查询词典 unit sphere

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simon\'s nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simons nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

In chapter 1, we introduce the definitions of area integral S_β and invariant g-function on unit sphere, and study their boundedness on BMO and non-isotropic Lipschitz spaces.

共分三章，第一章引进了C~n单位球面上的面积积分和不变g函数，研究它们在BMO空间以及non-isotropic Lipschitz空间上的有界性问题。

We consider Grassmann manifold G(2,8) as a submanifold of the unit sphere of /\2 which is the exterior vector space on Rn. Thus we have the induced metric and connection on G(2, n).

把Grassmann流形G（2，n）看作等距地嵌入在欧氏空间R~n上2-外向量空间∧~2中的单位球面上的子流形，得到它上面的度量和联络。

Let x: M→S(superscript n+1)(n≥3) be a hypersurface in the (n+1)-dimensional unit sphere without umbilic points. Denote the Mbius metric, the Mbius form, the Blaschke form and the Mbius second fundamental form of x by G,Ф, A and B, repcectively, which are Mbius invariants in Mbius differential geometry.

设x： M→S(上标 n+1)(n≥3)是n+1-维单位球中的无脐点超曲面，Mbius不变量G，Ф，A和B分别表示x的Mbius度量，Mbius形式，Blaschke形式和Mbius第二基本形式。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

In this paper by use of a new differential operator similar as one introduced by Cheng and Yau,we obtain a rigidity result for a compact submanifold of constant scalar curvature in a unit sphere.

宣满友 ，盛为民本文利用一个类似于Cheng和Yau引进的微分算子的新微分算子，得到了单位球面中常数量率的紧致子流形的一个刚性结果。

The LP approximation by strong summability of Fourier-Laplace series of a function defined on unit sphere is discussed.

本文讨论了球面函数的Fourier—Laplace级数的强求和在LP尺度下的逼近问题，其结果是球面上强求和的某些已有结果的补充，也可以看成一元或多元Fourier级数相应结果的球面类比。

In 1936, J.Clarkson first introduced the concept of uniformly convex Banach spaces ,initiated from geometric structure of the unit sphere of Banach spaces to research the properties of Banach spaces, began to research convex theory of Banach spaces. The same year, J.

Clarkson首先引入了一致凸Banach空间的概念，开创了从Banach空间单位球的几何结构出发来研究Banach空间性质的方法，开始了Banach空间凸性理论的研究。

Procedures including the data generation of the unit sphere.

程序包括单位球体数据的生成。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。