By using the simplified method of factorization given by Valli, and the correspondence between the harmonic map φ∶S 2→U(N) and U(N) uniton bundle ν(φ) with energy corresponding to the bundles’ seco...By using the simplified method of factorization given by Valli, and the correspondence between the harmonic map φ∶S 2→U(N) and U(N) uniton bundle ν(φ) with energy corresponding to the bundles’ second Chern class, which is established by Anand, the energy in a case φ∶S 2→U(N) is investigated in order to estimate the energy of a uniton using the uniton number. It is proved that Uhlenbeck’s factorization is energy decreasing. And a method of estimating the energy of a uniton by the uniton number is given.展开更多
A diagnostic procedure based on maximum likelihood estimation, to study the convergence of the Markov chain produced by Gibbs sampler, is presented. The unbiasedness, consistent and asymptotic normality are considered...A diagnostic procedure based on maximum likelihood estimation, to study the convergence of the Markov chain produced by Gibbs sampler, is presented. The unbiasedness, consistent and asymptotic normality are considered for the estimation of the parameters produced by the procedure. An example is provided to illustrate the procedure, and the numerical result is consistent with the theoretical one.展开更多
文摘By using the simplified method of factorization given by Valli, and the correspondence between the harmonic map φ∶S 2→U(N) and U(N) uniton bundle ν(φ) with energy corresponding to the bundles’ second Chern class, which is established by Anand, the energy in a case φ∶S 2→U(N) is investigated in order to estimate the energy of a uniton using the uniton number. It is proved that Uhlenbeck’s factorization is energy decreasing. And a method of estimating the energy of a uniton by the uniton number is given.
文摘A diagnostic procedure based on maximum likelihood estimation, to study the convergence of the Markov chain produced by Gibbs sampler, is presented. The unbiasedness, consistent and asymptotic normality are considered for the estimation of the parameters produced by the procedure. An example is provided to illustrate the procedure, and the numerical result is consistent with the theoretical one.
