In this paper. based on large deviation formulas established in stronger topology generated by Hlder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hlder norm
Verifying the integrity of a hard disk is an important concern in computer forensics,as the law enforcement party needs to confirm that the data inside the hard disk have not been modified during the investigation.A t...Verifying the integrity of a hard disk is an important concern in computer forensics,as the law enforcement party needs to confirm that the data inside the hard disk have not been modified during the investigation.A typical approach is to compute a single chained hash value of all sectors in a specific order.However,this technique loses the integrity of all other sectors even if only one of the sectors becomes a bad sector occasionally or is modified intentionally.In this paper we propose a k-dimensional hashing scheme,kD for short,to distribute sectors into a kD space,and to calculate multiple hash values for sectors in k dimensions as integrity evidence.Since the integrity of the sectors can be verified depending on any hash value calculated using the sectors,the probability to verify the integrity of unchanged sectors can be high even with bad/modified sectors in the hard disk.We show how to efficiently implement this kD hashing scheme such that the storage of hash values can be reduced while increasing the chance of an unaffected sector to be verified successfully.Experimental results of a 3D scheme show that both the time for computing the hash values and the storage for the hash values are reasonable.展开更多
Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed...Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+2).展开更多
Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fracta...Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact Holder exponent were obtained for such Bush type functions.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
Unlike the detection of marked on-street parking spaces,detecting unmarked spaces poses significant challenges due to the absence of clear physical demarcation and uneven gaps caused by irregular parking.In urban citi...Unlike the detection of marked on-street parking spaces,detecting unmarked spaces poses significant challenges due to the absence of clear physical demarcation and uneven gaps caused by irregular parking.In urban cities with heavy traffic flow,these challenges can result in traffic disruptions,rear-end collisions,sideswipes,and congestion as drivers struggle to make decisions.We propose a real-time detection system for on-street parking spaces using YOLO models and recommend the most suitable space based on KD-tree search.Lightweight versions of YOLOv5,YOLOv7-tiny,and YOLOv8 with different architectures are trained.Among the models,YOLOv5s with SPPF at the backbone achieved an F1-score of 0.89,which was selected for validation using k-fold cross-validation on our dataset.The Low variance and standard deviation recorded across folds indicate the model’s generalizability,reliability,and stability.Inference with KD-tree using predictions from the YOLO models recorded FPS of 37.9 for YOLOv5,67.2 for YOLOv7-tiny,and 67.0 for YOLOv8.The models successfully detect both marked and unmarked empty parking spaces on test data with varying inference speeds and FPS.These models can be efficiently deployed for real-time applications due to their high FPS,inference speed,and lightweight nature.In comparison with other state-of-the-art models,our models outperform them,further demonstrating their effectiveness.展开更多
The author establishes a large deviation for k-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Holder norm can be obtained.
文摘In this paper. based on large deviation formulas established in stronger topology generated by Hlder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hlder norm
基金Project supported by the Research Grants Council of Hong Kong SAR,China (No. RGC GRF HKU 713009E)the NSFC/RGC Joint Research Scheme (No. N_HKU 722/09)HKU Seed Fundings for Basic Research (Nos. 200811159155 and 200911159149)
文摘Verifying the integrity of a hard disk is an important concern in computer forensics,as the law enforcement party needs to confirm that the data inside the hard disk have not been modified during the investigation.A typical approach is to compute a single chained hash value of all sectors in a specific order.However,this technique loses the integrity of all other sectors even if only one of the sectors becomes a bad sector occasionally or is modified intentionally.In this paper we propose a k-dimensional hashing scheme,kD for short,to distribute sectors into a kD space,and to calculate multiple hash values for sectors in k dimensions as integrity evidence.Since the integrity of the sectors can be verified depending on any hash value calculated using the sectors,the probability to verify the integrity of unchanged sectors can be high even with bad/modified sectors in the hard disk.We show how to efficiently implement this kD hashing scheme such that the storage of hash values can be reduced while increasing the chance of an unaffected sector to be verified successfully.Experimental results of a 3D scheme show that both the time for computing the hash values and the storage for the hash values are reasonable.
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Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+2).
基金The National Natural Science Foundation of China (No.10171080)
文摘Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact Holder exponent were obtained for such Bush type functions.
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.
基金supports this paper.Project Nos.NSTC-112-2221-E-324-003 MY3,NSTC-111-2622-E-324-002 and NSTC-112-2221-E-324-011-MY2.
文摘Unlike the detection of marked on-street parking spaces,detecting unmarked spaces poses significant challenges due to the absence of clear physical demarcation and uneven gaps caused by irregular parking.In urban cities with heavy traffic flow,these challenges can result in traffic disruptions,rear-end collisions,sideswipes,and congestion as drivers struggle to make decisions.We propose a real-time detection system for on-street parking spaces using YOLO models and recommend the most suitable space based on KD-tree search.Lightweight versions of YOLOv5,YOLOv7-tiny,and YOLOv8 with different architectures are trained.Among the models,YOLOv5s with SPPF at the backbone achieved an F1-score of 0.89,which was selected for validation using k-fold cross-validation on our dataset.The Low variance and standard deviation recorded across folds indicate the model’s generalizability,reliability,and stability.Inference with KD-tree using predictions from the YOLO models recorded FPS of 37.9 for YOLOv5,67.2 for YOLOv7-tiny,and 67.0 for YOLOv8.The models successfully detect both marked and unmarked empty parking spaces on test data with varying inference speeds and FPS.These models can be efficiently deployed for real-time applications due to their high FPS,inference speed,and lightweight nature.In comparison with other state-of-the-art models,our models outperform them,further demonstrating their effectiveness.
文摘The author establishes a large deviation for k-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Holder norm can be obtained.
