A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter

We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.     

一般生长曲线模型中共同均值参数的线性估计的可容许性

给出了生长曲线中共同均值参数的线性估计在一切估计类中可容许的一个充分条件 ,并给出了在线性估计类中可容许性的又一证法 .     

广义加权函数平均组合预测模型参数估计方法

提出一种新的组合预测模型--广义加权函数平均组合预测模型, 并利用二次规划算法给出其加权系数的2种不同的参数估计方法. 最后, 以预测实例说明了模型的有效性并对2种参数估计方法进行了比较, 得到一个对参数估计方法进行正确应用的有用结论.     

Unsteady flow structure of an airfoil in ground effect

Particle image velocimetry （PIV） experimental results of wake flow structure of a NACA0012 airfoil with small attack angle mounted above water surface are introduced.The experiment was carried out in a small-scale wind-wave tunnel.The diameter of wind-wave tunnel test section is 1.7 m （long） × 0.4 m （width） × 0.4 m （height）.The flow fields around the airfoil were measured under four diffierent conditions by varying the distance between the airfoil and the water surface.The attack angle of the airfoil was kept 10- during the experiment.For each experimental condition,the time series of particle images was captured to calculate continuous evolution of the velocity fields.The velocity fields were ensemble averaged to get the statistic parameters such as mean velocity and vorticity.Typical instantaneous velocity fields for each case are introduced to show the basic flow structure of wind surface flow separation.The aerodynamic loads acting on the airfoil are analyzed qualitatively according to the mean vorticity distribution in the flow field based on the theory of vorticity aerodynamics.The results indicate that the flow structures and drag/lift force of the airfoil alter remarkably with the changing distance between the airfoil and water surface.     

一种用于电类实验测量数据判决的改进KNN算法北大核心

电类实验教学过程中人工评判学生所测数据工作烦琐,影响了教学质量和效率。该文提出了改进的K近邻(K-nearest neighbors,KNN)分类算法,即基于均值漂移、安全间隔和核主成分分析(KPCA)的M-KPCA-KNN(KNN based on margin and KPCA)算法,以判断学生测量数据正确与否和错误原因。首先利用KPCA对高维实验数据进行降维,然后利用均值漂移向量找到不同类别数据的最密集位置,并在不同类别数据的边界设置安全间隔,最后,将与待测样本距离最近的k个数据设置权重,计算每个类别的权重和,权重和最大的类别为待测样本的类别。与现有的KNN算法相比,M-KPCA-KNN算法不仅提高了分类正确率,而且降低了时间复杂度。     

一道极限题的十一种解法

以一道极限题为例,给出了利用两边夹准则、等价无穷小代换、导数的定义、泰勒公式、微积分中值定理等十一种常用解法。