ON WEAK FILTER CONVERGENCE AND THE RADON-RIESZ TYPE THEOREM

The author shows a characterization of a （unbounded） weakly filter convergent sequence which is parallel to that every weakly null sequence （xn） in a Banach space admits a norm null sequence （yn） with yn ∈ co（xk）k≥n for all n ∈ N. A version of the Radon-Riesz type theorem is also proved within the frame of the filter convergence.

Modular Filter Convergence Theorems for Urysohn Integral Operators and Applications

We prove some versions of modular convergence theorems for nonlinear Urysohn-type integral operators with respect to filter convergence. We consider pointwise filter convergence of functions giving also some applications to linear and nonlinear Mellin operators. We show that our results are strict extensions of the classical ones.

Theoretical convergence analysis of complex Gaussian kernel LMS algorithm

With the vigorous expansion of nonlinear adaptive filtering with real-valued kernel functions,its counterpart complex kernel adaptive filtering algorithms were also sequentially proposed to solve the complex-valued nonlinear problems arising in almost all real-world applications.This paper firstly presents two schemes of the complex Gaussian kernel-based adaptive filtering algorithms to illustrate their respective characteristics.Then the theoretical convergence behavior of the complex Gaussian kernel least mean square（LMS） algorithm is studied by using the fixed dictionary strategy.The simulation results demonstrate that the theoretical curves predicted by the derived analytical models consistently coincide with the Monte Carlo simulation results in both transient and steady-state stages for two introduced complex Gaussian kernel LMS algonthms using non-circular complex data.The analytical models are able to be regard as a theoretical tool evaluating ability and allow to compare with mean square error（MSE） performance among of complex kernel LMS（KLMS） methods according to the specified kernel bandwidth and the length of dictionary.

Synthesis of the tetracyclic core of chlorospermines

Chlorospermines A and B are biologically interesting acridone natural products and recently isolated from Glycosmis chlorosperma.We report here a convergent approach to construct the tetracyclic core of the natural products.The two fragments are assembled together through Sonogashira coupling,and a cis-triene intermediate was prepared by using hydrosilylation/desilylation.A 6p-electrocyclization/aromatization sequence served as the key step of the synthesis,which formed the tetrasubstituted arene motif in one pot.