非对称射流形成的几何理论(二)

将平板非对称正碰撞形成射流满足的定常方程组封闭条件推广到非正碰情况，提出了平面二维条件下非对称射流形成的一般理论，给出了射流形成的临界条件和出流射流的理论公式。对斜碰撞情形下非对称射流的出流方向、厚度随碰撞角和来流初始位形的变化规律进行了理论预测和数值模拟，理论解与二维欧拉程序的仿真结果符合较好。     

作物垄作的数学模型

应用高等数学中对面积的曲面积分等方法,建立了垄作种植中半椭圆形、抛物线型和三角形垄的数学模型,比较了不同垄形、垄宽、垄高在增加单位土地表面积和突出地面垄体体积的效果.     

The characterizations of triangles using the nine-point circles

In this note, primarily intended for high school students and high school teachers, characterizations of a right triangle and an equilateral triangle in the Euclidean plane are presented using the nine-point circle of a given triangle. Geometrical applications are explored along with their possible uses in the teaching environment.     

A new family of Schröder's method and its variants based on power means for multiple roots of nonlinear equations

In this article, we derive one-parameter family of Schröder's method based on Gupta et al.'s (K.C. Gupta, V. Kanwar, and S. Kumar, A family of ellipse methods for solving non-linear equations, Int. J. Math. Educ. Sci. Technol. 40 (2009), pp. 571–575) family of ellipse methods for the solution of nonlinear equations. Further, we introduce new families of Schröder-type methods for multiple roots with cubic convergence. Proposed families are derived from modified Newton's method for multiple roots and one-parameter family of Schröder's method. Numerical examples are also provided to show that these new methods are competitive to other known methods for multiple roots.     

HE Plots for Multivariate Linear Models

Multivariate analysis of variance (MANOVA) extends the ideas and methods of univariate ANOVA in simple and straightforward ways. But the familiar graphical methods typically used for univariate ANOVA are inadequate for showing how measures in a multivariate response vary with each other, and how their means vary with explanatory factors. Similarly, the graphical methods commonly used in multiple regression are not widely available or used in multivariate multiple regression (MMRA). We describe a variety of graphical methods for multiple-response (MANOVA and MMRA) data aimed at understanding what is being tested in a multivariate test, and how factor/predictor effects are expressed across multiple response measures.

In particular, we describe and illustrate: (a) Data ellipses and biplots for multivariate data; (b) HE plots, showing the hypothesis and error covariance matrices for a given pair of responses, and a given effect; (c) HE plot matrices, showing all pairwise HE plots; and (d) reduced-rank analogs of HE plots, showing all observations, group means, and their relations to the response variables. All of these methods are implemented in a collection of easily used SAS macro programs.     

一种目标区域最佳椭圆描述方法

目标的最佳描述区域对于建立目标特征、目标跟踪、目标轮廓求取具有非常重要的意义。针对这类问题,提出了一种目标区域最佳椭圆描述确定方法。新方法首先根据目标和背景的差别确定出目标区域,然后利用尺度空间理论计算出目标的最佳椭圆描述。实验表明：新算法可以有效、准确地确定出目标包含区域的大小和方向。     

Photoinduced optical activity of C<Subscript>70</Subscript> fullerene in organic solvents

We have experimentally studied for the first time the effect of photoinduced rotation of the plane of polarization for pulsed laser radiation in solutions of C₇₀ fullerene in organic solvents and their mixtures. We have shown that the effect is observed for elliptical polarization of the laser radiation and is absent for linear polarization. We present the results of a study of the nonlinear optical characteristics of the C₇₀ solutions. We discuss the physical mechanisms by which nonlinear gyrotropy is induced in solutions. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 1, pp. 93–99, January–February, 2009.     

基于椭圆对数极坐标变换的尺度变化目标跟踪算法

针对传统对数极坐标变换局限于跟踪圆形或类圆形尺度变化目标这一问题,提出一种基于椭圆对数极坐标变换域下目标匹配的尺度变化目标跟踪算法。算法利用Mean Shift进行空间定位,确定目标的形心,通过椭圆对数极坐标变换域中目标和候选的最大相关匹配系数来确定目标的尺度参数。实验结果表明:该文算法在目标小形变和光照变化条件下,跟踪误差较小,尺度跟踪准确率更高,具有较好的鲁棒性。     

基于椭圆对数极坐标变换的尺度变化目标跟踪算法

针对传统对数极坐标变换局限于跟踪圆形或类圆形尺度变化目标这一问题,提出一种基于椭圆对数极坐标变换域下目标匹配的尺度变化目标跟踪算法。算法利用Mean Shift进行空间定位,确定目标的形心,通过椭圆对数极坐标变换域中目标和候选的最大相关匹配系数来确定目标的尺度参数。实验结果表明：该文算法在目标小形变和光照变化条件下,跟踪误差较小,尺度跟踪准确率更高,具有较好的鲁棒性。     

利用三角形及其九点圆的摄像机标定

提出基于三角形及其九点圆的摄像机标定方法.利用了三角形九点圆中其九个点的特殊性,并且利用透视投影变换保二次曲线不变性,得到其像点在像平面共椭圆,从而可以通过九点的映射关系将透视投影变换的非线性问题线性化.图像分割和角点提取的误差会直接影响标定的精度,在此三角形及其九点圆中的点特别是算法中的关键点三角形顶点和垂心都是三条直线的交点,减小图像分割与提取时造成的误差.DLT方法的不精确就源于图像分割和角点提取的误差,方法克服了DLT方法的不足.张的方法无法保证单应性矩阵的正交性,因此为了保证正交性和提高精度需要优化.与传统方法相比操作简单,应用九点圆定理,仿射变换的引入将透视投影非线性问题线性化,避免了参数之间的非线性方程求解,降低了参数求解的复杂性,因此其定标过程快捷,准确.模板的构造,减少了图像分割和交点提取误差,算法实现保证旋转矩阵的正交性.综合上述分析,理论上表明方法的有效性.同时实验表明,标定方法操作简单,不需要计算机视觉的专业知识,快速,精度高,鲁棒性好.