A second-order divided difference filter (SDDF) is derived for integrating line of sight measurement from vision sensor with acceleration and angular rate measurements of the follower to estimate the precise relative ...A second-order divided difference filter (SDDF) is derived for integrating line of sight measurement from vision sensor with acceleration and angular rate measurements of the follower to estimate the precise relative position,velocity and attitude of two unmanned aerial vehicles (UAVs).The second-order divided difference filter which makes use of multidimensional interpolation formulations to approximate the nonlinear transformations could achieve more accurate estimation and faster convergence from inaccurate initial conditions than standard extended Kalman filter.The filter formulation is based on relative motion equations.The global attitude parameterization is given by quarternion,while a generalized three-dimensional attitude representation is used to define the local attitude error.Simulation results are shown to compare the performance of the second-order divided difference filter with a standard extended Kalman filter approach.展开更多
In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.
In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the origi...In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.展开更多
Nowadays,many steganographic tools have been developed,and secret messages can be imperceptibly transmitted through public networks.This paper concentrates on steganalysis against spatial least significant bit(LSB) ma...Nowadays,many steganographic tools have been developed,and secret messages can be imperceptibly transmitted through public networks.This paper concentrates on steganalysis against spatial least significant bit(LSB) matching,which is the prototype of many advanced information hiding methods.Many existing algorithms deal with steganalysis problems by using the dependencies between adjacent pixels.From another aspect,this paper calculates the differences among pixel pairs and proves that the histogram of difference values will be smoothed by stego noises.We calculate the difference histogram characteristic function(DHCF) and deduce that the moment of DHCFs(DHCFM) will be diminished after stego bits are hidden in the image.Accordingly,we compute the DHCFMs as the discriminative features.We calibrate the features by decreasing the influence of image content on them and train support vector machine classifiers based on the calibrated features.Experimental results demonstrate that the DHCFMs calculated with nonadjacent pixels are helpful to detect stego messages hidden by LSB matching.展开更多
In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the ...In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.展开更多
Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditi...Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.展开更多
A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced （chemical） oil production in porous media....A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced （chemical） oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l^2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results ate quite interesting and satisfactory.展开更多
Rotatability is a desirable quality of fitting response surface experimental designs. The propertystates that the variance of the estimated response made from the Taylor’s series expansion areconstant on circles, sph...Rotatability is a desirable quality of fitting response surface experimental designs. The propertystates that the variance of the estimated response made from the Taylor’s series expansion areconstant on circles, spheres and hyper-spheres about the centre of the design. In this article,a measure of rotatability of modified second-order rotatable design is presented. The variancefunction of a second-order response design and an infinite class of supplementary difference setsis used in coming up with the design.展开更多
This paper considers the linear-quadratic(LQ)optimal control problem for systems governed by a class of second-order parabolic partial differential equations(PDEs).This problem is significant in many areas of mathemat...This paper considers the linear-quadratic(LQ)optimal control problem for systems governed by a class of second-order parabolic partial differential equations(PDEs).This problem is significant in many areas of mathematics,control,engineering and so on,and thus has received great attention in the past decades.Different from the previous articles where the operator is applied to present the controller,the main contribution of this paper is to propose the discretisation-then-continuousization method,which is explicit and implementable.The solvability condition of the LQ optimal control problems is given based on a set of differential Riccati equations,and an explicit numerical calculation way of these equations and the design of the optimal controller are provided.展开更多
基金Sponsored by the Aerospace Technology Innovation Funding(Grant No. CASC0209)
文摘A second-order divided difference filter (SDDF) is derived for integrating line of sight measurement from vision sensor with acceleration and angular rate measurements of the follower to estimate the precise relative position,velocity and attitude of two unmanned aerial vehicles (UAVs).The second-order divided difference filter which makes use of multidimensional interpolation formulations to approximate the nonlinear transformations could achieve more accurate estimation and faster convergence from inaccurate initial conditions than standard extended Kalman filter.The filter formulation is based on relative motion equations.The global attitude parameterization is given by quarternion,while a generalized three-dimensional attitude representation is used to define the local attitude error.Simulation results are shown to compare the performance of the second-order divided difference filter with a standard extended Kalman filter approach.
文摘In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.
文摘In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.
基金supported by the NSFC(61173141,61362032,U1536206, 61232016,U1405254,61373133,61502242,61572258)BK20150925+4 种基金the Natural Science Foundation of Jiangxi Province, China(20151BAB207003)the Fund of Jiangsu Engineering Center of Network Monitoring(KJR1402)the Fund of MOE Internet Innovation Platform(KJRP1403)the CICAEET fundthe PAPD fund
文摘Nowadays,many steganographic tools have been developed,and secret messages can be imperceptibly transmitted through public networks.This paper concentrates on steganalysis against spatial least significant bit(LSB) matching,which is the prototype of many advanced information hiding methods.Many existing algorithms deal with steganalysis problems by using the dependencies between adjacent pixels.From another aspect,this paper calculates the differences among pixel pairs and proves that the histogram of difference values will be smoothed by stego noises.We calculate the difference histogram characteristic function(DHCF) and deduce that the moment of DHCFs(DHCFM) will be diminished after stego bits are hidden in the image.Accordingly,we compute the DHCFMs as the discriminative features.We calibrate the features by decreasing the influence of image content on them and train support vector machine classifiers based on the calibrated features.Experimental results demonstrate that the DHCFMs calculated with nonadjacent pixels are helpful to detect stego messages hidden by LSB matching.
文摘In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.
基金supported by National Natural Science Foundation of China(11101244,11271231)National Tackling Key Problems Program(20050200069)Doctorate Foundation of the Ministry of Education of China(20030422047)
文摘Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.
基金supported by the Major State Basic Research Development Program of China(G19990328)National Tackling Key Program(2011ZX05011-004+6 种基金2011ZX0505220050200069)National Natural Science Foundation of China(11101244112712311077112410372052)Doctorate Foundation of the Ministry of Education of China(20030422047)
文摘A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced （chemical） oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l^2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results ate quite interesting and satisfactory.
文摘Rotatability is a desirable quality of fitting response surface experimental designs. The propertystates that the variance of the estimated response made from the Taylor’s series expansion areconstant on circles, spheres and hyper-spheres about the centre of the design. In this article,a measure of rotatability of modified second-order rotatable design is presented. The variancefunction of a second-order response design and an infinite class of supplementary difference setsis used in coming up with the design.
基金supported by the National Natural Science Foundation of China[grant numbers 61821004,62250056]the Natural Science Foundation of Shandong Province[grant numbers ZR2021ZD14,ZR2021JQ24]+2 种基金Science and Technology Project of Qingdao West Coast New Area[grant numbers 2019-32,2020-20,2020-1-4]High-level Talent Team Project of Qingdao West Coast New Area[grant number RCTD-JC-2019-05]Key Research and Development Program of Shandong Province[grant number 2020CXGC01208].
文摘This paper considers the linear-quadratic(LQ)optimal control problem for systems governed by a class of second-order parabolic partial differential equations(PDEs).This problem is significant in many areas of mathematics,control,engineering and so on,and thus has received great attention in the past decades.Different from the previous articles where the operator is applied to present the controller,the main contribution of this paper is to propose the discretisation-then-continuousization method,which is explicit and implementable.The solvability condition of the LQ optimal control problems is given based on a set of differential Riccati equations,and an explicit numerical calculation way of these equations and the design of the optimal controller are provided.
