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This paper analyzes irrational number series of square root of 2 and e in six aspects involving autocorrelation function,Power Spectral Density,phase space construction,correlation dimension,Principal Component Analysis and maximal Lyapunov exponent.

将已提出的π序列定义和分析方法推广到无理数领域，引出了无理数序列，并以常用的无理数根号2、e为例，对无理数序列的自相关、功率谱、相空间、关联维数、最大Lyapunov指数和主分量等6个方面进行深入分析。

The completely diagonalized Hamiltonian matrices of 3d2／3d8 ion configuration in the trigonal symmetry sites have been established by irreducible representation method. Taken into account microscopic magnetic interactions, the spectral fine structure, local structure and zero-field splitting parameters of V3+:α-Al2O3 and Ni2+:α-Al2O3 crystals are investigated as well as the influence of the doping.

应用不可约张量方法构造了三角晶场中3d2/3d8态离子的45阶可完全对角化的能量哈密顿矩阵，在考虑了微小磁相互作用的基础上计算了V3+：α-Al2O3和Ni2+：α-Al2O3晶体的光谱精细结构、晶体局域结构和零场分裂参量，研究了掺入Ni2+和V3+对α-Al2O3晶体光谱精细结构、晶体局域结构和零场分裂参量的影响。

It increases the spectral usage efficiency, and at the same time, it can reduce ISI greatly.

OFDM适用于多径环境和频率选择性衰落信道中的高速数据传输。

It is found that there are similarities in terms of spectral integral among the wind input source terms given by Jeffreys, Sverdrup and Munk, and Plant and among the wave breaking dissipation source terms given by Tsikunov,Hasselmann and Philips,although the original forms and the physical considerations of these source terms are significantly different.

发现Jeffreys，Sverdrup和Munk以及Plant的风能输入源函数在谱积分意义下具有相似性，而Tsikunov，Hasselmann和Phillips的破波耗散源函数在谱积分意义下也具有相似性，尽管这些源函数的原始形式和物理背景显著地不同。

In this thesis, we mainly study the theory of vector optimization in three aspects: the spectral scalarization of Euclidean Jordan algebra vector optimization, the robust methods for solving uncertain multiobjective linear optimization problem and the application in game theory.

本文共分四章，主要致力于向量优化三个方面的研究：欧几里德若当代数向量优化的谱标量化、不确定多目标线性优化问题的鲁棒方法和向量优化在对策论中的应用。

We also develope the corresponding spherical harmonic-generalized Laguerre polynomial mixed spectral method and apply them successfully to computation of three dimensional problems, exterior problems and nonlinear problems.

在第二章中，我们提出了一类新的广义Laguerre多项式正交逼近，其特点是适用于更多问题并能更好地拟合微分方程真解在无穷远处的性态，从而提高了计算精度。

We compared the spectral and its secondary structure of endostatin with and without of zinc, heparin and lanthanides. It demonstrated that the pH has strong effect on the interaction of endostatin and heparin.

研究了内皮抑素与锌离子、肝素、稀土离子作用后蛋白质的光谱学性质和二级结构的变化，首次发现偏酸性pH对肝素与内皮抑素的结合作用有特殊影响，为研究内皮抑素特异抑制肿瘤组织新生血管的生成提供了实验依据。

Our paper is mainly about the ordering of the connected graphs with thesmallest Laplacian spectral radii.

本文主要是对连通图的最小Laplace谱半径的排序问题的研究。

Children who do well in different information processing tasks appear different trails of relations between S-spectral power in left-brain and right-brain.

摘 要：以201名6～12岁小学生为研究对象，采用脑电波超慢涨落分析技术，对其脑波活动进行了记录和分析。

Methods The constituents in the ethanol extraction of the aerial parts of Lespedeza virgate were isolated and purified using column chromatography, and the isolated compounds were identified according to their physicochemical and spectral data.

对细梗胡枝子乙醇提取液的正丁醇部分进行反复分离纯化，根据光谱数据和理化性质确定化合物结构。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷