数

The quaternion calculation for spacecraft attitude determination is investigated in this paper,including the transformation between quaternion and the direction cosine matrix,the quaternion differential equation,the selection of time steps for integrating the quaternion equation,and the compensation methods for the noncommutativity error in high dynamic motion.

介绍了四元数计算中的相关问题，包括四元数与方向余弦阵之间的转换、四元数运动方程、求解四元数运动方程时积分步长的选取和高动态应用中非互易误差的补偿，此外还介绍了对偶四元数的发展。

ReduceMain fractionation tower,s press drop can enhance inlet pressure of compressor.At the condition of compress ratio is invariable,it can improve system pressure、increase NTS of stabilization tower、reduce stabilize gasoline C4 ratio、improve system absorbent ability.Generic design can hardly reach the best NTS of absorber,so adding absorber,NTS can obviously increase effect so absorb. Because adding absorber'NTS can reduce system dependence on other factors,and it can not lead to the increase of the energy,so it is the best economic method of improving absorb operation effect. For desorber,double feed stream is a economical means but it need adding the NTS.

降低主分馏塔的压降，可以提高压缩机的入口压力，在压缩比不变的情况下提高系统压力；增加稳定塔理论板数，可以降低稳定汽油中C4的含量，系统的吸收效果改善；一般的设计和吸收塔的最佳板数相距较大，所以改造吸收塔的理论板数，它对提高吸收效果往往最显著，又因为改善吸收塔的理论板数会降低系统对其它因素的依赖程度，而且改善它并不增加能耗，所以改造它对提高吸收效果又是最经济的手段之一；对于解吸塔来说，双股进料的工艺很有经济效益，但它需要增加理论板数来实现。

This paper analyzes the property of FNT, the characteristics of Kernel Matrixes and the relationship between Kernel Matrixes of two-dimensional Fermat number transform whose modulus are odd prime and image data, and presents and proves the deduction of the theorem which demonstrates the relationship among different transform matrixes corresponding to different roots of unity under the same odd prime modulus of FNT, and reveals the essence of FNT whose modulus are odd prime.

分析二维Fermat数变换性质、正反变换核的特点、二维模为奇素数的二维Fermat数变换正反变换核以及与图像数据的关系，提出了不同单位根对应变换矩阵间的关系定理的推论，证明了该推论中模为奇素数的二维Fermat数变换的不同单位根对应的变换矩阵之间的关系，揭示了模为奇素数的二维Fermat数变换的本质，在构造离散图象数据Fermat数变换时为单位根的选择奠定了理论基础。

According to the extent of the years you shall increase its price, and according to the fewness of the years you shall diminish its price; for it is the number of crop years that he sells to you.

25：16 年数若多，要照数加添买价；年数若少，要照数减去买价；因为他是照收成的年数卖给你。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

The reason why quaternion is used in flight simulation of fighter aircraft and the geometric meaning of quaternion are described,according to axis system used in flight simulation of fighter aircraft in China,three problems are introduced as follows:(1) quaternion kinematic equations,(2) relationship of quaternion and coordinate transformation matrix,(3) Euler angles in terms of quaternion.

阐述了在战斗机的飞行仿真中采用四元数的原因和四元数的几何意义，并按照中国战斗机飞行仿真中采用的坐标系，介绍了三个问题：四元数运动学方程；四元数与坐标变换矩阵的关系；用四元数表示的欧拉角。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

In this paper, the existence of isometric mapping between the manifold in the high-dimensional data space and the parameter space is proved. By distinguishing the intrinsic dimensionality of high-dimensional data space from the manifold dimensionality, and it is proved that the intrinsic dimensionality is the upper bound of the manifold dimensionality in the high-dimensional space in which there is a toroidal manifold.

首先给出了高维数据的连续流形和低维参数空间之间的等距映射存在性证明，然后区分了嵌入空间维数、高维数据空间的固有维数和流形维数，并证明存在环状流形高维数据空间的参数空间维数小于嵌入空间维数。

We will demonstrate the specification of reference prior distribution on the random covariance matrix. We will consider the approximate uniform shrinkage prior and approximate Jeffreys' prior. Both are formulated based on the approximated likelihood function. Under generalized linear mixed models, we show that the posterior mode under Jeffrey's prior is asymptotically closer to the REML estimate than the mode under uniform shrinkage prior does.

在广义线性混合模式下，我们证明了在样本数很大时，随机效应之变异数成份的后验众数和REML估计值会近似相等，同时也建立了后验众数和REML估计值的近似关系式，并提出了比较二种后验众数与REML估计值之间远近的准则。

Then,we improve CSFP Model in two aspects:when we ascertain the frequency of default,we use negative binomial distribution to substitute Poisson distribution so that the model can measure the data better;when we ascertain the loss distribution of default,we use Γ-distribution to substitute normal distribution.

其创新与特色一是对贷款组合的风险暴露数进行分段，在每一频段上分别确定风险暴露数分布，进而可以更准确的描述各笔贷款的风险暴露数。二是在确定风险暴露数分布时，用Γ分布替代了传统的正态分布，解决了贷款违约的风险暴露数分布的厚尾问题，进而解决了大宗贷款违约的风险度量问题。三是确定违约频率时，用负二项分布来代替传统的泊松分布，解决了违约频率的方差通常要大于其均值的分布拟合问题。

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。