In this Letter, a test method based on oblique incidence is practically implemented in the interferometric measurement process. Three sets of wavefront data are achieved through cavity interference measurement with a ...In this Letter, a test method based on oblique incidence is practically implemented in the interferometric measurement process. Three sets of wavefront data are achieved through cavity interference measurement with a Fizeau interferometer and one oblique incidence measurement. An iterative algorithm is applied to retrieve the absolute surface shape of the test flat. By adding two sets of measurements, the absolute surface error of the interferometer＇s reference flat can be obtained. The new method can not only calibrate the reference flat error of interferometer, but also provide the absolute measurement method for high precision optical components applied in high power laser systems.展开更多
In this paper the concept of absolute observability of nonlinear control systems is advanced.Different from the linear time-invariant version, there are different definitions of absolute observability for nonlinear co...In this paper the concept of absolute observability of nonlinear control systems is advanced.Different from the linear time-invariant version, there are different definitions of absolute observability for nonlinear control systems.Two algorithms for maximal absolutely observable subsystems are given.Correspondingly,there are two relevant normal forms.The relations with the largest controlled invariant distribution contained in kerdh,zero dynamics etc.,are discussed from the view point of maximal absolute observabilities.展开更多
Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symm...Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symmetric square L-function related to f, the estimate 1λf(n21) x2 k2(log(x + k))6n≤x is established, which improves the previous result.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11602280 and 61705246)
文摘In this Letter, a test method based on oblique incidence is practically implemented in the interferometric measurement process. Three sets of wavefront data are achieved through cavity interference measurement with a Fizeau interferometer and one oblique incidence measurement. An iterative algorithm is applied to retrieve the absolute surface shape of the test flat. By adding two sets of measurements, the absolute surface error of the interferometer＇s reference flat can be obtained. The new method can not only calibrate the reference flat error of interferometer, but also provide the absolute measurement method for high precision optical components applied in high power laser systems.
文摘In this paper the concept of absolute observability of nonlinear control systems is advanced.Different from the linear time-invariant version, there are different definitions of absolute observability for nonlinear control systems.Two algorithms for maximal absolutely observable subsystems are given.Correspondingly,there are two relevant normal forms.The relations with the largest controlled invariant distribution contained in kerdh,zero dynamics etc.,are discussed from the view point of maximal absolute observabilities.
基金supported by the National Natural Science Foundation of China(No.11301142)the Key Project of Colleges and Universities of Henan Province(No.15A110014)
文摘Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symmetric square L-function related to f, the estimate 1λf(n21) x2 k2(log(x + k))6n≤x is established, which improves the previous result.
