指数方程

The result showed that the single correlation between the characters of weight and heart girth, chest width and circumference of cannon bone was significantly different. The correlation between weight and heart girth, chest width, circumference of cannon bone was highly positive correlation. Among seven regression models, the correlation index of six regression models was over 0.7, but that of 60 days was 0.452. The result suggested that selecting body weight was efficient through heart girth, body high, chest width and circumference of cannon bone.

对不同日龄各项体尺与体重建立的了回归方程，结果表明，60日龄回归模型的决定系数R~2=0.452，其它6个回归模型的相关指数均在0.7以上，其中方程1、5、6、7的相关指数都在0.9以上，表明这些回归方程中各项体尺指标与体重之间相关密切，根据胸围、管围、体高和胸宽对体重的选择都是有效的，具有一定的参考作用。

An analytical model describing the dispersion with an exponential dispersion function is built, which be transformed into CDE problem with variable coefficient, using hypergeometric function and inversion technique, an analytical solution for two type boundary conditions is obtained.

文章对于具有指数弥散函数的弥散过程建立了对流-弥散微分方程模型，应用积分变换将问题转化为具有变系数的常微分方程问题；对于两种类型的边界条件，应用超几何函数和反演技术得到了问题的解析解，并分析了指数弥散过程和常数弥散过程的不同性质。

The influences of the shock thickness and Alfven waves on the particle acceleration by diffusive shock waves are numerically studied through solving one-dimensional diffusive equation including the second-order Fermi effect. It is shown that the spectral index of the energetic particles strongly depends on the shock thickness. For example, the spectral index increases from 2.1 to 3.7 in the low energy range of 3-10 MeV and from 2.5 to 5.0 in the high energy range of 20-60 MeV as the thickness increases. The spectral index decreases from 4.3 to 3.1 as the particle injection energy increases. The spectral index decreases from 4.0 to 1.8 at the quasi-steady stage with the enhancement of the compression ratio from 2 to 4. The results indicate that under the influence of Alfven waves, the energetic particle spectrum at lower energy becomes flat and the spectral index decreases from 2.5 to 0.6 in the low energy range of 3-10 MeV and from 11.6 to 5.0 in the high energy range of 20-60 MeV. At the same time, the rollover energy reaches 19.6 MeV. The spectral index decreases from 5.8 to 2.9 as the energy density of Alfven waves increase. All these results are basically consistent with the theoretical models, as well as the observations of typical energetic particle events.

通过数值求解包含二阶费米加速的一维扩散方程，探讨在准平行激波条件下激波厚度和级联阿尔芬波对粒子加速的影响，研究粒子分布函数的演化与激波厚度和阿尔芬波强度的内禀关系，计算结果表明：(1)考虑激波厚度时，谱指数明显依赖于激波厚度，随着厚度从0.32增大到2.56，低能端(3-10MeV)谱指数逐渐从2.1增加到3.7，高能端(20-60MeV)谱指数从2.4增大到5.0，能谱逐渐变软；当初始注入粒子动量增大1.3倍，质子能谱指数从4.3减小到3.1，且与零厚度激波加速的谱指数差值缩小；厚度不变时，随着压缩比从2增加到4，准稳态分布时低能端(3-10MeV)粒子能谱指数逐渐从4.0减小到1.8谱变硬；(2)在级联阿尔芬波的影响下，随着时间的增大，粒子在低能处(3-10MeV)的谱指数从2.5减小到0.6高能端(20-60MeV)谱指数从11.6减小到5.0，能谱变硬，拐点能量值从7.5MeV增大到为19.6MeV；随着波的能量密度增大，谱指数从5.8减小到2.9，这表明阿尔芬波强度越大，加速效率越高，通过与激波厚度解析结果和高能粒子事件的观测能谱比较发现两者是一致的，说明数值模拟结果是可靠的。

The existence and uniqueness of the solution with the help of the Banach fixed point theorem and the theory of operator semigroups are verified .The global exponential stability of KS equation and the global exponential stability and asymptotical stability of macro KS equation with the given boundary feedbacks are proved .

通过Banach不动点原理和算子半群理论证明了方程解的存在性和唯一性，并证明了KS方程在给定的边界反馈条件下是全局指数稳定的及广义的KS方程在给定的边界反馈条件下是全局指数稳定和渐近稳定的。

In chapter 2,we discuss the problem of the relationship between the solution of non - homogeneous linear differential and small function.

其中第二部分讨论了非齐次线性微分方程解取小函数的收敛指数，第三部分研究了齐次线性微分方程f~+Af=0的解的零点收敛指数与A的级的关系。

By using the index equation modular φ as transformation, the speed of encryption and decryption is further increased. By dividing information into groups, using multiple transformation, and eliminating the superincreasing property, the new scheme becomes more secure.

这种体制用模φ的指数方程进行变换运算，使得加解密过程的运算速度进一步提高；信息经过分组和多次模变换处理；避免了超递增序列的弱点，使其具有更强的保密性。

The natural releasing processes of Pb, Zn and Cd in the slags can be primely described with minus-exponent equation.

长期的风化淋滤作用对重金属的释放有影响，矿渣层的重金属含量随时间的增长而递减，其自然释放过程可用负指数方程描述。

Unitary linear regression is done between w~e、 w~ρ、 e~ρ、w_L~w_P. For α_v 、 C_ c between w、ρ、 e、 w_P in eastern China, unitary linear regression is done to silty clay as well as multivariant regression with coefficient iteration method and least-squares procedure are done to all kinds of soil, and the two results are compared. Unitary linear regression and multivariant regression are done to c_q、φ、 c_d、φ_d between e and I_P. Unitary linear regression and multivariant linear regression are done to napierian logarithm of q_u between e 、 I_L、 w_P and w_L, then the equations of regression are checked with other parameters.

对物理指标含水量～孔隙比、含水量～湿密度、孔隙比～湿密度、液限～塑限作了一元线性回归；对华东地区粉质粘土的压缩系数、压缩指数和含水量、湿密度、孔隙比及塑性指数作了一元线性回归；对华东地区所有土类的压缩系数、压缩指数和物理性质参数用系数迭代法和最小二乘法作了多元线性和非线性回归，并对两种方法得到的回归结果作了比较；作了快剪强度指标和固结快剪强度指标关于孔隙比和塑性指数的一元线性回归和多元线性及非线性回归；对无侧限抗压强度的自然对数值和孔隙比、液性指数、液限及塑限作了一元和多元线性回归，并用其它工程的参数对回归方程进行了检验。

The critical nitrogen content in heading period was used to calculate the biggest accumulation quantity of nitrogen. The latent distribution index of leaf and stem, which was the variety heredity parameter, were used to distinguish the difference in nitrogen assignment in different varieties. The dynamic content of the nitrogen accumulation before anthesis could be described with a Richards model. The dynamic content of the nitrogen remobilization in leaf with leaf area index could be described with a power model, and the nitrogen absorption of grain from soil with dry weight could be described with a power model. The dynamic content of nitrogen density in stem and spike with physiological development time could be described with a nonlinear model.

模型利用抽穗期植株临界含氮量来表达氮素最大积累量，引入叶片潜在分配指数和茎鞘潜在分配指数2个品种遗传参数来区别不同品种在器官间的氮素分配差异，采用Richards方程来描述大麦花前氮素积累动态变化；采用指数函数方程来描述叶片氮的转移量随叶面积指数的动态变化以及籽粒从土壤中吸收的氮量随干物重的动态变化；采用非线性函数方程描述茎鞘和穗部的氮浓度随生理发育时间的动态变化。

The substructure in the deformed specimens consists of very small amount and fine precipitates with equaixed polygonized subgrains in the elongated grains and developed serrations in the grain boundaries.

指数方程中的平均热变形激活能Q为157.9kJ/mol。变形试样中的亚结构由拉长后晶粒中的少量细小的等轴多边形亚晶粒和晶界上的锯齿状组织构成。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

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如果有任何问题，你可以随时联系我。