计算多项式

This paper studies QinJiuShao algorithm for fast computation of high-rank polynomial,analyses fast algorithm of modular exponentiation in RSA,and gives its implementation.

介绍了用于快速计算高次多项式值的"秦九韶算法"，并用类似思路分析了RSA算法中方幂模快速实现算法，最后给出了该算法的具体实现。

Based on a kind of orthogonal complete functions in L2[0,1], another one (called V-system) which has equivalence relation with U-system is created. It is a kind of new and effective mathematical tool on signal multi-resolution analysis. Besides that V-system keeps the favorable properties of U-system and can accurately reconstruct geometry information which expressed in piecewise polynomials by finite sum of functions in V-system, it has more special properties, such as simple construction, abundant levels, convenience of application, quick calculation, local support, and so on. V-system is the generalization of Haar orthogonal functions, and to be a class of wavelet base. It has a good future for some applications in the fields of wavelet analysis and signal processing.

从L2[0，1]空间的一类正交完备函数系U系统出发，构造了另一类与之等价的正交完备函数系，称之为V系统，它是信号多分辨分析方面的一种新型的、有效的数学工具。V系统不仅保持了U系统的优良特性，对多项式表达的几何信息能够做到有限项精确重构，并且较之U系统，它更有结构简单、层次分明、计算快捷、局部支集等特点，应用起来将更加灵活方便。V系统可以看作是Haar函数系的推广，是一类小波基，在某些数字信号处理及小波分析问题中有良好的应用前景。

Boley and Golub used Gauss quadrature formula to solve the inverse problem, but I used other different methods and thoughts. I obtained a new decomposition form of orthogonal matrix consisted by the unit eigenvectors of Jacobi matrix and found the direct relations between the first row and the orther rows of this orthogonal matrix.

Boley和Golub的算法是用高斯求积公式，而本人另辟蹊径，推出了关于Jacobi矩阵单位特征向量组成的正交阵的一种分解形式，并找到此正交阵第一行和其它行的直接联系，由此避免了通过求特征多项式计算尾主子阵的特征值，得到了新的稳定解法。

A third order ENO finite volume method for hyperbolic conservation laws on unstructured triangular mesh is introduced.In order to obtain the third order accuracy on spatial discretization,a weighted quadratic interpolation is constructed on every triangular mesh.Two point Gauss quadrature formula is also used on each edge of every triangular mesh and the third order TVD Runge-Kutta method is used for time discretization.The numerical order of convergence and the numerical result of a mesh 3 wind tunnel with one step are given.

摘 要 基于双曲型守恒律方程，对非结构三角形网格给出了一种ENO(Essentially Nonoscillatory Scheme)型有限体积格式，方法的主要思想是先对每一个三角形单元构造一个加权的二次插值多项式，而在计算交界面的流通量时采用了两点高斯积分公式以保证格式的整体精度，时间离散采用三阶TVD Runge-Kutta方法。

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。

For a 3D system, formulae for a general polynomial controller applied to the normal form of a system and for the relvant stability index are derived. Thereby the amplitude approximation in terms of control gains of the controlled system is solved.

对于三维系统，研究了作用于标准型下系统的普适的多项式控制器设计以及相应的极限环稳定性指标的计算，建立了受控系统的极限环幅值与控制增益之间的近似解析关系。

The applied result shows that the new PP regression model based on particle swarm optimization and Hermite polynomial fitting is simple in use, fast in computation and effective in optimization. This algorithm may serve as a useful tool in synthetic earthquake prediction study.

通过计算和分析表明，基于粒子群优化算法与厄米多项式构建的投影寻踪回归模型具有简单、快速、有效的特点，在实际地震综合预测建模中取得了满意的效果，可作为地震预测的一种综合分析方法。

Based on particle swarm optimization and Hermite polynomial fitting. Then the improved PP algorithm is applied to synthetic prediction modeling of poly-dimensional seismicity time series and general disordered seismic data samples.

利用数值仿真技术进行基于粒子群优化算法与厄米多项式构建的投影寻踪回归模型建模能力与计算精度的检验，再将其应用于多维地震时间序列和一般多维无序地震样本回归综合建模预测中。

Ythagorean hodograph curves enjoy a number of remarkable properties, such as, its offset curves have exact rational representations; the arc length function of a Pythagorean hodograph curve is simply a polynomial function of the curve parameter; and the lower degree Pythagorean hodograph curves have intuitive geometrical interpretation.

H曲线具有诸如有精确的有理 Offset、弧长函数可由多项式函数表示以及几何解释优美等一系列优良性质。基于复分析方法，避免了实分析讨论中出现的复杂表示及繁琐计算，构造了满足给定 C1 Hermite插值条件且以C1拼接连续的三次 PH曲线偶。该曲线偶可灵活处理拐点，从而克服了一般三次 PH曲线因恒凸而无法处理拐点的缺陷。

Compared with the previous polynomial interpolating method, this method can avoid ill-conditioned matrices in the process of the calculation and obtain more accurate values.

相比于以前介绍的多项式方法，此方法不但能避免矩阵的病态，而且提高了计算的精度和效率。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。