Unified theory of gravitational interactions and electromagnetic interactions is discussed in this paper. Based on gauge principle, electromagnetic interactions and gravitational interactions are formulated in the same manner and are unified in a semi-direct product group of U(1) Abel gauge group and gravitational gauge group. email address: [email protected] mailing address

2 The “algebra” K[[x]] ⋊ M of formal power series under multiplication and substitution 3 2.1 Basics on formal power series . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 “Algebra” of formal power series under substitution . . . . . . . . . . . . 4 2.2.1 Right-distributive algebras . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Substitution of formal power series . . . . . . . . . ....

2 The Riordan skew algebra K[[x]] ⋊ M of formal power series under multiplication and substitution 3 2.1 Basics on formal power series . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Skew algebra of formal power series under substitution . . . . . . . . . . 4 2.2.1 Right-distributive algebras . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Substitution of formal power series . . . . ....

In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitational interactions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basis and are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamental interactions of Nature. email address: [email protected]...

If W is an infinite rank 3 Coxeter group, whose Coxeter diagram has no infinite bonds, then the automorphism group of W is generated by the inner automorphisms and any automorphisms induced from automorphisms of the Coxeter diagram. Indeed Aut(W ) is the semi-direct product of Inn(W ) and the group of graph automorphisms.

A quantum algorithm for the Hidden Subgroup Problem over the group Z/pZ o Z/qZ is presented. This algorithm, which for certain parameters of the group qualifies as ‘efficient’, generalizes prior work on related semi-direct product groups. 1998 ACM Subject Classification F.1.2 Modes of Computation, F.2.2 Nonnumerical Algorithms and Problems

We give an algorithm for enumerating cosets of a group defined as a finite homomorphic image of a semi-direct product of free products of cyclic groups by a group of monomial automorphisms. Lots of finite groups, including some of the sporadic simple groups can be defined in this mannar. Mathematics Subject Classification: 20Bxx

The family of rational subsets of a direct product of free monoids Σ∗ 1×. . .×Σ ∗ n (the rational relations) is not closed under Boolean operations, except when n = 1 or when all Σi’s are empty or singletons. In this paper we introduce the family of generalized rational subsets of an arbitrary monoid as the closure of the singletons under the Boolean operations, concatenation and Kleene star (j...

Strictly positive definite functions are used as basis functions for approximation methods in various contexts. Using a group theoretic interpretation of Bochner’s Theorem we give a sufficient condition for strictly positive definite functions on a semi-direct product which are invariant under the natural action of a given subgroup. As an application strictly positive definite, reflection invar...

The microwave spectrum of 2,5-dimethylthiophene, a sulfur-containing five-membered ring with two conjugated double bonds, was recorded in the frequency range from 2 to 40 GHz using molecular beam Fourier transform technique. Highly accurate molecular parameters were determined. A labeling scheme for the group G36 written as the semi-direct product (C(I)(3) × C(I)(3)) ⋊ C(2v) was introduced.