维数

Using derivations and skewderivations,we get the dimension of the second cohomology groups of finite-dimensional Lie superalgebras of Cartan type with a non-degenerate associativeform.

利用导子与斜导子，我们又给出了具有非退化结合型的有限维Cartan型李超代数的第二上同调群〓的维数。

The new method does not require the formation of the covariance matrix and its eigendecomposition.

不仅使得智能天线的结构尺寸减小了30%，通过多级嵌套维纳滤波器前向递推的方法，子空间的分解和维数确定可同时进行，不需要估计接收信号的协方差矩阵和对其作特征值分解，运算量可以明显降低，收敛速度快。

The inconsistencies of dimensional reduction and naive dimensional regularization in dealing withChern-Simons-matter theory are analyzed.The consistent dimensional regularization combiningwith higher covariant derivative regularization is adopted to consider Chern-Simons field theorycoupled to complex scalar and spinor field.All the local parts of one-loop two-point functionsand three-point functions are computed.Slavnov-Taylor identity is combined with these explicitcalculation results to give the one-loop local effective action.The finite gauge invariant quantumcorrection is shown and finite wave function renormalization constant for each field is defined.Thelocal part of one-loop three gauge field vertex is especially evaluated and it is verified that thereexists a renormalization choice compatible with BRST symmetry.

然后计算了所有的两点函数和三点函数单圈修正的定域部分，利用S-T恒等式给出了单圈定域有效作用量，定义了场的重正化常数，发现物质场和规范场都存在有限的规范不变的量子修正，并讨论了这些有限的规范不变的量子修正的物理意义，进而通过考察单圈三规范场顶角，表明存在与BRST对称性相容的重正化选择。5、在背景场方法的框架下，选择高阶协变导数正规化与维数正规化的杂化正规化方案计算了背景场两点函数的两圈量子修正，结果表明，标志紫外发散的极点项恰好抵消；进一步利用背景场方法中明显的规范对称性，证明背景场三点函数的两圈图贡献也是有限的。

On the other hand, Let M~n be an z-dimensional complete noncompactoriented submanifold with finite total curvature in an-dimensional simplyconnected space form F~ of constant curvature c. In this thesis, we provethat if M satisfies one of the following: n≥3, c=0 and integral from n=M H~n＜∞;n≥5, c=-1 and H＜1-2/n~(1/2); n≥3, c=1 and H is bounded, where Hdenotes the mean curvature of M. then the dimension of the space of L~2 harmonic1-forms on M is finite.

本文还证明：若具常曲率c的完备单连通空间型F~中具有有限全曲率的n维完备非紧可定向子流形M满足下面条件之一：n≥3，c=0且integral from n=M H~n＜∞；n≥5，c=-1且H＜1-2/n~(1/2；n≥3，c=1且H有界的，则M上L~2调和1-形式空间的维数是有限的，这里H为M的平均曲率。

High imaging speed is obtained by decreasing the dimensions of 2-D OCT image, which are generated by converting the point focus mode of traditional OCT into line focus mode with a cylindrical lens.

利用柱面镜的成像特性将传统OCT的点聚焦成像模式改变为线聚焦成像模式，从而降低二维OCT图像的扫描维数，达到提高成像速度的目的。

Which statement is correctly declare a variable a which is suitable for refering to an array of 50 string empty object?

注意，题中问的是如何正确声明一个一维数组，并非实例化或者初始化数组

Empirical evidence in this paper shows that the price of A shares in Shanghai and Shenzhen Stock market is inconstant with the random walk model, and that low-dimension deterministic chaos process are found in the time series of Shanghai A shares index with a Correlation Dimension of 1.4, which means that the degree of randomness is lower than that of grown-up capital markets, and so the lower of the efficiency degree to some extent.

本论文所做的实证研究表明，沪深A股市场价格并不呈随机行走状态，而是存在非线性结构；上海A股市场指数收益率序列存在低维确定性混沌过程，其维数大约为1.4，这一数值远低于成熟资本市场的指标，这表明上海股票市场指数收益率序列随机性低于成熟资本市场。

For example, Keyfitz made the classification of the bifurcations in one state variable, without symmetry up to codimension 7; Golubitsky and Schaeffer obtained the classification of the bifurcation problems in one state variable with Z_2 symmetry, in one parameter up to codimension 3; Golubitsky and Roberts studied the classification of degenerate Hopf bifurcation in two state variables with dihedron D_4 symmetry, in one parameter up to topological codimension 2; Melbourne obtained the classification of bifurcations in three state variables with octahedral symmetry, in one parameter, up to

需要指出的是以上研究均没有考虑分歧参数的对称性，Futer，Sitta和Stewart的工作虽然考虑了分歧参数的对称性，但仅限于分歧参数与状态变量具有相同的对称性，他们得到了状态变量与分歧参数均关于二面体群D_4对称，拓扑余维数不大于1的分歧问题的分类。高守平和李养成则讨论状态变量和分歧参数均具有对称性且对称性可以不同的分歧问题，并给出了状态(来源：A770707BC论文网www.abclunwen.com)变量关于二面体群D_4对称，分歧参数关于S~1对称，拓扑余维不超过1的分歧问题的分类。本文第一章讨论两个状态变量关于二面体群D_3对称，两个分歧参数关于O(2)对称的分歧问题，给出了该类分歧问题在非退化条件q(0)≠0下所有情形的分类与相应的识别条来源：AdadaBC论文网www.abclunwen.com

Second,around each of m-dimensional tori of elliptic or mixed type there arehigher-dimensional invariant tori.

第二，环绕在m维椭圆型和混合型环面的周围存在维数更高的不变环面。

It provides a way to find optimal lower dimensional approximations of the given data, and It enormously reduce the storage of the data which is needed when the physical processes is recurred. The physical process can be described in series expansion function that only is related to the time and space. It is optimal approximation of the given data in a certain least squares optimal sense. The most obvious advantage of the method is that it reduces the computation cost and computation time markedly.

它提供了一种描绘物理过程的有效方法，该物理过程可以写成一个只与时间相关的函数和一个只与空间相关的函数的展开式序列，且它们在均方意义上是最优的，在展开式中只需要少量的项数就可较准确地描述该物理过程，因此降低计算维数、减少计算量和节省计算时间是这个方法最明显的优点。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。