The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the ...The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).展开更多
The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integ...The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.展开更多
The stabilization and trajectory tracking problems of autonomous airship＇s planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying L...The stabilization and trajectory tracking problems of autonomous airship＇s planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying Lyapunov stability method, the state feedback control laws are designed and the close-loop error systems are proved to be uniformly asymptotically stable by Matrosov theorem. In particular, the controller does not need knowledge on system parameters in the case of set-point stabilization, which makes the controller robust with respect to parameter uncertainty. Numerical simulations illustrate the effectiveness of the controller designed.展开更多
This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both ...This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.展开更多
For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been st...For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been studied.In order to obtain six real RR dyads,based on Strum＇s theorem,the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method.Moreover,the Grashof condition and the circuit defect condition are taken into account.Given the relationships between the design parameters and the aforementioned two conditions,two objective functions are constructed and optimized by the adaptive genetic algorithm（AGA）.Two examples with six real spherical RR dyads are obtained by optimization,and the results verify the feasibility of the proposed method.The paper provides a method to synthesize the complete real solution of the five-orientation motion generation,which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.展开更多
In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking ...In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.展开更多
The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formul...The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.展开更多
Define the incremental fractional Brownian field ZH（τ, s） = BH（s＋τ） -BH（s）,where BH（s） is a standard fractional Brownian motion with Hurst parameter H ∈ （0, 1）. Inthis paper, we first derive an exact asy...Define the incremental fractional Brownian field ZH（τ, s） = BH（s＋τ） -BH（s）,where BH（s） is a standard fractional Brownian motion with Hurst parameter H ∈ （0, 1）. Inthis paper, we first derive an exact asymptotic of distribution of the maximum MH（Tu） =supτ∈[0,1],s∈[0,xτu] ZH（τ, s）, which holds uniformly for x ∈ [A, B] with A, B two positive con-stants. We apply the findings to analyse the tail asymptotic and limit theorem of MH （τ） witha random index τ. In the end, we also prove an almost sure limit theorem for the maximum M1/2（τ） with non-random index T.展开更多
Let B={B^H(t)}t≥0 be a d-dimensional fractional Brownian motion with Hurst parameter H∈(0,1).Consider the functionals of k independent d-dimensional fractional Brownian motions 1/√n∫0^ent1⋯∫0^entk f(B^H,1(s1)+⋯+B...Let B={B^H(t)}t≥0 be a d-dimensional fractional Brownian motion with Hurst parameter H∈(0,1).Consider the functionals of k independent d-dimensional fractional Brownian motions 1/√n∫0^ent1⋯∫0^entk f(B^H,1(s1)+⋯+B^H,k(sk))ds1⋯dsk,where the Hurst index H=k/d.Using the method of moments,we prove the limit law and extending a result by Xu\cite{xu}of the case k=1.It can also be regarded as a fractional generalization of Biane\cite{biane}in the case of Brownian motion.展开更多
In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at larg...In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at large distance from the plate, in both cases, are obtained by a suitable application of Green＇s integral theorem. These are then studied graphically for various values of the ice cover parameter.展开更多
We use reflecting Brownian motion(RBM)to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary.The boundary integrand is obtained by carefully analyzing the asymptotic behav...We use reflecting Brownian motion(RBM)to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary.The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary local time of RBM for small times.展开更多
基金the National Natural Science Foundation of China!(No.19361060)and the Mathematical Center of the State Education Commission of
文摘The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).
基金The project supported by Natural Science Foundation of Heilongjiang Province of China under Grant No. 9507
文摘The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.
文摘The stabilization and trajectory tracking problems of autonomous airship＇s planar motion are studied. By defining novel configuration error and velocity error, the dynamics of error systems are derived. By applying Lyapunov stability method, the state feedback control laws are designed and the close-loop error systems are proved to be uniformly asymptotically stable by Matrosov theorem. In particular, the controller does not need knowledge on system parameters in the case of set-point stabilization, which makes the controller robust with respect to parameter uncertainty. Numerical simulations illustrate the effectiveness of the controller designed.
基金supported by the National Science Foundations (DMS0504783 DMS0604207)National Science Fund for Distinguished Young Scholars of China (70825005)
文摘This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.
基金Supported by National Natural Science Foundation of China(Grant Nos.51375059,61105103)National Hi-tech Research and Development Program of China(863 Program,Grant No.2011AA040203)Beijing Municipal Natural Science Foundation of China(Grant No.4132032)
文摘For a spherical four-bar linkage,the maximum number of the spherical RR dyad（R：revolute joint）of five-orientation motion generation can be at most 6.However,complete real solution of this problem has seldom been studied.In order to obtain six real RR dyads,based on Strum＇s theorem,the relationships between the design parameters are derived from a 6th-degree univariate polynomial equation that is deduced from the constraint equations of the spherical RR dyad by using Dixon resultant method.Moreover,the Grashof condition and the circuit defect condition are taken into account.Given the relationships between the design parameters and the aforementioned two conditions,two objective functions are constructed and optimized by the adaptive genetic algorithm（AGA）.Two examples with six real spherical RR dyads are obtained by optimization,and the results verify the feasibility of the proposed method.The paper provides a method to synthesize the complete real solution of the five-orientation motion generation,which is also applicable to the problem that deduces to a univariate polynomial equation and requires the generation of as many as real roots.
文摘In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.
文摘The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.
基金supported by National Science Foundation of China(11501250)Natural Science Foundation of Zhejiang Province of China(LQ14A010012,LY15A010019)+2 种基金Postdoctoral Research Program of Zhejiang ProvinceNatural Science Foundation of Jiangsu Higher Education Institution of China(14KJB110023)Research Foundation of SUST
文摘Define the incremental fractional Brownian field ZH（τ, s） = BH（s＋τ） -BH（s）,where BH（s） is a standard fractional Brownian motion with Hurst parameter H ∈ （0, 1）. Inthis paper, we first derive an exact asymptotic of distribution of the maximum MH（Tu） =supτ∈[0,1],s∈[0,xτu] ZH（τ, s）, which holds uniformly for x ∈ [A, B] with A, B two positive con-stants. We apply the findings to analyse the tail asymptotic and limit theorem of MH （τ） witha random index τ. In the end, we also prove an almost sure limit theorem for the maximum M1/2（τ） with non-random index T.
基金Q.Yu is partially supported by ECNU Academic Innovation Promotion Program for Excellent Doctoral Students(YBNLTS2019-010)the Scientific Research Innovation Program for Doctoral Students in Faculty of Economics and Management(2018FEM-BCKYB014).
文摘Let B={B^H(t)}t≥0 be a d-dimensional fractional Brownian motion with Hurst parameter H∈(0,1).Consider the functionals of k independent d-dimensional fractional Brownian motions 1/√n∫0^ent1⋯∫0^entk f(B^H,1(s1)+⋯+B^H,k(sk))ds1⋯dsk,where the Hurst index H=k/d.Using the method of moments,we prove the limit law and extending a result by Xu\cite{xu}of the case k=1.It can also be regarded as a fractional generalization of Biane\cite{biane}in the case of Brownian motion.
基金Supported by the Department of Science and Technology,Government of India for their financial support of this work through the SERC Fast Track Scheme for Young Scientist(No.SR/FTP/MS-037/2011)
文摘In this paper we study the problem of generation of surface waves produced due to a） rolling of the plate and b） presence of a line source in front of a fixed vertical plate. The amplitudes of radiated waves at large distance from the plate, in both cases, are obtained by a suitable application of Green＇s integral theorem. These are then studied graphically for various values of the ice cover parameter.
文摘We use reflecting Brownian motion(RBM)to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary.The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary local time of RBM for small times.
