Gamma distribution nests exponential, chi-squared and Erlang distributions;while generalized Inverse Gaussian distribution nests quite a number of distributions. The aim of this paper is to construct a gamma mixture u...Gamma distribution nests exponential, chi-squared and Erlang distributions;while generalized Inverse Gaussian distribution nests quite a number of distributions. The aim of this paper is to construct a gamma mixture using Generalized inverse Gaussian mixing distribution. The </span><i><span style="font-family:Verdana;">rth</span></i><span style="font-family:Verdana;"> moment of the mixture is obtained via the </span><i><span style="font-family:Verdana;">rth</span></i><span style="font-family:Verdana;"> moment of the mixing distribution. Special cases and limiting cases of the mixture are deduced.展开更多
In this paper, we prove that, if 0【k【l, 2k=n, Ω R^n, u∈H^l(Ω), theSobolev inequality holds in limiting cases:LetWe consider the following problem:-△U_ρ~s(X)=W_ρ~s(x-b) in Ω, u_ρ~s(x)=0 on Γ.Let u_ρ(s)=max ...In this paper, we prove that, if 0【k【l, 2k=n, Ω R^n, u∈H^l(Ω), theSobolev inequality holds in limiting cases:LetWe consider the following problem:-△U_ρ~s(X)=W_ρ~s(x-b) in Ω, u_ρ~s(x)=0 on Γ.Let u_ρ(s)=max x∈Ω u_ρ~s(x). By(1), if s is increasing, the gradual change of W_ρ~s(x-b) givesrise to the sudden change of uρ(s). This sudden change occurs in the neighborhood ofs=2 for n≥2.展开更多
文摘Gamma distribution nests exponential, chi-squared and Erlang distributions;while generalized Inverse Gaussian distribution nests quite a number of distributions. The aim of this paper is to construct a gamma mixture using Generalized inverse Gaussian mixing distribution. The </span><i><span style="font-family:Verdana;">rth</span></i><span style="font-family:Verdana;"> moment of the mixture is obtained via the </span><i><span style="font-family:Verdana;">rth</span></i><span style="font-family:Verdana;"> moment of the mixing distribution. Special cases and limiting cases of the mixture are deduced.
基金This research was supported by the National Natural Science Foundation of China.
文摘In this paper, we prove that, if 0【k【l, 2k=n, Ω R^n, u∈H^l(Ω), theSobolev inequality holds in limiting cases:LetWe consider the following problem:-△U_ρ~s(X)=W_ρ~s(x-b) in Ω, u_ρ~s(x)=0 on Γ.Let u_ρ(s)=max x∈Ω u_ρ~s(x). By(1), if s is increasing, the gradual change of W_ρ~s(x-b) givesrise to the sudden change of uρ(s). This sudden change occurs in the neighborhood ofs=2 for n≥2.
