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Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N ∪ {0}. The p-adic absolute value on Cp is normalized so that |p|p 1/p. Assume that q ∈ Cp(More)
We derive eight basic identities of symmetry in three variables related to Euler polynomials and alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundances of symmetries shed new light even on the existing identities so as to yield some further(More)
and Applied Analysis 3 The Hermite polynomials are given by Hn x H 2x n n ∑ l 0 ( n l ) 2xHn−l, 1.11 see 23, 24 , with the usual convention about replacing H by Hn. In the special case, x 0, Hn 0 Hn are called the nth Hermite numbers. From 1.11 , we note that d dx Hn x 2n H 2x n−1 2nHn−1 x , 1.12 see 23, 24 , and Hn x is a solution of Hermite differential(More)
In this paper, a home network message specification for white goods based on power line communication is proposed. It is designed for white goods such as air conditioners, refrigerators, washing machines, etc. The proposed home network message specification is composed of a virtual device service and a device-specific attribute. For practical(More)
Let P = n11 ⊕ · · · ⊕ nt1 be the poset given by the ordinal sum of the antichains ni1 with ni elements. Then we consider the P-weight enumerator for the linear code C of length n (n = n1 + · · · + nt) over Fq on P, and derive a MacWilliams-type identity relating the weight enumerator for the dual code C⊥ of C on P and that for C on the dual poset 5 P of P.(More)