- 更多网络例句与紧致定理相关的网络例句 [注：此内容来源于网络，仅供参考]
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The topics covered include the basic concepts of information theory--entropy, mutual information, channel capacity, information rate, Shannon's noiseless coding theorem and Shannon's fundamental coding theorem; modeling of information sources--zero-memory and Markov models; modeling of information channels--BSC and BEC channels, additivity of information and cascaded channels; construction of compact source codes--Kraft inequality, compact codes, Huffman and LZW compression codes; and analysis and design of error-control channel codes--Hamming distance, binary linear codes and the parity-check matrix, Hamming codes, checksum codes, cyclic codes and the generator polynomial and CRC codes.
课程的内容包括：信息论的基本概念（熵、交互信息、信道容量、信息率、 Shannon无噪声编码定理和Shannon基本编码定理）、信源模型（无记忆模型和Markov模型）、信息信道模型（BSC 和 BEC模型、信息的可加性和级联信道），紧致信源编码设计（Kraft不等式，紧致编码，Huffman 和LZW压缩编码）以及差错控制信道码的设计与分析（海明距离，二元线性码，奇偶校验矩阵，海明码，校验和，循环码，生成多项式和CRC码）。
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The compactness theorem of model theory has an extensive application in algebra.
模型论中的紧致性定理在代数中有很广泛的应用。
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As a particular of Rado's theorem and the compactness theorem one obtains the following result.
作为Rado定理和紧致性定理的一种特殊情形，我们得到下面的结果。
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Using the continuity method, we will obtain a theorem of existence of solutions to the equation on 4-dimensional compact Riemannian Manifolds.Finally, we will consider a kind of Kazdan-Warner type equation on compact complex manifolds.
作为上述工作的补充，我们讨论了规范固定Yang-Mills方程，并用连续性方法得到了一个在四维紧致黎曼流形上解的存在性定理。
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The Pinching problems are discussed on the sectional curvature of compact space-like pseudo-umbilical submanifolds M~n with parallel mean curvature vector in De Sitter space S~_p, and the theory of reduction of the codimension is obtained in De Sitter space through evaluating the Laplacian of square of the length.
讨论了De Sitter空间Snp+p中，具有平行平均曲率向量的紧致类空伪脐子流形Mn的截面曲率的拼挤问题，通过估计第二基本形式模长平方的Laplacian，得到了De Sitter空间中的余维数压缩定理。
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In thisthesis, we first extend the vanishing theorem due to Lawson, Simons and Xinto the case of compact submanifolds of a hyperbolic space. Thus, by using thenew vanishing theorem for homology groups, we prove the topological spheretheorem for complete submanifolds in a hyperbolic space. Hence we generalizethe Shiohama-Xu topological sphere theorem.
本文进一步将Lawson-Simons-Xin同调群消没定理拓广到双曲空间中紧致子流形的情形，并运用这一新的同调群消没定理证明了双曲空间中完备子流形的拓扑球面定理，从而推广了Shiohama-Xu的拓扑球面定理。
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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。
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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。
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Theorem 2 Let M~n be a compact totally real minimal submanifold in M~n which is a locally symmetric Bochner-Kaehler manifold.If the infimum of sectional curvature R_c in M~n satisfies: then M~n must be totally geodesic in M~n.
定理2 M~n是局部对称Bochner-Kaehler流形M~n中紧致全实极小子流形，如果M~n截面曲率下确界R_c满足：则M~n必是全测地的。
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We introduce a set of real functions H, and use to it to give a fixed point theorem of tother type for complex mappings on complete metric spaces, which improves and generalizes the corresponding results on compact metric spaces or under the condition of weakening compactness obtained by Fisher, Telci and Xu Xiao-li, respectively.
利用引入的实函数类H，在完备度量空间上给出了复合映射的另一种类型的不动点定理，改进并推广了Fisher、Telci和徐晓立等在紧致度量空间上或在弱化紧性条件下得到的相应结果。
- 更多网络解释与紧致定理相关的网络解释 [注：此内容来源于网络，仅供参考]
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compactness theorem：紧致性定理
完备性定理 completeness theorem | 紧致性定理 compactness theorem | 可公理化 axiomatizable
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completeness theorem：完备性定理
可靠性定理 soundness theorem | 完备性定理 completeness theorem | 紧致性定理 compactness theorem
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connected sum：连通和
再如几何拓朴学(Geometric Topology)中的「紧致连通曲面(Compact Connected Surface)分类定理」告诉我们,任何紧致连通曲面在同胚(Homeomorphic)(注11)的意义下均可划归以下三类曲面的其中一类:球面( Sphere);圆环(Torus)的连通和(Connected Sum);射影平面(Pro
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projective plane：射影平面
再如几何拓朴学(Geometric Topology)中的「紧致连通曲面(Compact Connected Surface)分类定理」告诉我们,任何紧致连通曲面在同胚(Homeomorphic)(注11)的意义下均可划归以下三类曲面的其中一类:球面( Sphere);圆环(Torus)的连通和(Connected Sum);射影平面(Projective Plane)的连通和.