算这类积分主要是利用变量代换。例如计算Euler积分解作代换X=2t,则:就某些题目而言,若在变量代换的同时,再借助Euler积分,则计算会更简便。下面仅举凡例。方法同(Euler积分的变换)。例4求证当a’<1时,积分对第一个积分作变换o+0;一t,对第二个积分作变换点一0一t,对第三个积分作变换0-01一t,故利用Euler积分计算一些特殊函数的定积分@李文华$廊坊陆军导弹学院@李颖$廊坊陆军导弹学院… 相似文献
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探讨了一类非线性随机积分微分动力系统,并通过Banach不动点方法,给出了该系统零解均方渐近稳定的充要条件,形成了中立多变时滞Volterra型随机积分微分动力系统零解均方渐近稳定性定理。与前人的研究方法不同,该文根据多变时滞随机动力系统各时滞的特点,灵活构造算子,相比以往文献的方法更加灵活实用。文章的结论一定程度上改进和发展了相关研究论文的结果。另外,文章所得结论补充并推广了不动点方法在研究非线性中立多变时滞Volterra型随机积分微分动力系统零解稳定性方面的成果。 相似文献
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The introduction of linguistic quantifiers has provided an important tool to model a large number of issues in intelligent systems. Ying [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence 170 (2006) 581–606] recently introduced a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures, and the truth value of a quantified proposition is evaluated by using Sugeno’s integral. Representing linguistic quantifiers by fuzzy measures, this paper evaluates linguistic quantified propositions by the Choquet integral. Some elegant logical properties of linguistic quantifiers are derived within this approach, including a prenex normal form theorem stronger than that in Ying’s model. In addition, our Choquet integral approach to the evaluation of quantified statements is compared with others, in particular with Ying’s Sugeno integral approach. 相似文献
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Steven Vickers 《Mathematical Logic Quarterly》2008,54(1):109-123
An account of lower and upper integration is given. It is constructive in the sense of geometric logic. If the integrand takes its values in the non‐negative lower reals, then its lower integral with respect to a valuation is a lower real. If the integrand takes its values in the non‐negative upper reals, then its upper integral with respect to a covaluation and with domain of integration bounded by a compact subspace is an upper real. Spaces of valuations and of covaluations are defined. Riemann and Choquet integrals can be calculated in terms of these lower and upper integrals. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Jason P. Bell Stanley N. Burris 《Transactions of the American Mathematical Society》2003,355(9):3777-3794
Compton's method of proving monadic second-order limit laws is based on analyzing the generating function of a class of finite structures. For applications of his deeper results we previously relied on asymptotics obtained using Cauchy's integral formula. In this paper we develop elementary techniques, based on a Tauberian theorem of Schur, that significantly extend the classes of structures for which we know that Compton's theory can be applied.
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Radosav S. ordevi 《Mathematical Logic Quarterly》1993,39(1):228-230
The aim of the paper is to prove tha analytic completeness theorem for a logic L(∫1, ∫2)As with two integral operators in the singular case. The case of absolute continuity was proved in [4]. MSC: 03B48, 03C70. 相似文献
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M. Heydari Z. Avazzadeh H. Navabpour G.B. Loghmani 《Applied Mathematical Modelling》2013,37(1-2):432-442
In this work, we generalize the numerical method discussed in [Z. Avazzadeh, M. Heydari, G.B. Loghmani, Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem, Appl. math. modelling, 35 (2011) 2374–2383] for solving linear and nonlinear Fredholm integral and integro-differential equations of the second kind. The presented method can be used for solving integral equations in high dimensions. In this work, we describe the integral mean value method (IMVM) as the technical algorithm for solving high dimensional integral equations. The main idea in this method is applying the integral mean value theorem. However the mean value theorem is valid for multiple integrals, we apply one dimensional integral mean value theorem directly to fulfill required linearly independent equations. We solve some examples to investigate the applicability and simplicity of the method. The numerical results confirm that the method is efficient and simple. 相似文献
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定积分的主要思想是用近似的方法获得微元的表示,然后用积分得到精确值.合理选取积分元素是运用定积分元素法解决问题的关键.对一道用元素法求立体体积的习题进行了探讨. 相似文献
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本文基于Mellin变换法求解复杂更一般形式的对偶积分方程组.通过积分变换,由实数域化成复数域上的方程组,引入未知函数的积分变换,移动积分路径,应用Cauchy积分定理,实现退耦正则化为Cauchy奇异积分方程组,由此给出一般性解,并严格证明了对偶积分方程组退耦正则化为Cauchy奇异积分方程组与原对偶积分方程组等价性,以及对偶积分方程组解的存在性和唯一性.给出的解法和理论解,作为求解复杂对偶积分方程组一种有效解法,可供求解复杂的数学、物理、力学中的混合边值问题应用. 相似文献
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N.I. Ioakimidis 《Applied mathematics and computation》1983,12(1):49-60
The collocation method for the numerical solution of Fredholm integral equations of the second kind is applied, properly modified, to the numerical solution of Cauchy type singular integral equations of the first or the second kind but with constant coefficients. This direct method of numerical solution of Cauchy type singular integral equations is compared afterwards with the corresponding method resulting from applying the collocation method to the Fredholm integral equation of the second kind equivalent to the Cauchy type singular integral equation, as well as with another method, based also on the regularization procedure, for the numerical solution of the same class of equations. Finally, the convergence of the method is discussed. 相似文献
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求解一类具有Hibert核的奇异积分方程的小波方法 总被引:1,自引:0,他引:1
1 引 言近年来,用小波方法数值求解积分方程越来越引起人们的注意.文献[1]提出的算法可将一类积分算子所对应的矩阵稀疏化,为小波方法快速求解积分方程开辟了一条新的道路这方面的研究不仅可以深入发展小波理论和应用算法,深入发展小波方法的功效,而且对边界元方法有重要的指导意义.然而研究稳健快速的数值方法,一直是这方面研究的难点问题.本文考虑带Hilbert核的奇异积分方程q(y)=12π∫2π0f(x)ctg12(x-y)dx,y∈[0,2π],(1.1)的小波数值解法;其中f(x)∈H2π,q(y)∈H2π是以2π为周期的Holder类函数;q(y)已知,f(x)待求解;(1.1)式右… 相似文献