乘

Geometric Constraint Solving with Conics;2. By comparison, we conclude that the operations on conics are more efficien than those on elliptic curves is concluded.

文中介绍了有限域上的圆锥曲线的点群结构及加法运算，给出了三种不同的方法计算加法，并进一步比较了他们在数乘运算中的效率。

The content of our curriculum are:Optimization under unconstrained conditions and constrained conditions,we'll focus on common methods of this field like Conjugate gradient method,DFP,POWELL method,The multiplier method,Penalty Function Method and so on.

主要讲授内容为无约束条件及有约束条件下的优化设计，重点介绍了共轭梯度法，变尺度法，POWELL法，乘子法，惩罚函数法等电路优化的常用方法。

We alsostudy the Lie skew multiplicative bijective maps on B that is, the maps satisfyingΦ(AB- BA~*=ΦΦ-ΦΦ~*, and show that these maps must be of theformΦ=UAU~*, where U is a unitary or a conjugate unitary operator.

刻画了B(H是复Hilbert空间)上的Lie-skew可乘双射即满足Φ(AB-BA~*=ΦΦ-ΦΦ~*的双射，结果表明这样的映射一定是UAU~*的形式，其中U是酉算子或共轭酉算子。

Chapter 4 establishes the theory of convex fuzzy mappings: The concepts, such as Jensen's inequality, positively homogeneous, infimal convolution, right scalar multiplication and convex hull are introduced. The corresponding theorems are demonstrated by using the parametric representations of fuzzy numbers. In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved. The notions of subgradient, subdifferential, differential with respect to convex fuzzy mappings are investigated, which provides the basis of the theory of fuzzy extremum problems.

在第4章中，建立了有关凸模糊映射的理论：建立了关于凸模糊映射的Jensen不等式、模糊正齐次映射、凸模糊映射的下卷积、右数乘和凸包等概念，利用模糊数的参数化表示，给出了相应的定理；在反模糊数空间，对凸模糊映射的共轭也作了探讨，证明了凸模糊映射的共轭集合和共轭映射都是凸的；最后对凸模糊映射的次梯度、次微分和微分等概念进行了研究，为模糊极值理论打下了基础。

For the purpose of evaluating the efficacy of description dosage in a clinical trial in which compliance is observed, a new parameter estimation method is proposed for a structure linear model based on the combination of least square and pseudo-likelihood , and under general regular conditions, the consistency and asymptotic normality of the estimators are verified.

为了研究依从性对药物效果的影响，对一种结构线性模型，结合最小二乘和拟似然的思想，提出了一种新的参数估计方法，并在一般的条件下，证明了参数估计的相合性和渐近正态性。

This paper has studied the consistency of multiplication and ranking problem based on linguistic judgment matrix.

研究语言判断拒阵的乘性一致性及方案排序问题。

We show that under appropriate conditions,the SCAD-penalized least squares estimator is consistent for variable selection and that the estimators of nonzero coefficients have the same asymptotic distribution as they would have if the zero coefficients were known in advance.

在一定的条件下，我们证明了SCAD惩罚最小二乘估计的变量选择具有相合性，并且得到非零系数的估计与零系数已知情况下的估计具有相同的渐近分布。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

This is an untouched measuring way. The cameras are calibrated in the way of RAC two steps, first. With the polynomial interpolation, the pictures catched from the steel plate are treated to detect the edge in subpixel with a cross window arithmetic operators, which can fit non uniform illumination, keep the edge character and do filter in a better way. Three-dimensional scenery could be rebuilt from the two-dimensional pictures with the methods of least square fitting and contradictorily clairvoyance. Thus, the distance and its variance of two points in the given position of the plate can be achieved. It is expected that this study can provide a new and useful tool to the research on the theory of distortion of line heating.

这种非接触的测量方式，采用RAC两步法对摄像机进行标定，然后对采集到的钢板图像进行分析处理，通过多项式插值的方法，采用具有保持边缘特征和滤波功能，且能适应非均匀照明的十字窗图像边缘检测算子进行象素级边缘检测，再用最小二乘拟合法和逆透视法对二维图像进行三维重建，便可测出钢板上给定点的距离及其变化值，以期为水火弯板的变形机理研究提供一种新的检测手段。

It follows from the full-invariant of 〓-multiplier convergent series that 〓-bounded sets also have full-invariant.

据〓数乘收敛级数的全称不变性，得到了〓有界集也具有全称不变性这一重要结论。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！