Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB e...Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O（n^-1）.展开更多
In this note we consider Wente＇s type inequality on the Lorentz-Sobolev space. If f∈L^p1,q1（Rn）,G∈L^p2,q2 （Rn） and div G ≡ 0 in the sense of distribution where 1/p1＋1/p2=1/q ＋1/q2=1,1〈p1,p2〈∞, it is k...In this note we consider Wente＇s type inequality on the Lorentz-Sobolev space. If f∈L^p1,q1（Rn）,G∈L^p2,q2 （Rn） and div G ≡ 0 in the sense of distribution where 1/p1＋1/p2=1/q ＋1/q2=1,1〈p1,p2〈∞, it is known that G. f belongs to the Hardy space H1 and furthermore ‖G· f‖N1≤C‖ f‖Lp1,q1（R2）‖G‖Lp2,q2（R2）Reader can see [9] Section 4 Here we give a new proof of this result. Our proof depends on an estimate of a maximal operator on the Lorentz space which is of some independent interest. Finally, we use this inequality to get a generalisation of Bethuel＇s inequality.展开更多
In this study,we construct a family of single root finding method of optimal order four and then generalize this family for estimating of all roots of non-linear equation simultaneously.Convergence analysis proves tha...In this study,we construct a family of single root finding method of optimal order four and then generalize this family for estimating of all roots of non-linear equation simultaneously.Convergence analysis proves that the local order of convergence is four in case of single root finding iterative method and six for simultaneous determination of all roots of non-linear equation.Some non-linear equations are taken from physics,chemistry and engineering to present the performance and efficiency of the newly constructed method.Some real world applications are taken from fluid mechanics,i.e.,fluid permeability in biogels and biomedical engineering which includes blood Rheology-Model which as an intermediate result give some nonlinear equations.These non-linear equations are then solved using newly developed simultaneous iterative schemes.Newly developed simultaneous iterative schemes reach to exact values on initial guessed values within given tolerance,using very less number of function evaluations in each step.Local convergence order of single root finding method is computed using CAS-Maple.Local computational order of convergence,CPU-time,absolute residuals errors are calculated to elaborate the efficiency,robustness and authentication of the iterative simultaneous method in its domain.展开更多
Let(E,H,μ)be an abstract Wiener spacein the sense of L.Gross.It is proved that if u is a measurable map from E to H such that u∈W 2.1(H,μ)and there exists a constantα,0<α<1,such that either∑n‖D nu(w)‖2 H...Let(E,H,μ)be an abstract Wiener spacein the sense of L.Gross.It is proved that if u is a measurable map from E to H such that u∈W 2.1(H,μ)and there exists a constantα,0<α<1,such that either∑n‖D nu(w)‖2 Hα2 a.s.or‖u(w+h)-u(w)‖Hα‖h‖H a.s.for every h∈H and E exp108(1-α)2∑‖D n u‖H)<∞,then the measureμT-1 is equivalent toμ,where T(w)=w+u(w)for w∈E.And the explicit expression of the Radon-Nikodym derivative(cf.Theorem 2.1)is given.展开更多
基金Supported by the Natural Science Foundation of China(70471057)Supported by the Natural Science Foundation of Education Department of Shaanxi Province(03JK065)
文摘Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O（n^-1）.
基金Supported by the National Natural Science Foundation of China(11271330,11371136,11471288)the Zhejiang Natural Science Foundation of China(LY14A010015)China Scholarship Council
文摘In this note we consider Wente＇s type inequality on the Lorentz-Sobolev space. If f∈L^p1,q1（Rn）,G∈L^p2,q2 （Rn） and div G ≡ 0 in the sense of distribution where 1/p1＋1/p2=1/q ＋1/q2=1,1〈p1,p2〈∞, it is known that G. f belongs to the Hardy space H1 and furthermore ‖G· f‖N1≤C‖ f‖Lp1,q1（R2）‖G‖Lp2,q2（R2）Reader can see [9] Section 4 Here we give a new proof of this result. Our proof depends on an estimate of a maximal operator on the Lorentz space which is of some independent interest. Finally, we use this inequality to get a generalisation of Bethuel＇s inequality.
文摘In this study,we construct a family of single root finding method of optimal order four and then generalize this family for estimating of all roots of non-linear equation simultaneously.Convergence analysis proves that the local order of convergence is four in case of single root finding iterative method and six for simultaneous determination of all roots of non-linear equation.Some non-linear equations are taken from physics,chemistry and engineering to present the performance and efficiency of the newly constructed method.Some real world applications are taken from fluid mechanics,i.e.,fluid permeability in biogels and biomedical engineering which includes blood Rheology-Model which as an intermediate result give some nonlinear equations.These non-linear equations are then solved using newly developed simultaneous iterative schemes.Newly developed simultaneous iterative schemes reach to exact values on initial guessed values within given tolerance,using very less number of function evaluations in each step.Local convergence order of single root finding method is computed using CAS-Maple.Local computational order of convergence,CPU-time,absolute residuals errors are calculated to elaborate the efficiency,robustness and authentication of the iterative simultaneous method in its domain.
文摘Let(E,H,μ)be an abstract Wiener spacein the sense of L.Gross.It is proved that if u is a measurable map from E to H such that u∈W 2.1(H,μ)and there exists a constantα,0<α<1,such that either∑n‖D nu(w)‖2 Hα2 a.s.or‖u(w+h)-u(w)‖Hα‖h‖H a.s.for every h∈H and E exp108(1-α)2∑‖D n u‖H)<∞,then the measureμT-1 is equivalent toμ,where T(w)=w+u(w)for w∈E.And the explicit expression of the Radon-Nikodym derivative(cf.Theorem 2.1)is given.
