有了曼德尔勃特集合，蔬菜和二次多项式都变得有趣多了。这个方程序表现了类似图中的花椰菜菜籽的重复的复杂性。
Both vegetables and quadratic polynomials are made more interesting with the Mandelbrot set. The formula explains the repeating complexity of broccoli heads like this one.
拟和线是一个三次多项式的形式，但是任何形式的平滑都会告诉你有一个大的上升趋势。
The fitted line in the figure is a 3rd-degree polynomial, but any sort of smoothing would tell you that there is a massive upward trend.
本文从不同种植密度和施氮量对玉米籽粒产量的影响，建立了二次多项式回归方程。
Second-degree polynomials equation of maize(Zea Mays L. ) grain yield with both planting density and nitrogen fertilization was established by means of regression analysis.
今天的例子是评测一个三次多项式。
Today's example function is evaluating a third order polynomial.
构造的曲面是分片双三次有理参数多项式曲面。
This surface is a piecewise bi-cubic rational parametric polynomial surface.
结果表明，采用高次多项式动力凸轮用于高速汽油机凸轮设计，能够获得相对平稳的气门运动特性。
The research results reveal that comparative valve balanced movement characteristic can obtain using high order polynomial dynamic cam in high speed gasoline engine.
利用五次多项式曲线对挑线凸轮进行了设计；并根据刺绣机的特殊要求，提出了刺绣机最优化设计方法。
Based on the curve of quintic polynomial, the take-up CAM is designed, and the method of optimized design is presented in this paper.
建立了七次多项式动力凸轮型线的优化设计数学模型；
The mathematical model of optimizing design for hepta polynomial dynamic cam was established.
在反演计算中，射线轨迹点处的慢度可用三次多项式基函数予以计算。
In inversion, the slowness at points on ray path can be calculated by using three order polynomial primary function.
本文主要研究双二次多项式的动力系统。
D dissertation is concerned with the dynamics of biquadratic polynomials.
利用牛顿方向和中心路径方向，获得了求解单调线性互补问题的一种内点算法，并证明该算法经过多项式次迭代之后收敛到原问题的一个最优解。
By using Newton direction and centering direction, we establish a feasible interior point algorithm for monotone linear complementarity problem and show that this method is polynomial in complexity.
对每个候选变化点，经过一次判断即可确定多项式的合适阶次。
At each candidate change point, a reasonable order of the polynomial function can be determined by once estimating.
柠条地土壤储水量与坡面位置和时间的关系可用一个二元三次多项式来表达。
The relationship between soil moisture content, slope position and time can be expressed through a binary cubic polynomial.
实践证明，三至五次多项式就能产生足够小的残差和单调递增的导数。
In general, experience has shown that third-to fifth-degree polynomials produce sufficiently low residuals and monotonically increasing derivatives .
本文采用三次多项式插值和曲线拟合相结合的方法可简单有效地提取出在线掌纹的线特征。
In this dissertation, a line extraction method based on cubic polynomial interpolation and minimum mean square error fitting are proposed, which can effectively extract lines out.
本文通过几个例子介绍了三次单位根在复数计算、证明与多项式整除中的应用。
This paper, by examples, introduces the application of triple root in the calculation and proof of complex number, and exact division in multinomial.
最后，我们给出了一种计算多项式矩阵最小多项式或特征多项式的有效算法，它从低次项到高次项逐项确定最小多项式的系数多项式。
Finally, we present an efficient algorithm for computing the minimal polynomial of a polynomial matrix. It determines the coefficient polynomials term by term from lower to higher degree.
本文讨论了具有一个零特征根的非线性齐次系统的局部拓扑结构，并给出利用系统右端多项式系数的判断准则。
In this paper, we discuss the locally topological structures of nonlinear homogeneous systems with one zero characteristic root, and give a criteria by the right-hand polynomial coefficients.
利用这个结果并借助于计算机可以给出一大批齐次对称多项式不等式的可读性机器证明。
By means of this result and computer, the readable machine proofs for a lot of the inequalities of homogeneous and symmetric polynomials can be obtained.
用三次多项式在硬阈值的基础上插值，使新的阈值函数保持了连续性和可导性。
The continuity and differentiability are achieved by using cubic polynomial interpolation based on hard thresholding.
在矩阵元素的高次多项式中，任一变元的幂次不得高于9次，矩阵元素最大的字符串长度一般在2500左右。
Any of the high order polynomials of the matrix elements should not be higher than 9 degrees, and, in general, the maximum string length of matrix elements is about 2500.
在第二章中，我们采用截断多项式函数为核函数，解析的给出点、直线段、圆弧、二次曲线和三角面片等骨架的势函数。
In chapter two, using piecewise quartic polynomial as kernel function, we give analytical convolution solutions for points, line segments, arcs, quadratic Bezier curves and triangle segments.
一个完整四次的多项式由15项组成。
提出了用二次多项式重构励磁涌流的新算法，并确定了相应的采样率。
A new algorithm by use of quadratic polynomial is proposed to reconstruct inrush, and the corresponding sampling rate is determined.
在求解域上，利用迦辽金法，将泊松方程的非齐次部分用一个5阶多项式近似表示，而这些多项式对应的方程特解可以很容易获得。
In the solution domain, thePoisson equation is approximated with the 5-order polynomial using Galerkin method, and the particular solution of the polynomial can be determined easily.
大量的关于随机的凸二次规划问题的数值实验结果表明它的计算效率是高的，在某些条件下可能是多项式时间算法。
Some numerical results for a large number of random convex quadratic programming problems show that the new algorithm is efficient and might be a polynomial-time algorithm under some conditions.
大量的关于随机的凸二次规划问题的数值实验结果表明它的计算效率是高的，在某些条件下可能是多项式时间算法。
Some numerical results for a large number of random convex quadratic programming problems show that the new algorithm is efficient and might be a polynomial-time algorithm under some conditions.
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