查询词典 exponential function

In order to solve the problem,We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential manifold. The travel time are expressed as polynomials of the horizontal offset between the two points, and the single-square-root operator in frequency-wavenumber domain are expressed as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddle-point method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量(地面点到地下相点的水平距离)的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

In order to solve the problem, We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddlepoint method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量（地面点到地下相点的水平距离）的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

However, unlike the simple exponential that describes radioactivity, which has only one variable, a stretched exponential describes a process controlled by several independent factors.

不过，与只有一个变量的放射性简单指数不同的是，延伸型指数函数描述的是被几个独立因素控制的过程。

In this paper, a disease transmission model of SEIRS type with exponential demographic structure is studied. Two sufficient conditions are obtained to guarantee the local or global exponential stability of the disease free equilibrium by using a new technique based on the concept of comparison.

本文研究了一类具指数人口统计与结构的SEIRS传染病模型，利用一种新的基于比较原理的分析，获得了无病平衡点局部和全局指数稳定的两个充分条件。

When product life time follows exponential distribution, an approximate method of the point-estimation for the exponential distribution under multiply type-Ⅰ censoring is provided.

文中在寿命分布为指数分布时，给出寻求定时截尾寿命试验数据缺失场合下样本分布参数点估计的一种近似方法。

Based on the water resources survey of Shanghai in 1999 and the 1:50 000 color infrared aerial photos obtained in early 2000, a case study of the upper Huangpu River was carried out. The exponential method, pair-sample t test, and remote sensing analysis are used to analyze water environmental characteristics and land use pattern in the river network plain. In order to explore response of water quality in the waterhead region to the changes in land use and its driving force, five land use patterns are selected and a new type of exponential is designed.

以黄浦江上游水源地为例，利用1999年上海水资源普查数据及2000年初成像的上海市1：50000彩红外航空像片，采用GIS空间分析技术、灰色关联分析技术，划分土地利用样带，设计水质改善指数，探讨平原河网地区水环境质量对土地利用结构的响应，以及水源水质对土地利用变化驱动力的响应。

Results based on experiment and measurement data indicate that, when 244 nm argon ion laser emits 40 mW UV light, the curve of refractive index changes in single mode hydrogen loading fiber is exponential type (Ac=1.632×10-6 t 0.76912), exponential growth is obvious in the beginning, a very good linear region is following, and then refractive index increments reach saturated.

结果表明， 244 nm氩离子倍频激光器输出光功率为40 mW时，普通载氢光纤光致折射率变化量随曝光时间总体上呈现指数分布关系Ac=1.632×10-6 t 0.76912；在曝光时间较短时，造成的光栅强度较弱，光致折射率变化量有明显的指数增长趋势，之后是一段较好的线性区域，这时两个测量模型的结果得到了很好的印证，随着曝光时间的继续增加，光致折射率变化量达到饱和。

It′s found that the GVD-caused chirp in the exponential type of DDF is least likely to be affected by the initial chirp,the GVD-caused chirp in exponential, linear,Logarithm and Guassian types of DDF has the synchronous character of saturation as the nonlinear-effect-caused chirp ,and the two kinds of chirp are found to counteract to balance, which makes the sum chirp tend to be zero.

发现指数型色散缓变光纤中初始啁啾对GVD所致啁啾的影响最小，在指数型、线型、对数型和高斯型色散缓变光纤中GVD所致啁啾具有同非线性效应所致啁啾相似的饱和性，二者相消，使净啁啾趋于零。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列，主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等，得到如下主要结果：(1)系统讨论椭圆曲线-线性同余序列的一致分布性质，即该类序列是渐近一致分布的，并给出了它的非线性复杂度下界；(2)讨论两类由椭圆曲线构造的二元序列的"良性"分布与高阶相关性(correlation of order κ)，这两类序列具有"优"的密码性质，也正面回答了Goubin等提出的公开问题；(3)利用椭圆曲线及其挠曲线构造一类二元序列，其周期为4p(其中椭圆曲线定义在有限域F_p上)，0-1分布基本平衡，线性复杂度至少为周期的四分之一；(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计，并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性；(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布；(6)讨论椭圆曲线-子集和序列的一致分布；(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布，线性复杂度等性质。

Calculating the functions of the matrix exponential e has special significance in the theory of linear systems and the theory of semi-groups. Especially, in the modern control theory, no matter the equation is homogeneous or non-homogeneous, the result depends on the calculation of the matrix exponential e.

矩阵指数函数e的计算在线性系统理论及半群理论中有着特殊的作用，在现代控制理论中，无论是齐次方程还是非齐次方程的求解，主要取决于矩阵指数函数e的计算和近似。

Fostering the concept of multi-culture firmly and mastering the development of advanced culture correctly are conductive to resisting terrorism, separatism of nationalities and ultraism of religion, which is of great academic theoretical, immediate and profound historical si...

牢固树立多元文化的理念和正确把握先进文化的发展方向，有助于在世界范围内自觉地抵制恐怖主义，民族分裂主义和宗教极端主义。不仅具有重大的学术理论意义，而且也具有重大的现实意义和深远的历史意义。

But if anyone walks in the night, he stumbles, because the light is not in him.

11：10 若在黑夜行走，就必碰跌，因为那光不在他里面。