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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。

Hence a theoretical basis is establised for design and grinding of the hyperboloid twist drill.

给出了该钻型设计参数与刃磨参数之间的函数关系式，为双曲面麻花钻型的设计和刃磨提供了一定的理论基础。

Hence, we can hypothesize: H4: Perceived enjoyment is positively associated with satisfaction.

因此，我们可以假设： H4的：享受知觉满意程度呈正相关。

When God orders the angels to bow to Adam one of those present, Satan (Iblis in Islam, regarded as a jinn rather than an angel, and hence avoiding questions about angels having free will), refuses due to his pride, and is summarily banished from the heavens.

当神命令天使们向亚当下跪的时候，其中一位，撒旦（在伊斯兰教里面是恶魔，被认为是一位精灵，而不是天使，从而避免了天使是否有自由意志的问题），由于他的骄傲而拒绝，立刻被逐出天堂。

Hence, to invite to the right point of ice cream, beer, chenye se taste.

遂邀来心仪，来点儿冰激凌、啤酒，趁夜色品尝所爱。

Hence, it is very necessary to estimate and compensate the phase noise ICI.

所以，对相噪ICI进行估计和补偿显得尤为必要。

The Iliad (Greek:λι, Iliás) is an epic poem recounting significant events during a portion of the final year of the Trojan War — the Greek siege of the city of Ilion — hence the title ("pertaining to Ilion").

伊里亚特（ΙΛΙΑΣ，Ilias，Iliad，又译《伊利昂记》，今译《伊利亚特》。）是古希腊盲诗人荷马(Homer， 800BC-600BC)的叙事诗史诗。是重要的古希腊文学作品，也是整个西方的经典之一。

Hence she had been trapped in an illusionary battlefield, and fell in love with the biggest imaginary enemy.

她太在乎他，倚重他又希望超越他，自此陷入无物之阵，爱上最大的假想敌。

Hence, the algorithm and model proposed in this paper are of great value in theoretic and application to image compression.

因此，本文算法和模型具有较高的理论意义和在图像压缩方面的应用价值。

The economic crisis should be regarded as an unavoidable consequence and hence a "just" price we have to pay for immodest and over- confident politicians playing with the market.

经济危机应被视作是不可避免的结果，是狂妄自大的政客们玩弄市场的结果，因此是我们必须付出的"合理"代价。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。