结构公式

Firstly, the structure of all phase spectrum is analyzed and the all phase spectral interpolation formula is derived.

首先分析了全相位频谱的结构，给出全相位频域插值公式。

The results show that the experimental results are in good agreement with the values of viscosity in a part of temperature range that has been reported, with the relative error of less than 2.5%; In the process of ascent and descent temperature, the irreversible phenomenon of the curve of viscosity versus temperature V presents interzone characteristic, and the break of viscosity at critical temperature reflects jump change of melt structural information; It is one to one correspondence between viscosity and atomic size, and this relation is consistent with the Hall-Petch formula in expression way.

结果表明：实验结果与已报道的部分温度区间内的黏度值基本一致，相对误差低于2.5％；升温和降温过程中，黏度－温度关系曲线V的不可逆现象具有区间特征，临界温度时黏度的突变反映出熔体结构信息的跳跃变化；黏度与原子集团尺寸之间存在一一对应关系，该关系在表达上符合Hall-Petch公式。

By using in a sequence the eigen-decomposition,a permutation,the inverse discrete Fourier transformand a truncation on the matrix,an exact and explicit parametrization formula for Loop subdivision surfaces is proposed.

利用控制网格拓扑结构的对称性，通过将奇异点周围1-环和2-环的控制顶点进行离散Fourier变换得到分块对角阵，将其进行特征分解及排序之后，再通过离散Fourier逆变换和截断等操作得到细分矩阵的高次幂的表达式，从而得到Loop 细分曲面新的精确参数化公式

In our thesis, contents are organized as following In Chapter 1 we present our topic's internal and overseas research situations, theoretical and practical significance, and introduce the research object and contents, and the main contributions of this dissertation. Chapter 2 reviews the development of the stability results for nonlinear systems and some relevant recent results, which include Lyapunov and LaSalle-Yoshizawa theorems for nonlinear systems, and stochastic edition for stochastic nonlinear systems. Sontag's formula for systems affine in control is presented in the frame of CLF. The concepts of disturbance attenuation and the inverse optimality are also explained in this Chapter. In chapter 3 we present the solvable theorem of inverse optimal gain assignment problem, design the inverse optimal controller and the inverse optimal tracking controller for strict-feedback nonlinear continuous systems with unknown time-varing bounded disturbances and constant unknown parameters using an adaptive backstepping algorithm, which are nonlinear, continuous and are easier to realize. These designs are fully systematic and the algorithm can be directly coded in symbolic software. The results of simulation show the effectiveness of the control algorithms.

论文的结构如下：在第1章中，给出了本文研究课题的研究现状、理论意义和实际应用，并介绍了本文的研究对象、研究内容以及主要贡献；在第2章中，针对确定性非线性系统和随机非线性系统，分别介绍了Lyapunov定理、LaSalle-Yoshizawa定理及其随机版本；对仿射系统，在控制Lyapunov函数框架下，给出了Sontag公式；同时给出了非线性系统扰动抑制和逆最优控制问题的基本概念；在第3章中，针对具有未知时变有界扰动和未知定常参数的一类不确定非线性系统，给出并证明了逆最优增益配置可解定理，使用自适应Backstepping算法和均值定理，系统地设计了自适应逆最优控制器和逆最优跟踪器，这种设计方法可同时获得逆最优控制策略和自适应律，简单明了，仿真结果表明该控制算法的有效性，并给出了性能估计。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundle For a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained.

中文摘要：本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundleFor a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained. Then, the monotonicity formula and the small action regularity theorem can be proved. We will give the locally uniform estimates for the higher derivatives of the curvature.

本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

Of these is proposed, which is significant for the design of masonry structural buildings.

墙体中窄墙肢的应力计算公式，对砌体结构房屋的设计具有重要的意义。

The universal formulases of a average internal energy of atom in metal and the two different kinds of metal atomic interaction potential have been derived by applying to the classical concept of the metalic structure and concerning the Gauss type ball symmetry of the around electronic density of atomic nucleus.

本文介绍了亚稳态Fe50Cu50固溶体晶格常数的测量结果，应用金属结构的经典概念并考虑到原子核周围电子密度的高斯型球对称分布，导出了计算金属中一个原子的平均内能和两种不同金属原子相互作用势的普遍公式。

It can access structures in the NCI database by name, CAS number, or formula.

它可以访通过名字，CAS号，或公式来问NCI数据库中的结构。

Secondly, three kinds of mathematics model of optical vortex beams were introduced here. Then the propagation dynamics of optical vortex beams through the non-axis symmetry system is studied, this chapter includes the introduction of the symmetry vortex beam and the non- symmetry vortex beam, the deduction of the Collins diffract integral formula for the non-axis symmetry system, and the transformation of the vortex beam passing through the non-axis symmetry system has been described by using the numerical simulation. Then the general calculation for the orbit momentum of vortex beams, the matrix form for the orbit momentum of vortex beams, and the photon method to describe the orbit momentum of vortex beams are also introduced here. Finally, the interference about optical vortex beams was studied.

本文对涡旋光束进行了较为全面的介绍和研究，主要内容包括：（1）光学涡旋光束的基本理论，主要是介绍了单个光学涡旋光束在柱坐标中的一些表征，涡旋光束的奇异相位和光学涡旋的相位结构；（2）光学涡旋光束的三种数学模型；（3）光学涡旋光束在非轴对称光学系统中的传播动力学，其中介绍了对称涡旋光束与非对称涡旋光束，推导了非轴对称光学系统的 Collins 衍射积分公式，并利用计算机模拟图描述了对称涡旋光束经过非轴对称光学系统后涡旋形态的改变；（4）涡旋光束轨道角动量的一般计算，涡旋光束轨道角动量的矩阵形式，光子法描述涡旋的轨道角动量；（5）涡旋光束的干涉。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。