幂函数

In this paper perturbation of eigenvalue and eigenfunction for higher order ordinary differential equation in the case of boundary perturbation combined with operator perturbation we considered.

本文研究了在边界和算子摄动相结合的情况下高阶常微分方程特征值与特征函数的摄动，把摄动问题A_6，μ的特征值λ_ε，μ和特征函数y_6，μ按两参数ε、μ的次幂展开，并且证明这些展开式当ε、μ充分小时是收敛的。

The radius of convergence of a power series ''f'' centered on a point '' a '' is equal to the distance from ''a'' to the nearest point where '' f '' cannot be defined in a way that makes it holomorphic.

一个中心为'' a ''的幂级数''f''的收敛半径'' R ''等于''a''与离'' a ''最近的使得函数不能用幂级数方式定义的点的距离。

By means of the dual of Said-Ball basis, the Marsden identity is got in terms of Said-Ball basis, and a degree reduction algorithm for Said-Ball curves is presented through the transform from Bezier curves to Said-Ball curves.

利用Said-Ball基函数的对偶基，得到幂基函数在Said-Ball基下的Marsden恒等式，及从Bézier曲线到Said-Ball曲线的转换。并给出Said-Ball曲线的降阶赋值算法。

When they built up the quantum Liouville equation inthe phase-space representaiton and discussed the mathematicaltransformation of the wave functions between the coordinate ormomentum and phase space,Torres-Vega and Frederick alwaysassumed the positive series expansion in coordinate of potentialsof systems.This is obviously incomplete because potentials ofreal systems contains in general negative powers of coordiante.

Torres-Vega和Frederick在建立相空间中的量子Liouville方程以及讨论和推导相空间波函数和坐标或动量空间中的波函数之间的的数学变换时，总是假定体系的相互作用势仅能展成坐标的正项级数，这显然是不全面的，因为实际体系的相互作用往往都含有坐标的负幂项。

Using the dynamic programming approach, an explicit solution to the value function of the optimal portfolio problem is obtained by the HJB equation, and the optimal investment strategy is given.

在风险投资服从Heston模型的假设下，研究了幂效用函数的最优投资组合问题，利用动态规划方法通过HJB方程得到最优投资组合价值函数的显式解，并给出最优投资策略。

The expression for radial wave function of a two dimensional harmonic oscillator is derived through an integral formula of general Lagurre function.

本文用广义Laguerre多项式的母函数表达式，证得文献〔1〕中，计算ρn次幂的类氢原子径向波函数Jd平均值的通式。

A function's Fourier transform is derived by integrating the product of the function and a kernel function (an exponential function raised to a negative complex power) over the interval from －∞to +∞.

欲取得一个函数的傅立叶变换，可以在－∞与＋∞的间隔中把该函数与核函数(提升至负复数幂的指数函数)的结果整合起来。

A function's Fourier transform is derive d by integrating the product of the function and a kernel function (an exponential function raised to a negative complex power) over the interval from －∞to +∞.

欲取得一个函数的傅立叶变换，可以在－∞与＋∞的间隔中把该函数与核函数(提升至负复数幂的指数函数)的结果整合起来。

Using the properties of the harmonic function and the theories of the expansion of the spherical harmonics,the equivalence between Moritz analytical continuation and Bjerhammar s virtual spherical solution is proved according to the power series expanded form of the real number field function,the differences in meaning between the two solutions are analyzed.

利用调和函数的性质以及球谐函数展开理论，并根据实数域上函数的幂级数展开式证明了Moritz解析延拓解与Bjerhammar虚拟球面解的等价性，同时分析了两种解的内在区别。

First, we consider nonholonomic chained systems with modeling error, in this section,based on back-stepping , using the so-called adding a integrator , state-scaling technique , we design discontinuous feedback law,such that the trival solution of the closed-loop systems global strong stable; Second,we consider high-order nonholonomic chained systems with modeling errors and external disturbances, in this section,using input/state-scaling and integrator backstepping methods , we design discontinuous feedback law and give out the switching strategy, such that the closed-loop systems global /C-exponential stable; Finally, we consider a class of more general power chained form systems with particular drift-terms, in this section , using Lyapunov method, we design time-varying feedback law , such that the closed -loop systems p—exponential stable.

第一部分考虑的模型为带有模型误差的高阶非完整链系统，我们运用加幂积分器、State-scaling技巧以及基于Back-stepping方法构造出不连续反馈律，从而使得所讨论系统的闭环系统的平凡解全局强稳定；第二部分考虑的模型为带有模型误差的不确定高阶非完整链系统，这一部分我们运用input／state scaling和integrator backstepping方法构造出不连续反馈律，并给出切换策略，使得所对应的闭环系统全局κ-指数稳定；第三部分考虑的系统是形式更为一般的且带有特殊形式漂移项的幂链系统，利用Lyapunov函数方法，设计出时变反馈律，从而使得相应的闭环系统ρ-指数稳定。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。