tailieunhanh - Báo cáo hóa học: "VISCOELASTIC FRICTIONLESS CONTACT PROBLEMS WITH ADHESION"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: VISCOELASTIC FRICTIONLESS CONTACT PROBLEMS WITH ADHESION | A NOTE ON EULER NUMBER AND POLYNOMIALS LEE-CHAE JANG SEOUNG-DONG KIM DAL-WON PARK AND YOUNG-SOON RO Received 21 September 2004 Accepted 16 October 2005 We investigate some properties of non-Archimedean integration which is defined by Kim. By using our results in this paper we can give an answer to the problem which is introduced by . Huang and . Huang in 1999. Copyright 2006 Lee-Chae Jang et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Throughout this paper Zp Qp and Cp will respectively denote the ring of p-adic rational integers the field of p-adic rational numbers and the completion of algebraic closure of Qp. Let Vp be the normalized exponential valuation of Cp with Ip p p-vp p p-1. Let p be a fixed prime number and let l be a fixed integer with p l 1. We set X fim Z lpN Z N X u a lpZp 0 a lp a p l a lpNZp x G X I x a modlpN where a G Z lies in 0 a lpN cf. 3 4 . For any positive integer N we set Ma lpN Zp -1 lp and this can be extended to a distribution on X see 3 9 . Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2006 Article ID 34602 Pages 1-5 DOI JIA 2006 34602 2 A note on Euler number and polynomials This distribution yields an integral for nonnegative integer m xmdạ1 x Bm X where Bm are called usual Bernoulli numbers cf. 8 . The Euler numbers Em are defined by the generating function in the complex number field as follows 2 _ tm e 1 m m m 0 Iti n where we use the technique method notation by replacing Em by Em m 0 symbolli-cally cf. 3 5 7 9 10 . The Bernoulli numbers with order k B jk were defined by V z B nk cf. 5 10 . et - 1 n 0 n Let u be algebraic in complex number field. Then Frobenius-Euler numbers were defined by 1-u et - u í Hn u n 0 n cf. 5 . By and note that Hn -1 En. In this paper we .