This problem was solved in the negative by Bridson and Grunewald in [6] who produced many examples of groups G, and proper subgroups H for which û an isomorphism. The method of proof of [6] was a far reaching generalization of an example of Platonov and Tavgen [33] that produced finitely generated examples that answered Grothendieck’s problem in the negative (see also [5]). Henceforth, we will ...

We prove that if q is a power of a prime p and p divides a, with k ≥ 0, then 1 + (q − 1) ∑ 0≤b(q−1)<a ( a b(q − 1) ) ≡ 0 (mod p). The special case of this congruence where q = p was proved by Carlitz in 1953 by means of rather deep properties of the Bernoulli numbers. A more direct approach produces our generalization and several related results.

The efficient and flexible incorporating of decision procedures into theorem provers is very important for their successful use. There are several approaches for combining and augmenting of decision procedures; some of them support handling uninterpreted functions, congruence closure, lemma invoking etc. In this paper we present a variant of one general setting for building decision procedures ...

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...

This article celebrates the 50th anniversary of the introduction of John L. Holland's (1959) theory of vocational personalities and work environments by describing the theory's development and evolution, its instrumentation, and its current status. Hallmarks of Holland's theory are its empirical testability and its user-friendliness. By constructing measures for operationalizing the theory's co...

This paper considers how the Internet can be used to leverage commercial sponsorships to enhance audience attitudes toward the sponsor. Definitions are offered that distinguish the terms leverage and activation with respect to sponsorship-linked marketing; leveraging encompasses all marketing communications collateral to the sponsorship investment, whereas activation relates to those communicat...

We present a generalization of a result due to Thuswaldner and Tichy to the ring of polynomials over a finite fields. In particular we want to show that every polynomial of sufficiently large degree can be represented as sum of k-th powers, where the bases evaluated on additive functions meet certain congruence restrictions.