When building an experimental platform for light propagation along an inhomogeneous turbulent path,it is very essential to set up the reasonable distribution of phase screen.Based on multi-layered model of phase scree...When building an experimental platform for light propagation along an inhomogeneous turbulent path,it is very essential to set up the reasonable distribution of phase screen.Based on multi-layered model of phase screen,an iterative optimization algorithm of phase screen position is given in this paper.Thereafter,the optimal position of phase screens is calculated under the Hufnagel-Valley5/7 and Hefei-day turbulence profile.The results show that the positions of phase screen calculated by the iterative algorithm can fit well with the turbulence profile rather than mechanically placed phase screens at equal distance.Compared with the uniform distribution of phase screens position,the residual phase error of the iterative algorithm decreases very significantly.The similarity degree between them is minimal when number of layers is equal to two.展开更多
Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the conve...Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the convergence rate for iterates of both q-Bernstein polynomials and their Boolean sum are estimated. Moreover, the saturation of {Bn（., qn）} when n → ∞ and convergence rate of Bn（f,q;x） when f ∈ C^n-1 [0, 1], q → ∞ are also presented.展开更多
By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f（t,u） is non-increasing respect to u.
In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In o...In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61308082)
文摘When building an experimental platform for light propagation along an inhomogeneous turbulent path,it is very essential to set up the reasonable distribution of phase screen.Based on multi-layered model of phase screen,an iterative optimization algorithm of phase screen position is given in this paper.Thereafter,the optimal position of phase screens is calculated under the Hufnagel-Valley5/7 and Hefei-day turbulence profile.The results show that the positions of phase screen calculated by the iterative algorithm can fit well with the turbulence profile rather than mechanically placed phase screens at equal distance.Compared with the uniform distribution of phase screens position,the residual phase error of the iterative algorithm decreases very significantly.The similarity degree between them is minimal when number of layers is equal to two.
文摘Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the convergence rate for iterates of both q-Bernstein polynomials and their Boolean sum are estimated. Moreover, the saturation of {Bn（., qn）} when n → ∞ and convergence rate of Bn（f,q;x） when f ∈ C^n-1 [0, 1], q → ∞ are also presented.
基金supported by Program for Scientific research innovation team in Colleges and universities of Shandong Provincethe Doctoral Program Foundation of Education Ministry of China(20133705110003)+1 种基金the Natural Science Foundation of Shandong Province of China(ZR2014AM007)the National Natural Science Foundation of China(11571197)
文摘By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f（t,u） is non-increasing respect to u.
基金Supported by NNSF of China(11201213,11371183)NSF of Shandong Province(ZR2010AM022,ZR2013AM004)+2 种基金the Project of Shandong Provincial Higher Educational Science and Technology(J15LI07)the Project of Ludong University High-Quality Curriculum(20130345)the Teaching Reform Project of Ludong University in 2014(20140405)
文摘In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.
