Let {Ak}k=1? be a sequence of finite subsets Rd satisfying that #Ak?2 for all integers k?1. In this paper, we first give sufficient and necessary condition the existence infinite convolution?=?A1??A2????An??, where sets Ak?R+d ?A=1#A?a?A?a. Then study spectrality class convolutions generated by Hadamard triples in R construct singular spectral measures without compact support. Finally show such...

This paper deals with a family of balanced implicit methods for the stochastic delay integro-differential equations. It is shown that the balanced methods, which own the implicit iterative scheme in the diffusion term, give strong convergence rate of at least 1/2. It proves that the mean-square stability for the stochastic delay integro-differential equations is inherited by the strong balanced...