查看更多>>摘要：In this paper,we consider the limit distribution of the error density function estima-tor in the first-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as confidence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density"estimator"which contains errors.
查看更多>>摘要：Fermat's Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat's Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat's Last Theorem for multivariate(skew)-polynomials with any characteristic.
查看更多>>摘要：Consider a pseudo-differential operator Taf(x)=∫Rn eix·ξa(x,ξ)(f)(ξ)dξwhere the symbol a is in the rough Hörmander class L∞Smρ with m ∈ R and ρ ∈[0,1].In this note,when 1 ≤ p ≤ 2,if m＜n(ρ-1)/p and a ∈ L∞Smρ,then for any f ∈ S(Rn)and x ∈ Rn,we prove that M(Taf)(x)≤ C(M(|f|p)(x))1/p where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.
查看更多>>摘要：The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy-Riemann operator and CR functions on the Heisenberg group in the the-ory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We inves-tigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.
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