In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-...In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.展开更多
The autonomous exploration and mapping of an unknown environment is useful in a wide range of applications and thus holds great significance. Existing methods mostly use range sensors to generate twodimensional (2D) g...The autonomous exploration and mapping of an unknown environment is useful in a wide range of applications and thus holds great significance. Existing methods mostly use range sensors to generate twodimensional (2D) grid maps. Red/green/blue-depth (RGB-D) sensors provide both color and depth information on the environment, thereby enabling the generation of a three-dimensional (3D) point cloud map that is intuitive for human perception. In this paper, we present a systematic approach with dual RGB-D sensors to achieve the autonomous exploration and mapping of an unknown indoor environment. With the synchronized and processed RGB-D data, location points were generated and a 3D point cloud map and 2D grid map were incrementally built. Next, the exploration was modeled as a partially observable Markov decision process. Partial map simulation and global frontier search methods were combined for autonomous exploration, and dynamic action constraints were utilized in motion control. In this way, the local optimum can be avoided and the exploration efficacy can be ensured. Experiments with single connected and multi-branched regions demonstrated the high robustness, efficiency, and superiority of the developed system and methods.展开更多
Volume parameter is the basic content of a spatial body object morphology analysis.However,the challenge lies in the volume calculation of irregular objects.The point cloud slicing method proposed in this study effect...Volume parameter is the basic content of a spatial body object morphology analysis.However,the challenge lies in the volume calculation of irregular objects.The point cloud slicing method proposed in this study effectively works in calculating the volume of the point cloud of the spatial object obtained through three-dimensional laser scanning(3DLS).In this method,a uniformly spaced sequent slicing process is first conducted in a specific direction on the point cloud of the spatial object obtained through 3DLS.A series of discrete point cloud slices corresponding to the point cloud bodies are then obtained.Subsequently,the outline boundary polygon of the point cloud slicing is searched one by one in accordance with the slicing sequence and areas of the polygon.The point cloud slice is also calculated.Finally,the individual point cloud section volume is calculated through the slicing areas and the adjacent slicing gap.Thus,the total volume of the scanned spatial object can be calculated by summing up the individual volumes.According to the results and analysis of the calculated examples,the slice-based volume-calculating method for the point cloud of irregular objects obtained through 3DLS is correct,concise in process,reliable in results,efficient in calculation methods,and controllable on accuracy.This method comes as a good solution to the volume calculation of irregular objects.展开更多
In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions（in sense of mean value）. Appealing to the decomposition of equations, the existence of solutions is obtain...In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions（in sense of mean value）. Appealing to the decomposition of equations, the existence of solutions is obtained by using the contraction mapping principle and Leray-Schauder fixed point theorem, respectively.展开更多
The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrig...The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.展开更多
制图要素符号化是利用形式多样的地图符号,对地物的空间位置、分布特点以及数量、质量等基本特征进行可视化表达的过程。CorelDRAW极强的图形、文字及矢量线划编辑功能颇受制图人员青睐,尤其在要素符号化工作中扮演着重要角色。文章从...制图要素符号化是利用形式多样的地图符号,对地物的空间位置、分布特点以及数量、质量等基本特征进行可视化表达的过程。CorelDRAW极强的图形、文字及矢量线划编辑功能颇受制图人员青睐,尤其在要素符号化工作中扮演着重要角色。文章从点、线、面三个角度对制图要素符号化进行了理论探析,并基于CorelDRAWX5及其宏编辑器,引用CorelDRAW 15.0 Type Library控件进行了二次开发,实现了点状符号的九位替换、工字型国界符号的生成和自定义点符号的面域填充,不仅提高了地图制图效率,而且确保了图面内容的美观性。展开更多
基金Supported by the National Nature Science Foundation of China(11071001)Supported by the Key Program of Ministry of Education of China(205068)
文摘In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.
基金the National Natural Science Foundation of China (61720106012 and 61403215)the Foundation of State Key Laboratory of Robotics (2006-003)the Fundamental Research Funds for the Central Universities for the financial support of this work.
文摘The autonomous exploration and mapping of an unknown environment is useful in a wide range of applications and thus holds great significance. Existing methods mostly use range sensors to generate twodimensional (2D) grid maps. Red/green/blue-depth (RGB-D) sensors provide both color and depth information on the environment, thereby enabling the generation of a three-dimensional (3D) point cloud map that is intuitive for human perception. In this paper, we present a systematic approach with dual RGB-D sensors to achieve the autonomous exploration and mapping of an unknown indoor environment. With the synchronized and processed RGB-D data, location points were generated and a 3D point cloud map and 2D grid map were incrementally built. Next, the exploration was modeled as a partially observable Markov decision process. Partial map simulation and global frontier search methods were combined for autonomous exploration, and dynamic action constraints were utilized in motion control. In this way, the local optimum can be avoided and the exploration efficacy can be ensured. Experiments with single connected and multi-branched regions demonstrated the high robustness, efficiency, and superiority of the developed system and methods.
文摘Volume parameter is the basic content of a spatial body object morphology analysis.However,the challenge lies in the volume calculation of irregular objects.The point cloud slicing method proposed in this study effectively works in calculating the volume of the point cloud of the spatial object obtained through three-dimensional laser scanning(3DLS).In this method,a uniformly spaced sequent slicing process is first conducted in a specific direction on the point cloud of the spatial object obtained through 3DLS.A series of discrete point cloud slices corresponding to the point cloud bodies are then obtained.Subsequently,the outline boundary polygon of the point cloud slicing is searched one by one in accordance with the slicing sequence and areas of the polygon.The point cloud slice is also calculated.Finally,the individual point cloud section volume is calculated through the slicing areas and the adjacent slicing gap.Thus,the total volume of the scanned spatial object can be calculated by summing up the individual volumes.According to the results and analysis of the calculated examples,the slice-based volume-calculating method for the point cloud of irregular objects obtained through 3DLS is correct,concise in process,reliable in results,efficient in calculation methods,and controllable on accuracy.This method comes as a good solution to the volume calculation of irregular objects.
基金The NSF(1308085MA01,1508085QA01)of Anhui Provincethe Provincial Natural Science Research Project(KJ2014A010)of Anhui Colleges+1 种基金the National Natural Science Youth Foundation(11301004)of ChinaOutstanding Youth Key Foundation(2013SQRL087ZD)of Colleges and Universities in Anhui Province
文摘In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions（in sense of mean value）. Appealing to the decomposition of equations, the existence of solutions is obtained by using the contraction mapping principle and Leray-Schauder fixed point theorem, respectively.
基金Supported by the National Natural Science Foundation of China(10671174, 10401036)a Foundation for the Author of National Excellent Doctoral Dissertation of China(200518)
文摘The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.
文摘制图要素符号化是利用形式多样的地图符号,对地物的空间位置、分布特点以及数量、质量等基本特征进行可视化表达的过程。CorelDRAW极强的图形、文字及矢量线划编辑功能颇受制图人员青睐,尤其在要素符号化工作中扮演着重要角色。文章从点、线、面三个角度对制图要素符号化进行了理论探析,并基于CorelDRAWX5及其宏编辑器,引用CorelDRAW 15.0 Type Library控件进行了二次开发,实现了点状符号的九位替换、工字型国界符号的生成和自定义点符号的面域填充,不仅提高了地图制图效率,而且确保了图面内容的美观性。
