By utilizing symmetric functions,this paper presents explicit representations for Hermite interpolation and its numerical differentiation formula.And the corresponding error estimates are also provided.
Necessary and sufficient conditions for homogeneous polynomial functions of n variables of degree m with m odd, m=2 or m=4 to be Schur-concave on Rn are given.
In this note, we give comments on a very recent paper by J. S. Respondek [1]. In [1], the author claims that an algorithm in [2] contains a severe error. We show that the algorithm in [2] can be implemented properly w...In this note, we give comments on a very recent paper by J. S. Respondek [1]. In [1], the author claims that an algorithm in [2] contains a severe error. We show that the algorithm in [2] can be implemented properly without causing any errors by using vectors (one-dimensional arrays) rather than using 2-dimensional arrays. To enable users and programmers of the algorithm to carry out the computations using all existing subscripts and superscripts in the algorithm, we give a correction in the first line of the algorithm. A Maple implementation for the algorithm, as it is in [2], is given as an example for symbolic programming.展开更多
Exponential generalizations of Newman＇s inequality and Klamkin＇s inequality are established by the Wang Wan-lan＇s inequality, and they are extended to the cases involving general elementary symmetric functions. As ...Exponential generalizations of Newman＇s inequality and Klamkin＇s inequality are established by the Wang Wan-lan＇s inequality, and they are extended to the cases involving general elementary symmetric functions. As an application, some new inequalities for a simplex are established. In addition, an open problem is posed.展开更多
In this paper, we construct two classes of permutation polynomials over finite fields. First, by one well-known lemma of Zieve, we characterize one class permutation polynomials of the finite field, which generalizes ...In this paper, we construct two classes of permutation polynomials over finite fields. First, by one well-known lemma of Zieve, we characterize one class permutation polynomials of the finite field, which generalizes the result of Marcos. Second, by using the onto property of functions related to the elementary symmetric polynomial in multivariable and the general trace function, we construct another class permutation polynomials of the finite field. This extends the results of Marcos, Zieve, Qin and Hong to the more general cases. Particularly, the latter result gives a rather more general answer to an open problem raised by Zieve in 2010.展开更多
基金Supported by the Education Department of Zhejiang Province (Y200806015)
文摘By utilizing symmetric functions,this paper presents explicit representations for Hermite interpolation and its numerical differentiation formula.And the corresponding error estimates are also provided.
文摘Necessary and sufficient conditions for homogeneous polynomial functions of n variables of degree m with m odd, m=2 or m=4 to be Schur-concave on Rn are given.
文摘In this note, we give comments on a very recent paper by J. S. Respondek [1]. In [1], the author claims that an algorithm in [2] contains a severe error. We show that the algorithm in [2] can be implemented properly without causing any errors by using vectors (one-dimensional arrays) rather than using 2-dimensional arrays. To enable users and programmers of the algorithm to carry out the computations using all existing subscripts and superscripts in the algorithm, we give a correction in the first line of the algorithm. A Maple implementation for the algorithm, as it is in [2], is given as an example for symbolic programming.
文摘Exponential generalizations of Newman＇s inequality and Klamkin＇s inequality are established by the Wang Wan-lan＇s inequality, and they are extended to the cases involving general elementary symmetric functions. As an application, some new inequalities for a simplex are established. In addition, an open problem is posed.
基金Supported by the Research Initiation Fund for Young Teachers of China West Normal University(412679)
文摘In this paper, we construct two classes of permutation polynomials over finite fields. First, by one well-known lemma of Zieve, we characterize one class permutation polynomials of the finite field, which generalizes the result of Marcos. Second, by using the onto property of functions related to the elementary symmetric polynomial in multivariable and the general trace function, we construct another class permutation polynomials of the finite field. This extends the results of Marcos, Zieve, Qin and Hong to the more general cases. Particularly, the latter result gives a rather more general answer to an open problem raised by Zieve in 2010.
