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After that, using the method of group action we get the formula for computing of dimensions of cohomology of holomorphic vector bundles with trivial pull-back on non-primary Hopf manifold, of which the fundamental group is Abelian 〓.

我们利用群作用的方法，给出了具有Abel基本群〓的非主Hopf流形上具有平凡拉回的全纯向量丛的上同调维数的计算公式。

In the P0442 example above, the fuel level, intake air temperature and manifold absolute pressure sensors are used.

在上面所给出 P0442 示例中，燃油箱液面位置，进气空气温度和歧管绝对压力传感器将被应用。

After a historical motivation of the definition of a Lie group we shall develop basic manifold theory, vector fields, tangent spaces leading to the Exponential mapping for an affine connection.

在简单介绍了李群的定义的历史来源之后，我们将讨论关於流形理论、向量场和切空间，进而引出仿射联络的指数映射的基本知识。

This gives a new description of human recognition mechanism from the view of information geometrical and algebraic topological treatment, the results include Propose a structure representation and system identification approach for neural networks, based on the concept of simplical complexes and dual affine coordinates in the dual flat manifold.

主要的结果包括：提出用对偶平坦流形上的单、复形结构和对偶平坦流形的对偶仿射坐标作为神经网络内在结构表示的一种方法，具有广泛的意义。

That is that information processing of neural networks is viewed as the composition of the two steps: field organization and field action, in which, field organization transformation converts input pattern into relevant structure representation, extracting the underlying architecture features and forms a architecture representation in action transformation space; The field action transformation converts the features representation into expected output. In strategies, we use the dual affine coordinates in dual flat manifold as way of representation of field organization system and field action system, which established a theoretical framework of analysis the coupling mechanism of information processing from the view of point of structure representation and model generation.

在具体人工神经网络结构描述的策略上，利用对偶流形空间上的对偶仿射坐标概念分别表示场组织变换系统和场反应变换系统，建立起从问题的结构表示和模型生成两种观点来分析信息处理的理论框架；分析了有监督和非监督学习人工神经网络模型在神经场变换机理下的形式化描述。

We researched the problem of Lagrange interpolation of polynomial space on the algebraic manifold.

研究高维空间中代数流形上多项式空间的Lagrange插值问题。

We posed the concept of sufficient intersection about s(1≤s≤n) algebraic hypersurfaces in n-dimensional space and proved the dimension of polynomial space Pm(which denotes the space of all multivariate polynomials of total degree≤m) on the algebraic manifold S=s(f1,…, fs) where f1(X=0,…, f s=0denote s algebraic hypersurfaces of sufficient intersection, then gave a convenient expression for dimension calculation by using the backw ard difference operator.

给出了n维空间中s(1≤s≤n)个代数超曲面充分相交的概念，证明了n元m次多项式空间Pm在充分相交的代数流形S=s(f1，…， fs)（f1=0，…， fs=0表示s个代数超曲面）上的维数，并利用倒差分算子给出一个方便计算的表达式；构造了沿代数流形上插值适定结点组的叠加插值法；证明了在充分相交的代数流形上任意次插值适定结点组的存在性；给出代数流形上插值适定结点组的性质和判定条件。

Finally, the idea of using new numerical method such as Discontinuous Deformation Analysis and Numerical Manifold Method to simulate the joint of CFRD is proposed, which can make guidance on the design and calculation of CFRD built on thick alluvium deposits.

提出引进新的数值方法，如不连续变形分析方法和数值流形方法，来模拟和计算面板坝接缝变形的设想，对深覆盖层上面板堆石坝的设计和计算有指导意义。

As face space is always believed to be a low-dimensional submanifold embedded in high-dimensional ambient space, many methods of subspace feature extraction adopt manifold learning to explore intrinsic structure of face patterns.

在人脸识别中，提取有效的鉴别特征是实现人脸准确识别的一个关键因素。

We got the result: Bufo Raddei Strauch Tadpole (1) Bufo Raddei Strauch Tadpole was capable of lens regeneration, which originated from the epithelial cells at iris dorsal margin by dipigmentation.(2) Dipigmentation of Bufo Raddei Strauch by two methods: one was licked up by amoebocyte, the other one was flowed from the pigment cells.(3) In the lens regeneration cells of Bufo Raddei Strauch profiles of the mitochondria became complicated ribosome manifold, and the endoplasmic reticulum was cisternal dilation. During the process of deferentiation of lens fiber the cell nucleolus became little and chromatin shrinked.(4)The crystalline electrophoresis of Bufo Raddei Strauch Tadpole lens regeneration showed that during lens regeneration P-crystalline was expressed earliest then was γ-crystalline and α-crystallin, this result is consistent with newt.

结果表明：花背蟾蜍蝌蚪(1)具有晶状体再生的能力，其晶状体的再生来源于虹膜背缘的上皮细胞；(2)虹膜背缘去色素是转分化的前提，主要有两种方式：一种也是最主要的方式是在晶状体被摘除后虹膜外侧产生巨噬细胞，巨噬细胞吞噬虹膜色素上皮细胞中的色素颗粒；另一种方式是虹膜色素上皮细胞自身释放色素颗粒；(3)电镜观察发现虹膜色素上皮细胞转分化过程中线粒体有明显变化，核糖体增多，粗面内质网增多，晶状体纤维分化过程中细胞核逐渐凝聚；(4)SDS-PAGE电泳发现，花背蟾蜍蝌蚪晶状体再生中相关蛋白表达顺序与有尾类蝾螈相似，蛋白表达顺序依次是β-晶状体蛋白、γ-晶状体蛋白和α-晶状体蛋白，并且后两种蛋白几乎同时表达。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。