Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + ...Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.展开更多
目的在临床随访研究中,基于时间尺度指标的限制平均生存时间(restricted mean survival time,RMST)越来越受到关注,然而目前基于RMST的统计推断主要用于两组比较,缺少进行两组以上比较的方法。方法本文提出RMST多组间的假设检验法,包括...目的在临床随访研究中,基于时间尺度指标的限制平均生存时间(restricted mean survival time,RMST)越来越受到关注,然而目前基于RMST的统计推断主要用于两组比较,缺少进行两组以上比较的方法。方法本文提出RMST多组间的假设检验法,包括经典法(naive)、对数转换法(log)、双对数转换法(cloglog)三种检验法,并通过Monte Carlo模拟评价其Ⅰ类错误和检验效能,最后进行实例分析。结果综合Monte Carlo模拟的Ⅰ类错误及检验效能结果,显示所提出的RMST检验可以处理多组比较的问题,特别是cloglog转换法最为稳健。结论针对生存数据的多组比较问题,若考虑从时间尺度指标分析,推荐使用cloglog转换法的RMST多组检验。展开更多
文摘Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.
基金国家电网公司科技项目(<提高特高压互感器可靠性技术研究>)(合同编号EPRIGYKJ[2012]4939号)Science and Technology Project of the State Grid Corporation of China("Research to Improve the Reliability of UHV Instrument Transformer")(No.EPRIGYKJ[2012]4939)
