D. E. Knuth has widely discussed some combinatorial properties and the application in computer science on binary trees, ordered trees, oriented trees and free trees, and given some formulas for the number of all the a...D. E. Knuth has widely discussed some combinatorial properties and the application in computer science on binary trees, ordered trees, oriented trees and free trees, and given some formulas for the number of all the above structurally different trees with n nodes. Recently Wang Zhenyu gave formulas of the total leaf number for the preceding trees. Classifying these results carefully, Wang展开更多
Manipulating the self-assembly of transition metal telluride nanocrystals(NCs) creates opportunities for exploring new properties and device applications. Iron ditelluride(FeTe2) has recently emerged as a new class of...Manipulating the self-assembly of transition metal telluride nanocrystals(NCs) creates opportunities for exploring new properties and device applications. Iron ditelluride(FeTe2) has recently emerged as a new class of magnetic semiconductor with three-dimensional(3D) magnetic ordering and narrow band gap structure, yet the self-assembly of FeTe2 NCs has not been achieved. Herein, the tree-like FeTe2 nanoarchitectures with orthorhombic crystal structure have been successfully synthesized by hot-injection solvent thermal approach using phosphine-free Te precursor. The morphology, size, and crystal structure have been investigated using transmission electron microscopy(TEM), high-resolution TEM(HRTEM),and powder x-ray diffraction(XRD). We study the formation process of tree-like FeTe2 NCs according to trace the change of the sample morphology with the reaction time. It was found that the FeTe2 nanoparticles show oriented aggregation and self-assembly behavior with the increase of reaction time, which is attributed to size-dependent magnetism properties of the samples. The magnetic interaction is thought to be the driving force of nanoparticle self-organization.展开更多
A spanning tree with no more than 3 leaves is called a spanning 3-ended tree. In this paper, we prove that if G is a k-connected （k≥ 2） almost claw-free graph of order n and σk＋3（G） ≥ n ＋ k ＋ 2, then G conta...A spanning tree with no more than 3 leaves is called a spanning 3-ended tree. In this paper, we prove that if G is a k-connected （k≥ 2） almost claw-free graph of order n and σk＋3（G） ≥ n ＋ k ＋ 2, then G contains a spanning 3-ended tree, where σk（G） = min{∑es deg（v） ： S is an independent set of G with ｜S｜ = k}.展开更多
In order to clarify the correlations between the free spindle pruning mode and various factors in Fuji apple,the growth data of the free spindle-shaped short branch Fuji apple Tianhong No. 2 and the free spindle-shape...In order to clarify the correlations between the free spindle pruning mode and various factors in Fuji apple,the growth data of the free spindle-shaped short branch Fuji apple Tianhong No. 2 and the free spindle-shaped long branch Fuji apple Changfu No. 2 in the Apple Demonstration Park of Xingtang County,Hebei Province were investigated. Using SPSS statistical software,the correlations between the stem tapering grade and various growth traits were analyzed. The results showed that in Tianhong No. 2,the stem tapering grade was negatively correlated with various growth traits of the central shaft,and the correlation coefficients between the stem tapering grade and the central shaft total thickness,the central shaft average thickness,the central shaft total length and the central shaft average length were-0. 228,-0. 033,-0. 411 and-0. 430,respectively; and in Changfu No. 2,the stem tapering grade was positively correlated with various growth traits of the central shaft,and the correlation coefficients between the stem tapering grade and the central shaft total thickness,the central shaft average thickness,the central shaft total length and the central shaft average length were 0. 475,0. 181,0. 120 and 0. 258,respectively. This paper can provide a scientific basis for guiding the construction of free spindle pruning mode in densely planted dwarf apple trees.展开更多
Graphical representation of hierarchical clustering results is of final importance in hierarchical cluster analysis of data. Unfortunately, almost all mathematical or statistical software may have a weak capability of...Graphical representation of hierarchical clustering results is of final importance in hierarchical cluster analysis of data. Unfortunately, almost all mathematical or statistical software may have a weak capability of showcasing such clustering results. Particularly, most of clustering results or trees drawn cannot be represented in a dendrogram with a resizable, rescalable and free-style fashion. With the “dynamic” drawing instead of “static” one, this research works around these weak functionalities that restrict visualization of clustering results in an arbitrary manner. It introduces an algorithmic solution to these functionalities, which adopts seamless pixel rearrangements to be able to resize and rescale dendrograms or tree diagrams. The results showed that the algorithm developed makes clustering outcome representation a really free visualization of hierarchical clustering and bioinformatics analysis. Especially, it possesses features of selectively visualizing and/or saving results in a specific size, scale and style (different views).展开更多
The comparison of networks with different orders strongly depends on the stability analysis of graph features in evolving systems. In this paper, we rigorously investigate the stability of the weighted spectral distri...The comparison of networks with different orders strongly depends on the stability analysis of graph features in evolving systems. In this paper, we rigorously investigate the stability of the weighted spectral distribution（i.e., a spectral graph feature） as the network order increases. First, we use deterministic scale-free networks generated by a pseudo treelike model to derive the precise formula of the spectral feature, and then analyze the stability of the spectral feature based on the precise formula. Except for the scale-free feature, the pseudo tree-like model exhibits the hierarchical and small-world structures of complex networks. The stability analysis is useful for the classification of networks with different orders and the similarity analysis of networks that may belong to the same evolving system.展开更多
【目的】针对传统快速扩展随机树(Rapidly-exploring Random Tree,RRT)算法在多自由度机械臂路径规划中搜索无引导、路径质量差等问题,提出一种基于无碰撞通道的启发式RRT算法。【方法】通过基于球面的波前扩展算法(Wavefront算法)获取...【目的】针对传统快速扩展随机树(Rapidly-exploring Random Tree,RRT)算法在多自由度机械臂路径规划中搜索无引导、路径质量差等问题,提出一种基于无碰撞通道的启发式RRT算法。【方法】通过基于球面的波前扩展算法(Wavefront算法)获取工作空间无碰撞通道,设置路径靶向点,利用环境信息启发树的生长而非传统的盲目搜索;改进随机点采样函数,分别采用路径靶向点在关节空间中对应关节角度的多维高斯分布模型和高斯混合模型(Gaussian Mixture Model,GMM)作为启发项,引导机械臂末端执行器在无碰撞通道内定向快速稳定扩展。【结果】仿真分析结果表明,与传统RRT算法相比,启发式RRT算法缩短了路径搜索时间,减少了迭代次数,路径长度缩短了39.32%。展开更多
基金Project supported by the National Natural Science Foundation of China
文摘D. E. Knuth has widely discussed some combinatorial properties and the application in computer science on binary trees, ordered trees, oriented trees and free trees, and given some formulas for the number of all the above structurally different trees with n nodes. Recently Wang Zhenyu gave formulas of the total leaf number for the preceding trees. Classifying these results carefully, Wang
基金Project supported by the National Natural Science Foundation of China(Grant No.11874027)the China Postdoctoral Science Foundation(Grant Nos.2019T120233 and 2017M621198)
文摘Manipulating the self-assembly of transition metal telluride nanocrystals(NCs) creates opportunities for exploring new properties and device applications. Iron ditelluride(FeTe2) has recently emerged as a new class of magnetic semiconductor with three-dimensional(3D) magnetic ordering and narrow band gap structure, yet the self-assembly of FeTe2 NCs has not been achieved. Herein, the tree-like FeTe2 nanoarchitectures with orthorhombic crystal structure have been successfully synthesized by hot-injection solvent thermal approach using phosphine-free Te precursor. The morphology, size, and crystal structure have been investigated using transmission electron microscopy(TEM), high-resolution TEM(HRTEM),and powder x-ray diffraction(XRD). We study the formation process of tree-like FeTe2 NCs according to trace the change of the sample morphology with the reaction time. It was found that the FeTe2 nanoparticles show oriented aggregation and self-assembly behavior with the increase of reaction time, which is attributed to size-dependent magnetism properties of the samples. The magnetic interaction is thought to be the driving force of nanoparticle self-organization.
基金Supported by the National Natural Science Foundation of China,Tian Yuan Special Foundation(Grant No.11426125)by Educational Commission of Liaoning Province(Grant No.L2014239)
文摘A spanning tree with no more than 3 leaves is called a spanning 3-ended tree. In this paper, we prove that if G is a k-connected （k≥ 2） almost claw-free graph of order n and σk＋3（G） ≥ n ＋ k ＋ 2, then G contains a spanning 3-ended tree, where σk（G） = min{∑es deg（v） ： S is an independent set of G with ｜S｜ = k}.
文摘In order to clarify the correlations between the free spindle pruning mode and various factors in Fuji apple,the growth data of the free spindle-shaped short branch Fuji apple Tianhong No. 2 and the free spindle-shaped long branch Fuji apple Changfu No. 2 in the Apple Demonstration Park of Xingtang County,Hebei Province were investigated. Using SPSS statistical software,the correlations between the stem tapering grade and various growth traits were analyzed. The results showed that in Tianhong No. 2,the stem tapering grade was negatively correlated with various growth traits of the central shaft,and the correlation coefficients between the stem tapering grade and the central shaft total thickness,the central shaft average thickness,the central shaft total length and the central shaft average length were-0. 228,-0. 033,-0. 411 and-0. 430,respectively; and in Changfu No. 2,the stem tapering grade was positively correlated with various growth traits of the central shaft,and the correlation coefficients between the stem tapering grade and the central shaft total thickness,the central shaft average thickness,the central shaft total length and the central shaft average length were 0. 475,0. 181,0. 120 and 0. 258,respectively. This paper can provide a scientific basis for guiding the construction of free spindle pruning mode in densely planted dwarf apple trees.
文摘Graphical representation of hierarchical clustering results is of final importance in hierarchical cluster analysis of data. Unfortunately, almost all mathematical or statistical software may have a weak capability of showcasing such clustering results. Particularly, most of clustering results or trees drawn cannot be represented in a dendrogram with a resizable, rescalable and free-style fashion. With the “dynamic” drawing instead of “static” one, this research works around these weak functionalities that restrict visualization of clustering results in an arbitrary manner. It introduces an algorithmic solution to these functionalities, which adopts seamless pixel rearrangements to be able to resize and rescale dendrograms or tree diagrams. The results showed that the algorithm developed makes clustering outcome representation a really free visualization of hierarchical clustering and bioinformatics analysis. Especially, it possesses features of selectively visualizing and/or saving results in a specific size, scale and style (different views).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61402485,61303061,and 71201169)
文摘The comparison of networks with different orders strongly depends on the stability analysis of graph features in evolving systems. In this paper, we rigorously investigate the stability of the weighted spectral distribution（i.e., a spectral graph feature） as the network order increases. First, we use deterministic scale-free networks generated by a pseudo treelike model to derive the precise formula of the spectral feature, and then analyze the stability of the spectral feature based on the precise formula. Except for the scale-free feature, the pseudo tree-like model exhibits the hierarchical and small-world structures of complex networks. The stability analysis is useful for the classification of networks with different orders and the similarity analysis of networks that may belong to the same evolving system.
文摘【目的】针对传统快速扩展随机树(Rapidly-exploring Random Tree,RRT)算法在多自由度机械臂路径规划中搜索无引导、路径质量差等问题,提出一种基于无碰撞通道的启发式RRT算法。【方法】通过基于球面的波前扩展算法(Wavefront算法)获取工作空间无碰撞通道,设置路径靶向点,利用环境信息启发树的生长而非传统的盲目搜索;改进随机点采样函数,分别采用路径靶向点在关节空间中对应关节角度的多维高斯分布模型和高斯混合模型(Gaussian Mixture Model,GMM)作为启发项,引导机械臂末端执行器在无碰撞通道内定向快速稳定扩展。【结果】仿真分析结果表明,与传统RRT算法相比,启发式RRT算法缩短了路径搜索时间,减少了迭代次数,路径长度缩短了39.32%。
