The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, ...The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.展开更多
The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e....The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.展开更多
The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Th...The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.展开更多
The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. ...The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.展开更多
Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is con...Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.展开更多
The momentary state of a semiconductor device is described by a system of three nonlinear partial differential equations. A finite difference scheme for simulating transient behaviors of a semiconductor device on grid...The momentary state of a semiconductor device is described by a system of three nonlinear partial differential equations. A finite difference scheme for simulating transient behaviors of a semiconductor device on grids with local refinement in time and space is constructed and studied. Error analysis is presented and is illustrated by numerical examples.展开更多
In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under m...In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.展开更多
Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system....Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.展开更多
The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact ana...The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions.展开更多
In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state...In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.展开更多
With the development of network and information technologies, information security is more and more widely researched in China. To know where the work is and where it goes, we focus on comprehensively surveying the tw...With the development of network and information technologies, information security is more and more widely researched in China. To know where the work is and where it goes, we focus on comprehensively surveying the twenty years of important fundamental research by Chinese scholars, and giving, from our point of view, the significance as well as the outlook of future work. Some of the reviewed work, including the researches on fundamental theory of cryptography, cryptographic algorithm, security protocol, security infrastructure and information hiding, greatly advances the related sub-fields, and is highly recognized in and outside of China. Nevertheless, the overall work, we think, is still facing the problems of unbalanced development of sub-areas, limited scope of research, lack of systematic work and application, etc., leaving much room for improvement in the near future.展开更多
The mathematical model of semiconductor devices is described by the initial boundary value problem of a system of three nonlinear partial differential equations.One equation in elliptic form is for the electrostatic p...The mathematical model of semiconductor devices is described by the initial boundary value problem of a system of three nonlinear partial differential equations.One equation in elliptic form is for the electrostatic potential;two equations of convection-dominated diffusion type are for the electron and hole concentrations.Finite volume element procedure are put forward for the electrostatic potential,while upwind volume element schemes for the two concentration equations.Error estimates in L2norm for our numerical schemes are derived.展开更多
A group of asymmetric difference schemes to approach the Korteweg-de Vries (KdV) equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segme...A group of asymmetric difference schemes to approach the Korteweg-de Vries (KdV) equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.展开更多
This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of...This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.展开更多
Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperatur...Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H1 norm error estimates are given.展开更多
Most image interpolation algorithms currently used suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This letter presents an adaptive feature preserving bidirectional flow ...Most image interpolation algorithms currently used suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This letter presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the iso-phote lines (edges), while a normal diffusion is done to remove artifacts ('jaggies') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first order and the second order directional derivatives of the image. Experimental results on the Lena image demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.展开更多
This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectatio...This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectations via nonlinear Markov chains. Com- pared to the author’s previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probabil- ity measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.展开更多
By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets (singular rough ...By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets (singular rough sets). S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By introducing the function equivalence class (law equivalence class) that proposes dynamic characteristic into S-rough sets, the first author improved S-rough sets and put forward function S-rough sets (function singular rough sets). Function S-rough sets have dynamic characteristic and law characteristic, and a function is a law. By using function S-rough sets, this paper presents law identification, law identification theorem, and law identification criterion and applications. Function S-rough sets are a new research direction of rough sets theory, and it is also a new tool to the research of system law identification.展开更多
This paper is on fuzzy decision theory and information security theory which are mutually independent and engrafted. This paper presents both-branch fuzzy decision and problems on decision encryption-authentication, p...This paper is on fuzzy decision theory and information security theory which are mutually independent and engrafted. This paper presents both-branch fuzzy decision and problems on decision encryption-authentication, puts forward two kinds of both-branch fuzzy decision on X: both-branch fuzzy decision on X having bounded domains X = X+∩X- ={x0}, both-branch fuzzy decision on X havingoverlapping domains X* = X+∩X- = {x_1~*,x_2~*,…,x_1~*}. It presents single branch separate-separate out theoremof both-branch fuzzy decision on X, single branch superposition theorem of both-branch fuzzy decision, exclusive-decompose principle of both-branch fuzzy decision. This paper presents encryption-authentication theorem of decision by engrafting information security theory and technique with both-branch fuzzy decision, and provides encryption-decryption and signature-authentication of both-branch fuzzy decision.展开更多
In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Benard type under the pointwise control constraint. The states and the co-states are approximat...In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Benard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence analysis for the states and the co-states. Then we derive error estimates in L^∞-norm and optimal error estimates in L^2-norm.展开更多
基金Supported by the "973" Project of P. R. China (G1998020300)
文摘The problem of global stabilization by state feedback for a class of time-delay nonlinear system is considered. By constructing the appropriate Lyapunov-Krasovskii functionals (LKF) and using the backstepping design, a linear state feedback controller making the closed-loop system globally asymptotically stable is constructed.
基金Postdoctoral Science Foundation of China (No. 20060400980)Postdoctoral Science Foundation of Shandong Province(No. 200603015)National Science Foundation of China (No. 10671112)
文摘The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.
基金Project supported by the National Natural Science Foundation of China (No.10371067) thePlanned Item for the Outstanding Young Teachers of Ministry of Education of China (No.2057) the Special Fund for Ph.D. Program of Ministry of Education of China ( No.20020422020) and the Fok Ying Tung Education Foundation for Young College Teachers(No.91064)
文摘The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
基金国家自然科学基金,Outstanding Young Teachers of Ministry of Education of China,Special Fund for Ph.D.Program of Ministry of Education of China,Fok Ying Tung Education Foundation
文摘The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
文摘Some new Saul'yev type asymmetric difference schemes for Burgers' equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers' equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.
基金Supported by the Major State Basic Research of China (Grant No. G1999032803)the National Natural Science Foundation of China (Grant No. 10372052,10271066)the Doctorate Foundation of the Ministry of Education of China (Grant No. 20030422047).
文摘The momentary state of a semiconductor device is described by a system of three nonlinear partial differential equations. A finite difference scheme for simulating transient behaviors of a semiconductor device on grids with local refinement in time and space is constructed and studied. Error analysis is presented and is illustrated by numerical examples.
基金The Major State Basic Research Program (19871051) of China the NNSF (19972039) of China and Yantai University Doctor Foundation (SX03B20).
文摘In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.
基金The NNSF.MTYF(10126029)of China and the YF of Shandong University.
文摘Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.
基金The project supported by the National Natural Science Foundation of China(10272067)the Doctoral Program Foundation of the Education Ministry of China(20030422046)+1 种基金the Natural Science Foundation of Shandong Province,China(Y2006A 14)the Research Foundation of Shandong University at Weihai.
文摘The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions.
基金the National Basic Research Program under the Grant 2005CB321703the NSFC under the Grants 10571108 and 10441005the Research Fund for Doctoral Program of High Education by China State Education Ministry under the Grant 2005042203
文摘In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.
基金Supported by the National Natural Science Foundation of China under Grant No. 60025205. Acknowledgements Xian-Feng Zhao et al. for of the survey. We would like to thank Dr. their assistance in our writing
文摘With the development of network and information technologies, information security is more and more widely researched in China. To know where the work is and where it goes, we focus on comprehensively surveying the twenty years of important fundamental research by Chinese scholars, and giving, from our point of view, the significance as well as the outlook of future work. Some of the reviewed work, including the researches on fundamental theory of cryptography, cryptographic algorithm, security protocol, security infrastructure and information hiding, greatly advances the related sub-fields, and is highly recognized in and outside of China. Nevertheless, the overall work, we think, is still facing the problems of unbalanced development of sub-areas, limited scope of research, lack of systematic work and application, etc., leaving much room for improvement in the near future.
基金Project supported by the National Natural Science Fbundation and the Natural Science Foundation of Shandong Province
文摘The mathematical model of semiconductor devices is described by the initial boundary value problem of a system of three nonlinear partial differential equations.One equation in elliptic form is for the electrostatic potential;two equations of convection-dominated diffusion type are for the electron and hole concentrations.Finite volume element procedure are put forward for the electrostatic potential,while upwind volume element schemes for the two concentration equations.Error estimates in L2norm for our numerical schemes are derived.
基金Project supported by the National Natural Science Foundation of China(No.10671113)the Natural Science Foundation of Shandong Province of China(No.Y2003A04)
文摘A group of asymmetric difference schemes to approach the Korteweg-de Vries (KdV) equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.
基金This paper is supported by NNSF project(10371059)China and Youth Teacher Foundation of Nankai University
文摘This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.
基金Supported by National Natural Science Foundation of China(10071044)the Research Fund of Doctoral Program of High Education by State Education Ministry of China.
文摘Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H1 norm error estimates are given.
基金Supported by the National Natural Science Foundation of China(No.60472033)the Key Laboratory Project of Information Science & Engineering of Railway of National Ministry of Railways, China (No.tdxx0510)the Technological Innovation Fund of Excellent Doctorial Candidate of Beijing Jiaotong University,China(No.48007)
文摘Most image interpolation algorithms currently used suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This letter presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the iso-phote lines (edges), while a normal diffusion is done to remove artifacts ('jaggies') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first order and the second order directional derivatives of the image. Experimental results on the Lena image demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.
基金Project supported by the National Natural Science Foundation of China(No.10131040).
文摘This paper deals with nonlinear expectations. The author obtains a nonlinear gen- eralization of the well-known Kolmogorov’s consistent theorem and then use it to con- struct ?ltration-consistent nonlinear expectations via nonlinear Markov chains. Com- pared to the author’s previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probabil- ity measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations. The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
基金the National Natural Science Foundation of China (Grant No. 60364001)the key Project of Chinese Ministry of Education (Grant No. 206089)the Natural Science Foundation of Shandong Province of China (Grant No. Y2007H02)
文摘By introducing element equivalence class that proposes dynamic characteristic into Pawlak Z rough sets theory, the first author of this paper improved Pawlak Z rough sets and put forward S-rough sets (singular rough sets). S-rough sets are defined by element equivalence class that proposes dynamic characteristic. S-rough sets have dynamic characteristic. By introducing the function equivalence class (law equivalence class) that proposes dynamic characteristic into S-rough sets, the first author improved S-rough sets and put forward function S-rough sets (function singular rough sets). Function S-rough sets have dynamic characteristic and law characteristic, and a function is a law. By using function S-rough sets, this paper presents law identification, law identification theorem, and law identification criterion and applications. Function S-rough sets are a new research direction of rough sets theory, and it is also a new tool to the research of system law identification.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 70271048) the Natural Science Foundation of Shandong Province (Y2001G07).
文摘This paper is on fuzzy decision theory and information security theory which are mutually independent and engrafted. This paper presents both-branch fuzzy decision and problems on decision encryption-authentication, puts forward two kinds of both-branch fuzzy decision on X: both-branch fuzzy decision on X having bounded domains X = X+∩X- ={x0}, both-branch fuzzy decision on X havingoverlapping domains X* = X+∩X- = {x_1~*,x_2~*,…,x_1~*}. It presents single branch separate-separate out theoremof both-branch fuzzy decision on X, single branch superposition theorem of both-branch fuzzy decision, exclusive-decompose principle of both-branch fuzzy decision. This paper presents encryption-authentication theorem of decision by engrafting information security theory and technique with both-branch fuzzy decision, and provides encryption-decryption and signature-authentication of both-branch fuzzy decision.
基金the Research Fund for Doctoral Program of High Education by China State Education Ministry under the Grant 2005042203
文摘In this paper, we consider the finite element approximation of the distributed optimal control problems of the stationary Benard type under the pointwise control constraint. The states and the co-states are approximated by polynomial functions of lowest-order mixed finite element space or piecewise linear functions and the control is approximated by piecewise constant functions. We give the superconvergence analysis for the control; it is proved that the approximation has a second-order rate of convergence. We further give the superconvergence analysis for the states and the co-states. Then we derive error estimates in L^∞-norm and optimal error estimates in L^2-norm.