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We've found that on symplectic manifolds there exists a series of Euler-Lagrange cohomology groups different from both de Rham and harmonic cohomology in general and proposed a set of general volume-preserving equations that contain the Hamiltonian equations as a special case.

中文摘要:我们发现在作为经典力学中的相空间的辛流形上有可能存在不同于de Rham上同调和调和形式的上同调,称之为Euler-Lagrange上同调;提出相空间上保体积的一般方程,通常的正则方程是其特殊形式;进而推广了经典力学中著名的刘维定理;同时把Noether定理与上同调联系起来。

At many occasions they arise quite natu-rally.For example,they appear in the Iwasawa decomposition of the isometry group ofa non-compact Riemannian symmetric space.Also,every connected homogeneous Rie-mannian manifold of non-positive sectional curvature can be represented as a connectedsolvable Lie group with a left-invariant Riemannian metric.

它们出现在非紧致黎曼对称空间的等距群的Iwasawa分解中;任一非正截面曲率的连通齐性和黎曼流形可以表为带有左不变黎曼度量的连通可解李群等,带有左不变黎曼度量的幂零及可解李群的微分几何,调和分析和谱几何是重要的研究课题。

We can never agree our views are irreconcilable .

我们永远不能一致彼此的看法无法调和。

In terms of honor, l stand aloof and will no reconcilement.

雷 为了荣誉,我的立场不会变,我们不可能调和。

Theorem 4 There is no compact totally real 2-harmonic submanifold with non-zero parallel mean curvature and positive sectional curvature in a locally symmetric Bochner -Kaehler manifold.

定理4局部对称Bochner-Kaehler流形中不存在具有非零平行平均曲率向量且截面曲率大于零的紧致全实2-调和子流形。

Neither is the spirit a man, for it is called the spirit, and not a man; but the commingling and union of all these constitutes the perfect man.

灵也不就是人,因为它称为灵,而不称为人。而是这三者充分地调和与联合才构成完全的人。

18 God reconciles the world to Himself, reaches to all, but that it is not sealed indiscriminately on the hearts of all to whom it comes so as to be effectual.

神调和世界上对自己,以达到所有的,但它不是密封,不分青红皂对心,所有的人来等,以行之有效的。

Among them we may occasionally see some man of deep conscientiousness, and subtle and refined understanding, who spends a life in sophisticating with an intellect which he cannot silence, and exhausts the resources of ingenuity in attempting to reconcile the promptings of his conscience and reason with orthodoxy, which yet he does not, perhaps, to the end succeed in doing.

在这一大群之中,我们还可以间或看到某个具有深刻良心和精细理解的人,用其一生以他所不能压熄的智力从事于矫作世故,并竭其一切巧思努力于把其良心和理性所迫促的东西与正统调和起来,而最后或许还办不成功。

The brush pen is sharp, soft and elastic so that Chinese calligraphy and painting is likely to become an art of line. Chinese ink can be diluted and attempered. Moreover, it is neither sticky, nor astringent nor stagnant. These properties make people able to write or paint freely. The paper for Chinese calligraphy and painting, especially rice paper, can absorb Chinese ink of various kinds. It is suitable for calligraphy and painting using brush pen.

其中,毛笔笔锋尖细、质地柔软而富有弹性,这使得中国书画更易成为一种自由表达的线的艺术;松墨和油墨易于稀释和调和,而且不粘、不涩、不滞,可以保持运笔的灵活,并通过墨汁的浓淡变化实现写意的目的;中国书画的用纸具有吸附软笔水墨的特性,不仅适宜于毛笔的书写,也有利于发挥墨的特性。

Another, as is sufficient for the harmony of society. Though they will never be unisons, they may beconcords, and this is all that is wanted or required.

虽然两者一定不会调和,它们可以成为一致和睦,这就是最终想要达到,想希望获得的结果。

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