查询词典 polynomial of a variable

Because the free form surface expressed by discret points has difficulties in aberration correction, manufacture and test, the Zernike polynomial was adopted to express the free form surface. The performance of this system was optimized on the basis of the relationship between Zernike polynomial and Seidel aberration.

由于离散点表述的自由曲面在像差校正、加工及检测等方面存在困难，提出了采用Zernike多项式表征自由曲面的面形，并利用Zernike多项式与Seidel像差之间的关系，优化自由曲面成像系统性能。

This paper presents a new class of piecewise trigonometric polynomial curves and a weighted trigonometric polynomial curve which has simple structure and can be used to design curves.

提出了一类新的分段三角多项式曲线，给出了加权三角多项式曲线，表示式结构简单，能用于曲线设计。

This trigonometric polynomial can be used to construct open and closed curves. Moreover, the class of piecewise trigonometric polynomial curves can be accurate and flexible to express ellipse.

利用该类分段三角多项式，给出了开曲线和闭曲线的构造方法，并提出了分段三角多项式可精确、灵活地表示椭圆。

A kind of blending functions with shape parameters is constructed based on trigonometric polynomial functions. Then the method of generating trigonometric polynomial Coons patch is discussed.

给出一类含参数的三角多项式混合函数，在此基础上构造一类三角多项式混合Coons曲面片，提出带形状参数的双三次三角多项式Coons曲面片的表达式。

Experiments show that C-B spline curve, uniform B-spline with shape parameter, hyperbolic polynomial uniform B-spline with shape parameter and trigonometric polynomial uniform B-spline with shape parameter can be used to produce some frequently used free form curves in the industrial field when the shape parameter is assigned with some specific values.

通过调整形状参数来修改曲线形状是计算机辅助几何设计中一个非常活跃的研究课题，研究形状参数的变化对样条曲线形状的影响，对于增加曲线造型的灵活性是非常必要的。

Experiments show that C-B spline curve, uniform B-spline with shape parameter, hyperbolic polynomial uniform B-spline with shape parameter and trigonometric polynomial uniform B-spline with shape parameter can be used to produce some frequently used free form curves in the industrial field when the shape parameter is assigned with some specific values. This process is simpler than producing these free form curves by using controlling vertex.

实验证明，C-B样条曲线、带形状参数的均匀B样条曲线、带形状参数双曲多项式的均匀B样条曲线、带形状参数三角多项式的均匀B样条曲线都可利用形状参数的特定取值表示一些工业领域常用的自由曲线，这比起用控制顶点表示同样的自由曲线更为简单。

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

我们把立体匹配过程看作泛函的极小化过程，因此选用变分问题近似解法的Ritz法构造数值算法，以多项式函数为基构作匹配函数的近似解，进而又利用多项式过样值点的拟合将离散的灰度图象变换为多项式函数，因此计算中所需的求导，积分，及梯度运算的结果仍然是多项式函数，最终将待定系数方程组化为线性代数方程组。

Based on Wu's elimination method and "divide-and-conquer" strategy, the undetermined coefficient method for constructing polynomial conservation laws of nonlinear differential-difference equations was improved. Furthermore, a Maple package CLawDDEs was developed to automatically derive conserved densities and associated fluxes of polynomial differential-difference equations.

基于吴消元法和"分治"策略，改进了基于标度不变性构造非线性微分差分方程多项式形式守恒律的待定系数算法，并在计算机代数系统Maple上实现了改进后的算法，其中的软件包CLawDDEs可自动推导出微分差分方程的守恒密度及连带流。

Babai, a more accurate estimate vector can be obtained and the coefficients of the multiple polynomial of the interpolation polynomial can be computed.

利用L.Babai最近向量格归约算法得到更精确的估计向量，再计算出插值多项式的倍数多项式的系数，从而计算出原插值多项式的系数。

The problems of robust stability and robust stabilization for interval systems were discussed. A necessary and sufficient condition for the robust stability of a line segment polynomial was proposed. The tested results of robust stability of a polynomial polytope and robust stabilization of an interval system were obtained in terms of the condition.

讨论了区间系统的鲁棒稳定性和鲁棒镇定性的有限检验问题，给出了线段多项式鲁棒稳定性的充分必要条件，利用该条件对多项式多面体鲁棒稳定性和区间系统鲁棒镇定性进行了有限检验，并给出了相应的检验结果。

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。