Green's Relations in Finite Transformation Semigroups

We consider the complexity of Green's relations when the semigroup is given by transformations on a finite set. Green's relations can be defined by reachability in the (right/left/two-sided) Cayley graph. The equivalence classes then correspond to the strongly connected components. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of magnitude as the number of elements. Another important parameter is the maximal length of a chain of components. Our main contribution is an exponential lower bound for this parameter. There is a simple construction for an arbitrary set of generators. However, the proof for constant alphabet is rather involved. Our results also apply to automata and their syntactic semigroups.Comment: Full version of a paper submitted to CSR 2017 on 2016-12-1

An Algebraic Approach to Mso-Definability on Countable Linear Orderings

We develop an algebraic notion of recognizability for languages of words indexed by countable linear orderings. We prove that this notion is effectively equivalent to definability in monadic second-order (MSO) logic. We also provide three logical applications. First, we establish the first known collapse result for the quantifier alternation of MSO logic over countable linear orderings. Second, we solve an open problem posed by Gurevich and Rabinovich, concerning the MSO-definability of sets of rational numbers using the reals in the background. Third, we establish the MSO-definability of the set of yields induced by an MSO-definable set of trees, confirming a conjecture posed by Bruyère, Carton, and Sénizergues

Estudio de necesidades de residencialización de la margen izquierda de la ría del Nervión

El presente estudio está contenido en una comunicación presentada en las I Jornadas de Gerontología Psicosocial del País Vasco, celebradas en Bergara, los días 23 y 24 de Junio de 1995.En él se pretende localizar las necesidades de residencialización de la Margen Izquierda de la Ría del Nervión. Las conclusiones son expuestas por colectivos atendidos: tercera edad, minusválidos físicos, enfermos convalecientes, infancia, juventud y sin techo

Nitrogen Response of Spring and Winter Wheat to Biosolids Compared to Chemical Fertiliser

Irish sewage sludge production was over 30,000 t/year in the 1990s (EPA, Ireland, 2003). Application to agricultural land is a management option for this organic material as it results in the recycling of the nutrients they contain for crop production. The EU Directive (91/271/EEC) encourages the recycling of sewage sludge as biosolids to agriculture. However, up to 1999, only about 5 % of biosolids produced was applied to agricultural land. In this study, several biosolids and a chemical fertiliser were used to assess N availability for spring and winter wheat (Triticum aestivum,) production in a pot experiment

Определение оптимальных параметров источника рентгеновского излучения на базе малогабаритного ускорителя электронов

Проведено моделирование спектров рентгеновского излучения, генерируемого электронами с энергией 4…10 МэВ в мишенях из различных материалов и разной толщины. Определены оптимальные параметры мишени-конвертора для использования ее в медицинских источниках монохроматического рентгеновского излучения на базе малогабаритных электронных ускорителей. Проведены оценки интенсивности излучения и сравнение источников на базе разных ускорителей

The Effect of Agricultural Practices on a Dairy Farm on Nitrate Leaching to 1m

Dairy farms, in Ireland, carry the highest stock densities and use the highest rates of fertiliser nitrogen (N). They constitute the highest risk of nitrate leaching, especially where soils are thin or free-draining. The effect of 4 grass managements on leaching was studied on a dairy farm having free-draining soils overlying Karst limestone. This was a new, farm-comprehensive approach to nitrate leaching which had not been carried out previously

Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis

The classic approaches to synthesize a reactive system from a linear temporal logic (LTL) specification first translate the given LTL formula to an equivalent omega-automaton and then compute a winning strategy for the corresponding omega-regular game. To this end, the obtained omega-automata have to be (pseudo)-determinized where typically a variant of Safra's determinization procedure is used. In this paper, we show that this determinization step can be significantly improved for tool implementations by replacing Safra's determinization by simpler determinization procedures. In particular, we exploit (1) the temporal logic hierarchy that corresponds to the well-known automata hierarchy consisting of safety, liveness, Buechi, and co-Buechi automata as well as their boolean closures, (2) the non-confluence property of omega-automata that result from certain translations of LTL formulas, and (3) symbolic implementations of determinization procedures for the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular, we present convincing experimental results that demonstrate the practical applicability of our new synthesis procedure

Recognisable languages over monads

The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of composing structures into bigger structures. It so happens that category theory has an abstract concept for this, namely a monad. The goal of this paper is to propose monads as a unifying framework for discussing existing algebras and designing new algebras

Structure of a 30S pre-initiation complex stalled by GE81112 reveals structural parallels in bacterial and eukaryotic protein synthesis initiation pathways

In bacteria, the start site and the reading frame of the messenger RNA are selected by the small ribosomal subunit (30S) when the start codon, typically an AUG, is decoded in the P-site by the initiator tRNA in a process guided and controlled by three initiation factors. This process can be efficiently inhibited by GE81112, a natural tetrapeptide antibiotic that is highly specific toward bacteria. Here GE81112 was used to stabilize the 30S pre-initiation complex and obtain its structure by cryo-electron microscopy. The results obtained reveal the occurrence of changes in both the ribosome conformation and initiator tRNA position that may play a critical role in controlling translational fidelity. Furthermore, the structure highlights similarities with the early steps of initiation in eukaryotes suggesting that shared structural features guide initiation in all kingdoms of life