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《中学生数学》2012年第2(下)期刊载了郑泉水老师的文章:"有趣的‘方中排圆’问题",文中提出的问题是:在一个边长为10cm×10cm的正方形中,排列直径为1cm的小圆,使所有的小圆都相切,问最多能排列多少个?郑老师给出的结论是:最多能排106个,共排11排,其中第1-3排每排排10个,第4排9个,第5排10个,第6排9个,第7排10个,第8排9个,第9排10个,第10排9个,第11排10个.笔者读了此文深受启发,同时也产生了对 相似文献
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<正>致《中学生数学》:我对贵刊今年3月下的《四阶幻方的几个有趣性质》有些疑问.作者找到一个很好的特例,据特例得到七个有趣的性质也无太多逻辑上的问题,但是第5个和第6个性质中提到"任意一个数",应该是中间四个数中的任意一个数(因为只有中间四个数两肩上才有数).第4个性质和第7个似乎是一样的,只是表示方法不同而已(因为可由第4个性质得出第7个性质,又可以由第7个性质得出第4个性质).按此特例,确实能得到这7个性质,非常有趣,但只据一个特例就得出四阶幻方的7个性质却未免仓促.因为四阶幻方并非只此一种.下面我另举一个四阶幻方的例子(已验算是幻方),上述7个性质中只有第5个符合.第1个性质:其中任意2×2的小方格图中,其四个数之和为34.对于此幻方,不符(如图1,10+11+3+2≠34). 相似文献
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针对某考研资料中的一道极限题目给出了两个解答.第一个依赖偏导数的定义,第二个依赖两个重要极限之一.且第二个解答的获得源于第一个解答所算出的答案.此外,还证明了有关等价无穷小代换的一个结论,扩大了其解决问题的范围. 相似文献
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We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals. 相似文献
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It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary. 相似文献
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Kunyang Wang Feng Dai 《分析论及其应用》2007,23(1):50-63
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths. 相似文献
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ZHENG ShiJun 《分析论及其应用》2004,20(3)
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V. 相似文献
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One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows 相似文献
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《数学研究及应用》2014,(6)
<正>Aims and Scope Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,is one of the transactions of China Society for Industrial and Applied Mathematics,and is a bimonthly journal.JMRA is dedicated to publishing first-rate original research papers in all areas of mathematics with applications,and making research findings available to a wide scientific world,as JMRE has for many years.In line with the name change,the new scope of Journal of Mathematical Research with Applications will not include the articles on mathematical methodology and mathematical philosophy.Copyright Information 相似文献
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