查询词典 exponential equation

Based on the improvement of exponential map, a novel motion parameterization method called Dual Exponential Map which can depict translation and rotation, linear velocity and angular velocity simultaneously was proposed.

对指数映射方法进行改进，提出一种双指数映射运动参数化方法，用于同时描述关节模型的平移与旋转、线速度与角速度。

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 Chapter 5, considering the uncertain returns of securities as fuzzy numbers which follow an exponential possibility distribution function, we give a semi-definite programming method to solve the non-linear problem in estimating the exponential possibility distribution function process. Furthermore, we extend the center spread model proposed by Tanaka and Guo to the case of a frictional financial market.

第五章将证券收益率看作是服从指数可能性分布的模糊数，提出了证券收益指数可能性分布估计过程中求解非线性问题的半正定规划方法，并且将Tanaka和Guo的中心差值可能性投资组合模型扩展到了带摩擦的金融市场的情况。

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。

So it was last week in Selma , alabama.

上星期在亚拉巴马州塞尔马市发生的事件也是这样一个转折点。

The group also spearheads various social programs in China.

该组织还带头参与中国的各种社会活动。