共查询到19条相似文献,搜索用时 78 毫秒
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本文应用 Smith周期变换理论 ,根据球面在周期变换下的指数 ,对球面到光滑流形的连续映射做了进一步探讨 ,从而得到了 Munkholm型定理 . 相似文献
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本应用Smith周期变换理论,根据球面在周期变换下的指数,对球面到光滑流形的连续映射做了进一步探讨,从而得到了Munkholm型定理。 相似文献
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高阶球形涡的一般性质及三阶球形涡的混沌现象 总被引:1,自引:1,他引:0
讨论了n阶球形涡的一般性质,找到了一族分布在同心球面上的周期轨道的代数表达式,讨论了不动点的分布和流动的对称性。对叠加的三阶球形涡进行了数值计算,结果表明:在Poincare截面上,伴随着岛形规则区,出现了不同程度的浑沌(Lagrange湍流)区,观察到了并分析了规则区和浑沌区随特征参数的变化而出现的一些有趣的现象。 相似文献
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一、问题的提出
“球面距离”是立体几何中的重要概念,上海市二期课改教材(高三年级)第41页关于“球面距离”的概念是这样阐述的:“可以证明,在连接球面上两点的路径中,通过该两点的大圆劣弧最短,因此该弧的长度就是这两点的球面距离.”最近在上海市青年数学教师教学评优中, 相似文献
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本文主要估计了球面到单位球面的等距极小浸入的覆盖层数,从而导出一些有关嵌入的结果。同时,在本文证明过程中,给出了一个构造指定覆盖层数的等距极小浸入的方法. 相似文献
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本文证明了2型球面紧致超曲面是1型的,因而是质量对称的.换言之,不存在2型球面紧致超曲面,推广了文[2,3,4,5」中的结论. 相似文献
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本文对单位球面S~3中的曲线在Mbius变换下的性质进行了研究.给S~3中的曲线定义了一套由共形弧长参数、共形曲率和共形挠率组成的Mbius不变参数系统,并证明这个系统决定S~3中所有光滑曲线在Mbius变换下的分类. 相似文献
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在有限变形动力学的框架下,研究了在非均匀温度场中组合热超弹性球体,在表面均布拉伸死载荷作用下的动态孔穴的生成和增长问题.首先建立了相应的非线性数学模型,利用换元积分方法求得了孔穴半径与外加载荷之间的一个精确的微分关系,并进行了数值计算,得到了不同温度下球体中孔穴生成时的临界载荷和分叉曲线.考察了参数对孔穴生成与增长的影响,并与相应的静态结果进行了比较.结果表明孔穴是以一个有限的半径突然出现的,且随时间的演变孔穴半径呈现周期性的非线性振动;当温度升高,临界值降低,同时在相同的条件下动态临界载荷低于静态临界载荷. 相似文献
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Tongzhu Li 《Geometriae Dedicata》2010,149(1):15-43
In this paper, we study surfaces of S
3 in the context of Lie sphere geometry. We construct invariants with respect to Lie sphere transformations on the surfaces,
which determine the surfaces up to a Lie sphere transformation. Finally we classify completely the homogeneous surfaces in
S
3 with respect to the Lie sphere transformation group of S
3. 相似文献
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We present an algorithm for automatic integration over an N-dimensional sphere. The quadrature formula is obtained by using a trapezoidal rule after a non-linear transformation, and allows to deal with integrand singularities on the surface or in the centre of the sphere.At the basis of the theoretical development lie the construction and the selection of suitable transformations.The algorithm is cast into an automatic integration program coded as a Standard Fortran sub-routine. 相似文献
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Let Mn(n≥2) be an immersed umbilic-free hypersurface in the(n+1)-dimensional unit sphere Sn+1. Then Mn is associated witha so-called M(o)bius metric g, and a M(o)bius second fundamental form Bwhich are invariants of Mn under the M(o)bius transformation groupof Sn+1.In this paper, we classify all umbilic-free hypersurfaces withparallel M(o)bius second fundamental form. 相似文献
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Doo-Sung Lee 《Applicable analysis》2020,99(8):1316-1332
ABSTRACTThe problem of light scattering by a homogeneous sphere above a plane boundary is considered in this paper. Hankel transformation and Erdélyi's formula are used to satisfy the boundary conditions on the plane and the determination of the unknown coefficients in the scattered field is achieved by matching the electromagnetic boundary conditions on the surface of the sphere. Existence and uniqueness of the solution involving these unknown coefficients are shown and the extinction efficiency factor is presented. 相似文献
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Let M2 be an umbilic-free surface in the unit sphere S3. Four basic invariants of M2 under the Moebius transformation group of S3 are Moebius metric g, Blaschke tensor A, Moebius second fundamental form B and Moebius form Φ. We call the Blaschke tensor is isotropic if there exists a smooth function λ such that A = λg. In this paper, We classify all surfaces with isotropic Blaschke tensor in S3. 相似文献
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A. Gasull 《Journal of Mathematical Analysis and Applications》2005,303(2):391-404
We consider planar cubic systems with a unique rest point of center-focus type and constant angular velocity. For such systems we obtain an affine classification in three families, and, for two of them, their corresponding phase portraits on the Poincaré sphere. We also prove that for two of these families there is uniqueness of limit cycle. With respect the third family, we give the bifurcation diagram and phase portraits on the Poincaré sphere of a one-parameter sub-family exhibiting at least two limit cycles. 相似文献