Avoiding 2-binomial squares and cubes

Two finite words $u,v$ are 2-binomially equivalent if, for all words $x$ of length at most 2, the number of occurrences of $x$ as a (scattered) subword of $u$ is equal to the number of occurrences of $x$ in $v$. This notion is a refinement of the usual abelian equivalence. A 2-binomial square is a word $uv$ where $u$ and $v$ are 2-binomially equivalent. In this paper, considering pure morphic words, we prove that 2-binomial squares (resp. cubes) are avoidable over a 3-letter (resp. 2-letter) alphabet. The sizes of the alphabets are optimal

Ship complexity assessment at the concept design stage

An innovative complexity metric is introduced that provides a way to compare similar or different ship types and sizes at the contract design stage. The goal is to provide the designer with this information throughout the design process so that an efficient design is obtained during the first design run. Application to and validation on real passenger ships indicate that there is a significant correlation between the error in an engineer's judgement of complexity and the cost assessment error. It follows that this tool could be used to improve knowledge of the ship's complexity at the contract design stage, and even to try to optimise the design if the complexity criteria are not fixed by the shipowners

Breadth-first serialisation of trees and rational languages

We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages corresponds to which class of words and,more specifically, using a known construction from numeration system theory, we prove that the signature of rational languages are substitutive sequences.Comment: 15 page

Maintenance/repair and production-oriented life cycle cost/earning model for ship structural optimisation during conceptual design stage

The aim of this paper is to investigate the effect of the change in structural weight due to optimisation experiments on life cycle cost and earning elements using the life cycle cost/earning model, which was developed for structure optimisation. The relation between structural variables and relevant cost/earning elements are explored and discussed in detail. The developed model is restricted to the relevant life cycle cost and earning elements, namely production cost, periodic maintenance cost, fuel oil cost, operational earning and dismantling earning. Therefore it is important to emphasise here that the cost/earning figure calculated through the developed methodology will not be a full life cycle cost/earning value for a subject vessel, but will be the relevant life cycle cost/earning value. As one of the main focuses of this paper is the maintenance/repair issue, the data was collected from a number of ship operators and was solely used for the purpose of regression analysis. An illustrative example for a chemical tanker is provided to show the applicability of the proposed approac

Synthesis and antigiardial activity of formononetin analogues

The synthesis and antigiardial activity of formononetin analogues is hereby reported. Formononetin, an isoflavone commonly obtained from the Leguminoseae family has previously been reported to possess antigiardial activity. In this paper, 10 analogues of formononetin were synthesized and tested for antigiardial activity. One compound was found to be active, 3 were moderately active and 6 were found to be inactive. All the 10 analogues were found to be inactive against other protozoa such as Trichomonas vaginalis and Tritrichomonas foetus.Keywords: Antigiardial, Formononetin, Activit