共查询到20条相似文献,搜索用时 296 毫秒
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著名数学家华罗庚说过:善于退,足够的退,退到最原始而不失去重要的地方,是学好数学的一个诀窍.这里所谓的退,当然不是逃跑,而是养精蓄锐,蓄势待发,是在为进寻求途径,即以退为进.它的实质是借助转化的数学思想,把复杂的问题简单化,运动的问题静止化,高维问题低维化,变量问题常量化,抽象问题具体化,代数问 相似文献
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香港海洋公园里有一条大鲸鱼,虽然重达8600 kg,却不但能跃出水面6.6m,还能向游客表演各种杂技.面对这条创造奇迹的鲸鱼,有人向训练师请教训练的秘诀.训练师说,在最初开始训练时,我们会先把绳子放在水面之下,使鲸鱼不得不从绳子上方通过,每通过一次,鲸鱼就能得到奖励.渐渐地,我们会把绳子提高,只不过每次提高的幅度都很小,大约只有2 cm,这样鲸鱼不需花费多大的力气就有可能跃过去,并获得奖励.于是,这条常常受到奖励的鲸鱼,便很乐意地接受下一次训练.随着时间的推移,鲸鱼跃过的高度逐渐上升,最后竟然达到了6.6m. 相似文献
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现实的数学课堂教学中,我们不难发现,看上去精彩纷呈的一堂课,学生、老师都表现得很积极,课堂气氛也热闹非凡,其实这样的课堂未必高效,而有时看似很普通的常规课,却往往透着高效.有人总认为高效课堂是名师的专利,对于普通老师来说,上好常规课,做到有效就已经是很努力的事情了,高效课堂是遥不可及的海市蜃楼,其实,在教学过程中,只要我们把功夫花在课前,抓住课堂这块教学的主阵地,落实课后反思,高效课堂也能触手可及. 相似文献
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浅谈图形语言在解题中的巧用 总被引:2,自引:0,他引:2
美国数学家斯蒂恩说:"如果一个特定的问题可以转化为图形,那么,思想就整体地把握了问题,并且能创造性地思索问题的解法."这就表明,解题时若能挖掘问题的几何意义,配以适当的图形,就有利于分析题中数量之间的关系,丰富表象,拓宽思路,化繁为简,化难为易,迅速找出解决问题的方法,提高分析和解决问题的能力,取得以简驭繁的效果. 相似文献
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在解有关反比例函数问题时,如果可以找到这样一个合适的点,这个点往往在坐标轴上,而且有垂直于(或者平行于)坐标轴的直线过此点.可设这个点的坐标,再根据题目中的等量关系,依次得到其他点的坐标,然后根据题目需要,将坐标转化为线段的长,从而得到线段之间的关系或者某些图形的面积,为问题的解答提供方便.这种先设某点坐标,然后逐一表示其他点的坐标的方法,叫旋转表示法.这种方法在解决两条双曲线问题中的应用十分广泛.本文以2010年中考试题为例,说明这种方法的应用,供同行参考. 相似文献
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Common fixed-point results are proved for I-nonexpansive maps, Ciric type maps, and ∗-nonexpansive multimaps. Invariant approximation results are obtained for these types of maps as applications. Our results extend or generalize several known results including the recent results of Chen and Li [J. Chen, Z. Li, Common fixed-points for Banach operators pairs in best approximation, J. Math. Anal. Appl. 336 (2007) 1466–1475]. In particular, we show that the results of Chen and Li on Banach operator pairs are particular cases of the results of Al-Thagafi and Shahzad [M.A. Al-Thagafi, N. Shahzad, Noncommuting selfmaps and invariant approximations, Nonlinear Anal. 64 (2006) 2778–2786]. 相似文献
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AbstractIn this article, we discuss Jacobi spectral Galerkin and iterated Jacobi spectral Galerkin methods for Volterra-Urysohn integral equations with weakly singular kernels and obtain the convergence results in both the infinity and weighted L2-norm. We show that the order of convergence in iterated Jacobi spectral Galerkin method improves over Jacobi spectral Galerkin method. We obtain the convergence results in two cases when the exact solution is sufficiently smooth and non-smooth. For finding the improved convergence results, we also discuss Jacobi spectral multi-Galerkin and iterated Jacobi spectral multi-Galerkin method and obtain the convergence results in weighted L2-norm. In fact, we prove that the iterated Jacobi spectral multi-Galerkin method improves over iterated Jacobi spectral Galerkin method. We provide numerical results to verify the theoretical results. 相似文献
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邱德华 《数学物理学报(A辑)》2011,31(1):132-141
该文研究了ρ 混合随机变量加权和的强大数律及完全收敛性, 获得了一些新的结果. 该文的结果推广和改进了Bai 等[1]及Baum 等[18] 在 i.i.d. 情形时相应的结果, 也推广和改进了Volodin 等[4]在实值独立时相应的结果. 该文还得到了一关于任意随机变量阵列加权和的完全收敛性定理. 相似文献
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The existence of common fixed point results for a weakly biased pair under Jungck contraction is established. We define a new class of subweakly biased pair which properly contains the classes of C q -commuting, pointwise R-subweakly commuting and R-subweakly commuting maps and establish common fixed point results for this class of maps. As applications several invariant best approximation results are proved which unify, extend, and complement the well-known results. 相似文献
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The midpoint method is an iterative method for the solution of nonlinear equations in a Banach space. Convergence results
for this method have been studied in [3, 4, 9, 12]. Here we show how to improve and extend these results. In particular, we use hypotheses on the second Fréchet derivative
of the nonlinear operator instead of the third-derivative hypotheses employed in the previous results and we obtain Banach
space versions of some results that were derived in [9, 12] only in the real or complex space. We also provide various examples that validate our results.
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《Mathematical Methods in the Applied Sciences》2018,41(7):2827-2847
In this paper, we consider the Bresse‐Cattaneo system with a frictional damping term and prove some optimal decay results for the L2‐norm of the solution and its higher order derivatives. In fact, we show that there is a completely new stability number δ that controls the decay rate of the solution. To prove our results, we use the energy method in the Fourier space to build some very delicate Lyapunov functionals that give the desired results. We also prove the optimality of the results by using the eigenvalues expansion method. In addition, we show that for the absence of the frictional damping term, the solution of our problem does not decay at all. This result improves some early results 相似文献
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Lai-Jiu Lin Qamrul Hasan Ansari 《Journal of Mathematical Analysis and Applications》2004,296(2):455-472
In this paper, we first establish collective fixed points theorems for a family of multivalued maps with or without assuming that the product of these multivalued maps is Φ-condensing. As an application of our collective fixed points theorem, we derive the coincidence theorem for two families of multivalued maps defined on product spaces. Then we give some existence results for maximal elements for a family of LS-majorized multivalued maps whose product is Φ-condensing. We also prove some existence results for maximal elements for a family of multivalued maps which are not LS-majorized but their product is Φ-condensing. As applications of our results, some existence results for equilibria of abstract economies are also derived. The results of this paper are more general than those given in the literature. 相似文献
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应用Hodge分解定理,得到了非齐次A-调和方程-div(A(x,Du(x)))=f(x,u(x))对应的障碍问题很弱解的局部和全局的W~(1,q)(Ω)-正则性,其中,A(x,Du(x)),f(x,u(x))满足文中所给的条件,从而推广了相关文献中的有关结果.该结果在优化控制问题中有着广泛的应用. 相似文献
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The main results of this paper are small-time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions
(Theorems 1 and 2). These results are based on the geometric concepts of (essential) distance from the complement and spherical area function. We also discuss some other geometric results about the heat development and illustrate them by examples.
Mathematics subject classifications (2000): 58J35, 35K05 相似文献
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In this paper, we establish Ekeland’s variational principle and an equilibrium version of Ekeland’s variational principle for vectorial multivalued mappings in the setting of separated, sequentially complete uniform spaces. Our approaches and results are different from those in Chen et al. (2008), Hamel (2005), and Lin and Chuang (2010) [13], [14] and [15]. As applications of our results, we study vectorial Caristi’s fixed point theorems and Takahashi’s nonconvex minimization theorems for multivalued mappings and their equivalent forms in a separated, sequentially complete uniform space. We also apply our results to study maximal element theorems, which are unified methods of several variational inclusion problems. Our results contain many known results in the literature Fang (1996) [21], and will have many applications in nonlinear analysis. 相似文献