Recently people proved that every f∈C[0, 1] can be uniformly approximated by polynomial sequences {P_n}, {Q_n} such for any x∈[0,1] and n=1,2,…that Q_n(x)<Q_(n+1)(x)<f(x)<P_(n+1)(x)<P_n(x). For example...Recently people proved that every f∈C[0, 1] can be uniformly approximated by polynomial sequences {P_n}, {Q_n} such for any x∈[0,1] and n=1,2,…that Q_n(x)<Q_(n+1)(x)<f(x)<P_(n+1)(x)<P_n(x). For example, Xie and Zhou showed that one can construct such monotone polynomial sequences which do achieve the best uniform approximation rate for a continuous func- tion. Actually they obtained a result as ‖P_n(x)-Q_n(x)‖≤42E_n (f), (1) which essentially improved a conclusion in Gal and Szabados. The present paper, by optimal procedure, improves this inequality to ‖[P_n(x)-Q_n(x)‖≤(18+ε)E_n(f), where εis any positive real number.展开更多
The involvement of small RNAs in cotton fiber development is under explored.The objective of this work was to directly clone,annotate,and analyze small RNAs of developing ovules to reveal
Taking Deyang as an example of middle and small city, this paper analysesmain factors related to industry development, constructs an appropriateAnalytic Hierarchy Process (AHP) model, and finally obtains the priordeve...Taking Deyang as an example of middle and small city, this paper analysesmain factors related to industry development, constructs an appropriateAnalytic Hierarchy Process (AHP) model, and finally obtains the priordevelopment sequence of major industries of Deyang.展开更多
文摘Recently people proved that every f∈C[0, 1] can be uniformly approximated by polynomial sequences {P_n}, {Q_n} such for any x∈[0,1] and n=1,2,…that Q_n(x)<Q_(n+1)(x)<f(x)<P_(n+1)(x)<P_n(x). For example, Xie and Zhou showed that one can construct such monotone polynomial sequences which do achieve the best uniform approximation rate for a continuous func- tion. Actually they obtained a result as ‖P_n(x)-Q_n(x)‖≤42E_n (f), (1) which essentially improved a conclusion in Gal and Szabados. The present paper, by optimal procedure, improves this inequality to ‖[P_n(x)-Q_n(x)‖≤(18+ε)E_n(f), where εis any positive real number.
文摘The involvement of small RNAs in cotton fiber development is under explored.The objective of this work was to directly clone,annotate,and analyze small RNAs of developing ovules to reveal
文摘Taking Deyang as an example of middle and small city, this paper analysesmain factors related to industry development, constructs an appropriateAnalytic Hierarchy Process (AHP) model, and finally obtains the priordevelopment sequence of major industries of Deyang.
