On Univalent Functions in Multiply Connected Domains

The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.

Health status assessment of axial piston pump under variable speed

The axial piston pump usually works under variable speed conditions.It is important to evaluate the health status of the axial piston pump under the variable speed condition.Aiming at the characteristic signals obtained under different wear levels of the port plate,a feature signal extraction method under variable speed conditions is proposed.Firstly,the combination of complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)energy spectrum and fast spectral kurtosis principle is used to accurately extract the intrinsic mode function(IMF)component containing the sensitive information of the degraded feature.Then,the aspect ratio analysis method of the angle domain variational mode decomposition(VMD)is used to process the feature index containing the sensitive information of the degraded feature.In order to evaluate the health status of the axial piston pump under variable speed,the vibration reliability analysis method for axial piston pump based on Weibull proportional failure rate model is proposed.The experimental results show that the proposed method can accurately evaluate the health status of the axial piston pump.