In this paper. based on large deviation formulas established in stronger topology generatedby H(?)lder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownianmotion in H(?)lder
The k-dimensional Piatetski-Shapiro prime number problem for k≥3 is studied. Let π（x; c<sub>1</sub>,…,c<sub>k</sub>）denote the number of primes p with p≤x, p=[n<sub>1</sub><...The k-dimensional Piatetski-Shapiro prime number problem for k≥3 is studied. Let π（x; c<sub>1</sub>,…,c<sub>k</sub>）denote the number of primes p with p≤x, p=[n<sub>1</sub><sup>c<sub>1</sub></sup>]=…[n<sub>k</sub><sup>c<sub>k</sub></sup>], where 1【c<sub>1</sub>【…【c<sub>k</sub> are fixed constants. It is proved that π（x; c<sub>1</sub>, …, c<sub>k</sub>） has an asymptotic formula if c<sub>1</sub><sup>-1</sup>+ …+c<sub>k</sub><sup>-1</sup>】k-k/（4k<sup>2</sup>+2）.展开更多
Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given....Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.展开更多
An unmanned aerial vehicle(UAV)is a small,fast aircraft with many useful features.It is widely used in military reconnaissance,aerial photography,searches,and other fields;it also has very good practical-application a...An unmanned aerial vehicle(UAV)is a small,fast aircraft with many useful features.It is widely used in military reconnaissance,aerial photography,searches,and other fields;it also has very good practical-application and development prospects.Since the UAV’s flight orientation is easily changeable,its orientation and flight path are difficult to control,leading to its high damage rate.Therefore,UAV flight-control technology has become the focus of attention.This study focuses on simulating a UAV’s flight and orientation control,and detecting collisions between a UAV and objects in a complex virtual environment.The proportional-integral-derivative control algorithm is used to control the orientation and position of the UAV in a virtual environment.A version of the bounding-box method that combines a grid with a k-dimensional tree is adopted in this paper,to improve the system performance and accelerate the collision-detection process.This provides a practical method for future studies on UAV flight position and orientation control,collision detection,etc.展开更多
文摘In this paper. based on large deviation formulas established in stronger topology generatedby H(?)lder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownianmotion in H(?)lder
基金Project supported by the National Natural Science Foundation of China (Grant No. 19801021)the Natural Science Foundation of Shandong Province (Grant No. Q98A02110).
文摘The k-dimensional Piatetski-Shapiro prime number problem for k≥3 is studied. Let π（x; c<sub>1</sub>,…,c<sub>k</sub>）denote the number of primes p with p≤x, p=[n<sub>1</sub><sup>c<sub>1</sub></sup>]=…[n<sub>k</sub><sup>c<sub>k</sub></sup>], where 1【c<sub>1</sub>【…【c<sub>k</sub> are fixed constants. It is proved that π（x; c<sub>1</sub>, …, c<sub>k</sub>） has an asymptotic formula if c<sub>1</sub><sup>-1</sup>+ …+c<sub>k</sub><sup>-1</sup>】k-k/（4k<sup>2</sup>+2）.
基金Supported by the Doctoral Programs Foundation of Education Ministry of China（2011 3401110009） Supported by the Universities Natural Science Foundation of Anhui Province（KJ2013A220） Supported by the Natural Science Research Project of Hefei Normal University（2012kj11）
文摘Some related problems of two n-dimensional simplices which are on an(n- 1)-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.
基金This work was supported by the National Key Technology Research and Development Program of China(Nos.2015BAK01B06,2017YFB1002705,2017YFB1002601,and 2017YFB0203002)the National Marine Public Service Project(No.201505014-3)+1 种基金the National Natural Science Foundation of China(NSFC)(Nos.61472010 and 61661146002)the Equipment Development Project(No.315050501).
文摘An unmanned aerial vehicle(UAV)is a small,fast aircraft with many useful features.It is widely used in military reconnaissance,aerial photography,searches,and other fields;it also has very good practical-application and development prospects.Since the UAV’s flight orientation is easily changeable,its orientation and flight path are difficult to control,leading to its high damage rate.Therefore,UAV flight-control technology has become the focus of attention.This study focuses on simulating a UAV’s flight and orientation control,and detecting collisions between a UAV and objects in a complex virtual environment.The proportional-integral-derivative control algorithm is used to control the orientation and position of the UAV in a virtual environment.A version of the bounding-box method that combines a grid with a k-dimensional tree is adopted in this paper,to improve the system performance and accelerate the collision-detection process.This provides a practical method for future studies on UAV flight position and orientation control,collision detection,etc.
