Solitons in classical field theories correspond to states quantum theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads infrared divergences, which generally regularized via wave packets or by compactification. However, some applications both possibilities undesirable. In present note, we introduce a finite inner product on translation-invari...

In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of product, first show that each group is a torsion-free normed group. We give examples such and describe norms induced by products. Among other results, Hilbert groups, midconvex orthogonal subgroups are presented, Riesz representation theorem divisible proved.

The concept of fuzzy multiply positive BCC-ideals of BCC-algebras is introduced, and then some related results are obtained. Moreover, we introduce the concept of T -fuzzy multiply positive implicative BCC-ideals of BCC-algebras and investigate T -product of T -fuzzy multiply positive implicative BCC-ideals of BCC-algebras, examining its properties. Using a t-norm T , the direct product and T -...

The various fuzzy subgroups of a group which are admissible under operator domains are studied. In particular, the classes of all inner automorphisms, automorphisms, and endomorphisms are applied on the fuzzy subgroups of a group. As results, several theorems and examples concerning the fuzzy subgroups following from these kinds of operator domains are obtained. Moreover, we prove that a necess...