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数学分析中的各中值定理都只肯定了“中间点”的存在性。并没有给出其具体位置和确定其位置的方法.通过对中值定理“中间点”的渐近性态的研究.可以确定“中间点”在某区间内的渐近位置,从而为近似计算提供帮助.综述在区间[a.x]上的各中值定理“中间点”当x→+∞时的渐近性态,给出两个新的渐近估计式. 相似文献
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提出了可渗透近球体轴对称流动的分析方法.用修正边界条件的办法反映可渗透性.用正规摄动法求解了Stokes方程,达到ε的2阶修正.ε是描述不变形球体半径偏差的小参数.计算了阻力和流量,并从几何方面和表面渗透性方面考查了计算结果.还尝试将此理论应用于过滤供水问题.小型的生态学上重要的水生生物体的过滤器,被模型化为轴对称可渗透物体,用扁球体或近球体建立了该问题的初级模型. 相似文献
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一类不可压广义neo-Hookean球体的空穴分岔问题的定性研究 总被引:1,自引:0,他引:1
研究了一类不可压的广义neo-Hookean材料组成的球体的空穴分岔问题,该类材料可以看作是带有径向摄动的均匀各向同性不可压的neo-Hookean材料,得到了球体内部空穴生成的条件.与均匀各向同性的neo-Hookean球体的情况相比,证明了当摄动参数属于某些区域时,从平凡解局部向左分岔的空穴分岔解上存在一个二次转向分岔点,空穴生成时的临界载荷会比无摄动的材料的临界载荷小.用奇点理论证明了,空穴分岔方程在临界点附近等价于具有单边约束条件的正规形.用最小势能原理分别讨论了空穴分岔解的稳定性和实际稳定的平衡状态. 相似文献
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球体是一种完美的几何体,上至行星天体,下至乒乓、足球,这些无时无刻不在给我们展示着球体的魅力.对于它的研究,不仅仅是天文学家的爱好,也是数学家们脑海和笔尖思索的焦点.作为我国古代最重要的一部数学经典的《九章算术》就记载了相关球体的知识,但是其对于球体体积的计算公式却是错误的.我国古代大数学家刘徽在公元263年前后为其作注解时发现了这个错误.刘徽摒弃了《九章算术》中错误的球体体积计算思路,而是创造性地构造了“牟合方盖”,巧妙地给出了球体体积计算的新思路.这种计算球体体积的方法, 相似文献
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本文是一篇关于Ricci曲率与固定半径度量球的局部回卷体积有下界流形M的近期研究综述.所谓在点x∈M处的度量球B_r(x)的局部回卷体积,是指B_r(x)的(不完备的)万有覆叠上以基本点为中心、r为半径的度量球体积. 相似文献
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具有拉格朗日余项的泰勒公式(下面简称为泰勒公式——译者)及作为它的特殊情况的中值定理中都有“中间点”。这里证明,当所论区间之长趋于零时,“中间点”的渐近状态的一个简单的结论。 设a与x属于某区间,在此区间上导数f~(n+p)(x) 相似文献
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泰勒中值定理中值点的分析性质 总被引:1,自引:0,他引:1
程希旺 《数学的实践与认识》2009,39(4)
讨论泰勒中值定理中中值点的连续性及可导性问题,给出泰勒中值定理中中值点连续及可导的充分条件,同时给出计算其导数的公式. 相似文献
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Włodzimierz Zwonek 《Israel Journal of Mathematics》1995,89(1-3):71-76
In this short note we prove that the only Carathéodory balls in domains given in the title (forn≥2) which are the norm balls are the ones with the center at 0. It is a generalization of the result of B. Schwarz, who proved
this theorem in casen=2. 相似文献
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It is proved that a real Banach spaceX is aG-space (C
σ - space)if and only if the non-empty intersection of three balls with equal radii (any three balls) has a center of symmetry. 相似文献
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Pengzi Miao Luen-Fai Tam 《Calculus of Variations and Partial Differential Equations》2009,36(2):141-171
We study the volume functional on the space of constant scalar curvature metrics with a prescribed boundary metric. We derive
a sufficient and necessary condition for a metric to be a critical point, and show that the only domains in space forms, on
which the standard metrics are critical points, are geodesic balls. In the zero scalar curvature case, assuming the boundary
can be isometrically embedded in the Euclidean space as a compact strictly convex hypersurface, we show that the volume of
a critical point is always no less than the Euclidean volume bounded by the isometric embedding of the boundary, and the two
volumes are equal if and only if the critical point is isometric to a standard Euclidean ball. We also derive a second variation
formula and apply it to show that, on Euclidean balls and “small” hyperbolic and spherical balls in dimensions 3 ≤ n ≤ 5, the standard space form metrics are indeed saddle points for the volume functional. 相似文献
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This paper is the second in a series of six papers devoted to the
proof of the Kepler conjecture, which asserts that no packing of
congruent balls in three dimensions has density greater than the
face-centered cubic packing. The top level structure of the proof
is described. A compact topological space is described. Each point
of this space can be described as a finite cluster of balls with
additional combinatorial markings. A continuous function on this
compact space is defined. It is proved that the Kepler conjecture
will follow if the value of this function is never greater than a
given explicit constant. 相似文献
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第二积分中值定理“中间点”渐近性的完善 总被引:1,自引:1,他引:0
樊守芳 《数学的实践与认识》2006,36(11):253-259
通过定义第二积分中值函数,用统一的方法继续探讨了第二积分中值定理“中间点”的一些渐近性质,得出一系列新结论,相信在积分学中有着很重要的作用. 相似文献
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积分第一、二中值定理的中间点的渐近性质的一般性定理 总被引:2,自引:1,他引:1
郑权 《数学的实践与认识》2005,35(5):240-243
把关于积分第一中值定理的中间点ξ的渐近性质的较多有关结果,归纳推广为一个弱条件下的一般性定理,并且在此弱条件下给出一种简洁的证明;而且,对于较少讨论的积分第二中值定理的中间点ξ的渐近性质,也得到相应的弱条件下的一般性定理,并且同样给出简洁证明. 相似文献
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A. M. Petrunin 《Journal of Mathematical Sciences》1994,72(4):3231-3233
If to every point x of a convex polyhedron M En there corresponds an open ball with center at x and radius f(x), where f is any positive function, then M can be split into simplexes so that every simplex is covered by those balls whose centers lie at the vertices of the simplexes.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 110–114, 1992. 相似文献
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The lilypond model on a point process in d ‐space is a growth‐maximal system of non‐overlapping balls centred at the points. We establish central limit theorems for the total volume and the number of components of the lilypond model on a sequence of Poisson or binomial point processes on expanding windows. For the lilypond model over a homogeneous Poisson process, we give subexponentially decaying tail bounds for the size of the cluster at the origin. Finally, we consider the enhanced Poisson lilypond model where all the balls are enlarged by a fixed amount (the enhancement parameter), and show that for d > 1 the critical value of this parameter, above which the enhanced model percolates, is strictly positive. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 相似文献