The product on smooth and generalized valuations

Valuations and Generalized Hypersubstitutions

Generalized hypersubstitutions were introduced by S. Leeratanavalee and K. Denecke as a way of making precise the concepts of strong hyperidentity and M strong hyperidentity. A variety V is called M strongly solid if every identity of V is an M strong hyperidentity. We produce a monoid M for which the k-normalized variety Nv k (V ) of an N -strongly solid variety V with respect to a valuation v...

On Generalized Smooth Groups

On 3-adic Valuations of Generalized Harmonic Numbers

We investigate 3-adic valuations of generalized harmonic numbers H n . These valuations are completely determined by the 3-adic expansion of n. Moreover, we also give 3-adic valuations of generalized alternating harmonic numbers.

Antimagic valuations of generalized Petersen graphs

A connected graph G is said to be (a, d)-antimagic, for some positive integers a and d, if its edges admit a labeling by the integers 1,2, ... , IE( G) I such that the induced vertex labels consist of an arithmetic progression with the first term a and the common difference d. In this paper we prove that the generalized Petersen graph P(n,2) is (3n2+6, 3)-antimagic for n == 0 (mod 4), n ~ B.

on translation of phatic communion and socio-cultural relationships between the characters of the novels

phatic communion is a cultural concept which differs across cultures. according to hofstede (2001), the u.s. tends to have individualistic culture; however, asian countries tend to have collectivistic cultures. these cultures view phatic communion differently. in individualistic cultures like u.s., phatic communion reflects speakers’ socio-cultural relationships in conversations. to see whether...