The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.
A new family of trigonometric summation polynomials, Gn,r（f; θ）, of Bernstein type is constructed. In contrast to other trigonometric summation polynomials, the convergence properties of the new polynomials are sup...A new family of trigonometric summation polynomials, Gn,r（f; θ）, of Bernstein type is constructed. In contrast to other trigonometric summation polynomials, the convergence properties of the new polynomials are superior to others. It is proved that Gn,r（f; θ） converges to arbitrary continuous functions with period 2π uniformly on （-∞ ＋∞） as n→ ∞. In particular, Gn,r（f; θ） has the best convergence order, and its saturation order is 1/n^2r＋4.展开更多
Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when the size of the ex...Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when the size of the experiment is relatively large. Suitably partitioning inhomogeneous units into homogeneous groups, known as blocks, is a practical design strategy. How to partition the experimental units for a given design is an important issue. The blocked general minimum lower order confounding is a new criterion for selecting blocked designs. With the help of doubling theory and second order saturated design, we present a theory on constructing optimal blocked designs under the blocked general minimum lower order confounding criterion.展开更多
基金This work is supported by the Doctor Foundation (No:02.T20102-06) and the Post Doctor Foundation of Ningbo University.
文摘The 'o' saturation theorem and the degree of Lwp, approximation by (0 - q' - q) type Hermite-Fejer interpolating polynomials for mean convergence are obtained.
文摘A new family of trigonometric summation polynomials, Gn,r（f; θ）, of Bernstein type is constructed. In contrast to other trigonometric summation polynomials, the convergence properties of the new polynomials are superior to others. It is proved that Gn,r（f; θ） converges to arbitrary continuous functions with period 2π uniformly on （-∞ ＋∞） as n→ ∞. In particular, Gn,r（f; θ） has the best convergence order, and its saturation order is 1/n^2r＋4.
文摘Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when the size of the experiment is relatively large. Suitably partitioning inhomogeneous units into homogeneous groups, known as blocks, is a practical design strategy. How to partition the experimental units for a given design is an important issue. The blocked general minimum lower order confounding is a new criterion for selecting blocked designs. With the help of doubling theory and second order saturated design, we present a theory on constructing optimal blocked designs under the blocked general minimum lower order confounding criterion.
