Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. F...Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.展开更多
In this research, we propose longitudinal generalised variance functions (LGVFs) to produceconvenient estimates of variances by incorporating time effect into modelling. Asymptoticproperties of some certain type of es...In this research, we propose longitudinal generalised variance functions (LGVFs) to produceconvenient estimates of variances by incorporating time effect into modelling. Asymptoticproperties of some certain type of estimators are investigated. Simulation studies and implementation of the proposed methods to Current Population Survey (CPS) data show that LGVFswork well in producing standard error estimates.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11171329,11203003 and 11373013
文摘Motivated by the effort to understand the mathematical structure underlying the Teukolsky equations in a Kerr metric background, a homogeneous integral equation related to the prolate spheroidal function is studied. From the consideration of the Fredholm determinant of the integral equation, a family of generalized error function is defined, with which the Fredholm determinant of the sinc kernel is also evaluated. An analytic solution of a special ease of the fifth Painlev~ transcendent is then worked out explicitly.
文摘In this research, we propose longitudinal generalised variance functions (LGVFs) to produceconvenient estimates of variances by incorporating time effect into modelling. Asymptoticproperties of some certain type of estimators are investigated. Simulation studies and implementation of the proposed methods to Current Population Survey (CPS) data show that LGVFswork well in producing standard error estimates.
