本文以贝塞尔函数级数和的形式，给出了动态特性的理论解析解。
This paper gives a theoretical and analytical solution of the dynamic response for long gas pipeline in the form of infinite series with Bessel functions.
重点是具有较大非线性的系统的方法，如FPK法，矩闭合法和函数级数法。
Emphasis is laid on the analysis, of large nonlinearities in system, for example, the FPK method, the closure method and the functional series expansion method.
然后连续利用多元函数级数展开，导出群角表示的相速度和群速度近似公式。
Then series expansions of multi-variable functions are applied to the derived approximations in terms of phase angles to generate the approximations in terms of group angles.
对于函数级数，研究其和函数的解析性质很重要，但函数级数必须具有一致收敛性，而判断函数级数的一致收敛性往往是比较困难的。
However, this study should be based on the fact that the series must have consistent convergence, the judgment of which is rather difficult.
仿真实验结果证明了改进演化算法对于实现函数级数字组合逻辑电路的硬件演化是可行的，并且提高了演化算法的演化效率和收敛性能。
The results of simulation prove that the improved algorithms are feasible for evolving the digital combinational logic circuits and improve the evolvable efficiency and convergence performance.
泰勒级数的效率也无法与现代桌面芯片的内置正弦函数相比。
The Taylor series is also inefficient compared to the built-in sine function of a modern desktop chip.
第 5章介绍了划分问题、递归函数到迭代函数的转换（我可以向您保证，这非常有趣）以及阶乘和斐波纳级数的实现。
Chapter 5 deals with partitioning problems, converting recursive functions to iterative functions (it's fun, I assure you), and more factorial and Fibonacci series implementations.
本文试应用求解一阶线性微分方程的方法导出几类常见的函数项级数的求和公式。
The sum formulas of several kinds of ordinary series with function term are deduced by using the method of solving linear differential equation.
组合计数器的最大数值是二进制计数器和反馈计数器的级数的函数。
The maximum count of a combination counter is thus a function of the number of stages of the binary and feedback counters .
在有限条法中，采用幂级数作基函数，运算较为简单、方便。
When the power series is used as the basic functions in the finite strip method, the computation becomes simple and convenient.
文摘：研究了十分一般的随机幂级数，并证明了有限级的随机幂级数几乎必然没有亏函数。
Abstract: the paper studies the random power series of general enough and proves that the random power series of finite order do not have almost surely deficient function.
并重点放在选用幂级数作为分部形态函数时对系统计算精度的影响方面。
And emphasis is laid on the effect upon the system computation accuracy by choosing power series as component shape functions.
采用将圆电流磁矢势表达式中一部分展成级数，使被积函数变成可积分的函数。
A part of results on magnetic vector potential of circular loop are expanded, so the integral function is transformed to integrable series.
也是函数的极值、幂级数理论等众多数学理论的基础。
Is also a function of extreme value theory, and many other mathematical theory of power series basis.
对静力问题，将指数矩阵函数展成级数来求解；对动力问题，采用状态空间迭代法来求解。
The exponential matrix function exhibition series was applied to solve the static problem; adopt the state space iterative method was applied to solve dynamic problem.
在数学中经常要用到复变函数在极点邻域内展开的罗朗级数。
It is widely used to develop complex functions into Laurent series at the neighborhood of a pole.
采用复变函数及摄动方法，最后以幂级数形式给出应力强度因子的计算公式。
Stress intensity factors at the craek tips are computed by complex variable functions and perturbation method and formulas are given in power series forms.
计算积分的方法、复数方法、无线级数、奇殊函数、微分方程、向量及矩阵、群论。
Methods in evaluating integrals, some complex variable methods, infinite series, special function, ordinary differential equations, vector and materials, groups and group representations.
如马尔萨斯所言，人口自然地以「几何级数」增加，或是我们现在的说法是函数增加。
Population, as Malthus said, naturally tends to grow "geometrically, " or, as we would now say, exponentially.
我们所关心的是函数项级数可否通过T矩阵广义求和。本文对这个问题进行了探讨。
In this article the problem of whether the T-matrix can also be used to generalize the summation for series of functional terms is discussed.
课程内容包括常微分方程、空间解析几何与向量代数、多元函数微分学、多元函数积分学和无穷级数等几大板块。
This course consists of several major parts such as ordinary differential equation vectors and analytic geometry derivatives integration and series.
课程内容包括空间解析几何与向量代数、多元函数微分学、多元函数积分学和无穷级数等几大板块。
This course consists of several major parts such as vectors and analytic geometry derivatives integration and series.
这些因变量展开为球函数的级数形式并在15处作菱形截断。
The dependent variables are expanded in series of spherical harmonics truncated rhomboidally at wavenumber 15.
该网络把级数中的函数看成非线性神经元，建立油藏系统的函数型连接人工神经网络模型。
In the net, the functions are served as nonlinear neural units to establish function link artificial neural networks models of oil reservoir systems.
本文推导了含边缘裂纹各向异性板与单向复合材料板的应力与位移的函数项级数表达式。
The series expressions of stresses and displacements of both anisotropic and unidirectional fiber-reinforced composite plates with cracks are derived.
同步热分析法是一个比较精确的方法，其不但可以计算活化能而且可以同时求解反应级数和反应机理函数。
Simultaneous thermal analysis method is a relatively accurate method, it can not only compute the activation energy but also get reaction order and the conversion function at the same time.
当指定Z为复数变元时，就有了形式幂级数的“变换”函数，即闭合形式的问题。
When Z is assigned the meaning of a complex variable, problem of "closed form" of formal power series emerges.
摘要利用由三角级数和幂级数复合构成的函数项级数的有关性质，得到了一类变系数非齐次调和方程边值问题的级数解。
In this paper by using the property of Fourier series a compound series consisting of trigonometric series and power series is established.
摘要利用由三角级数和幂级数复合构成的函数项级数的有关性质，得到了一类变系数非齐次调和方程边值问题的级数解。
In this paper by using the property of Fourier series a compound series consisting of trigonometric series and power series is established.
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