Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cu...Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on [-1,1]^2, as well as new results on [-1, 1]^3. In particular, compact formulas for the fundamental interpolation polynomials are derived, based on n3/4 ＋ O（n^2） nodes of a cubature formula on [-1,1]^3.展开更多
Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed...Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.展开更多
Let G be a connected semisimple Lie group with a maximal compact group K of equal rank. We use the Dirac cohomology of the unitary representations to define Dirac-induction from a representation of K to the discrete s...Let G be a connected semisimple Lie group with a maximal compact group K of equal rank. We use the Dirac cohomology of the unitary representations to define Dirac-induction from a representation of K to the discrete series of G. This is closely related to the Dirac induction for the reduced group C*-algebras C*red (G) and a geometric construction of discrete series for semisimple Lie groups. Furthermore, we use Dirac cohomology of the Kostant's cubic Dirac operator to define Dirac-induction for compact Lie groups. This induction for compact Lie groups is simpler than the Bott's induction and is easier for calculation.展开更多
基金supported by NSFC Grants 10601056,10431050 and 60573023supported by National Basic Research Program grant 2005CB321702supported by NSF Grant DMS-0604056.
文摘Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on [-1,1]^2, as well as new results on [-1, 1]^3. In particular, compact formulas for the fundamental interpolation polynomials are derived, based on n3/4 ＋ O（n^2） nodes of a cubature formula on [-1,1]^3.
文摘Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.
基金supported by research grants from the Research Grant Council of HKSAR, China
文摘Let G be a connected semisimple Lie group with a maximal compact group K of equal rank. We use the Dirac cohomology of the unitary representations to define Dirac-induction from a representation of K to the discrete series of G. This is closely related to the Dirac induction for the reduced group C*-algebras C*red (G) and a geometric construction of discrete series for semisimple Lie groups. Furthermore, we use Dirac cohomology of the Kostant's cubic Dirac operator to define Dirac-induction for compact Lie groups. This induction for compact Lie groups is simpler than the Bott's induction and is easier for calculation.
