Let H be a Krull monoid with finite class group where every class contains some prime divisor. It is known that every set of lengths is an almost arithmetical multiprogression. We investigate which integers occur as differences of these progressions. In particular, we obtain upper bounds for the size of these differences. Then, we apply these results to show that, apart from one known exception...

Let H be a Krull monoid with class group G and suppose that each class contains a prime divisor. Then every element a ∈ H has a factorization into irreducible elements, and the set L(a) of all possible factorization lengths for a is the set of lengths of a. We consider the system L(H) = {L(a) | a ∈ H} of all sets of lengths, and we characterize (in terms of the class group G) when L(H) is addit...

determination of allowable free span length plays a crucial role in design of offshore pipelines. the seabed intervention cost and safety of an offshore pipelines project are largely influenced by pipelines free spanning during the project life time. different criteria are proposed by both the current designing guidelines and researchers there is however lack of comprehensive assessment of inde...

Variable-length codes are the bases of the free submonoids of a free monoid. There are some important longstanding open questions about the structure of finite maximal codes. In this paper we discuss this conjectures and their relations with factorizations of cyclic groups.

after springs production, different residual stresses are created in the inner and outer surfaces of spring wires. some of these stresses for example compressive residual stresses are useful and some are harmful. the effects of vareation of these stresses are caused spring relaxation and decrising in their free length when they are loaded intermittently. for review this phenomena in this resear...

We propose a new type of regulation on the derivation of a context-free grammar: the productions used for passing from a level of a derivation tree to the next level should have the right-hand members of the same length. We prove that such length synchronized context-free grammars characterize the family of ET0L languages, and therefore are equivalent with the synchronization context-free gramm...