Dissertations / Theses on the topic 'Regular semigroup'

There has been much interest in algebras which have a basis consisting of diagrams, which are multiplied in some natural diagrammatic way. Examples of these so-called diagram algebras include the partition, Brauer and Temperley-Lieb algebras. These three examples all have the property that the product of two diagram basis elements is always a scalar multiple of another basis element. Motivated by this observation, we find that these algebras are examples of twisted semigroup algebras. Such algebras are an obvious extension of twisted group algebras, which arise naturally in various contexts; examples include the complex numbers and the quaternions, considered as algebras over the real numbers. The concept of a cellular algebra was introduced in a famous paper of Graham and Lehrer; an algebra is called cellular if it has a basis of a certain form, in which case the general theory of cellular algebras allows us to easily derive information about the semisimplicity of the algebra and about its representation theory, even in the non-semisimple case. Many diagram algebras (including the above three examples) are known to be cellular. The aim of this thesis is to deduce the cellularity of these examples (and others) by proving a general result about the cellularity of twisted semigroup algebras. This will extend a recent result of East. In Chapters 2 and 3 we discuss semigroup theory and twisted semigroup algebras, and realise the above three examples as twisted semigroup algebras. Chapters 4 to 7 detail and extend slightly the theory of cellular algebras. In Chapter 8 we state and prove the main theorem, which shows that certain twisted semigroup algebras are cellular. Under the assumptions of the main theorem, we explore the cell representations of twisted semigroup algebras in Chapter 9. Finally in Chapter 10, we apply the theorem to various examples, including the three diagram algebras mentioned above.

Thesis (M.A.)--Kutztown University of Pennsylvania, 1994.
Source: Masters Abstracts International, Volume: 45-06, page: 3173. Abstract precedes thesis as [2] preliminary leaves. Typescript. Includes bibliographical references (leaves 52-53).

An e-pseudovariety is a class of finite regular semigroups closed under the taking of homomorphic images, regular subsemigroups and finite direct products. Chapter One consists of a survey of those results from algebraic semigroup theory, universal algebra and lattice theory which are used in the following two chapters. In Chapter Two, a theory of generalised existence varieties is developed. A generalised existence variety is a class of regular semigroups closed under the taking of homomorphic images, regular subsemigroups, finite direct products and arbitrary powers. Equivalently, a generalised e-variety is the union of a directed family of existence varieties. It is demonstrated that a class of finite regular semigroups is an e-pseudovariety if and only if the class consists only of the finite members of some generalised existence variety. The relationship between certain lattices of e-pseudovarieties and generalised existence varieties is explored and a usefu l complete surjective lattice homomorphism is found. A study of complete congruences on lattices of existence varieties and e-pseudovarieties forms Chapter Three. In particular it is shown that a certain meet congruence, whose description is relatively simple, can be extended to yield a complete congruence on a lattice of e-pseudovarieties of finite regular semigroups. Ultimately, theorems describing the method of construction of all complete congruences of lattices of e-pseudovarieties whose members are finite E-solid or locally inverse regular semigroups are proved.

The Generalised Star-Height Problem is an open question in the field of formal language theory that concerns a measure of complexity on the class of regular languages; specifically, it asks whether or not there exists an algorithm to determine the generalised star-height of a given regular language. Rather surprisingly, it is not yet known whether there exists a regular language of generalised star-height greater than one. Motivated by a theorem of Thérien, we first take a combinatorial approach to the problem and consider the languages in which every word features a fixed contiguous subword an exact number of times. We show that these languages are all of generalised star-height zero. Similarly, we consider the languages in which every word features a fixed contiguous subword a prescribed number of times modulo a fixed number and show that these languages are all of generalised star-height at most one. Using these combinatorial results, we initiate work on identifying the generalised star-height of the languages that are recognised by finite semigroups. To do this, we establish the generalised star-height of languages recognised by Rees zero-matrix semigroups over nilpotent groups of classes zero and one before considering Rees zero-matrix semigroups over monogenic semigroups. Finally, we explore the generalised star-height of languages recognised by finite groups of a given order. We do this through the use of finite state automata and 'count arrows' to examine semidirect products of the form A x Zr where A is an abelian group and Zr is the cyclic group of order r.

La 1ère partie traite des automates boustrophédons, du semi-groupe de Birget et du monoïde inversif libre. La 2ème partie étudie le comportement infini d'un automate boustrophédon, la 3ème partie est consacrée aux variétés de semi-groupes et aux mots infinis. La 4ème partie poursuit la classification des langages rationnels de mots infinis à l'aide des variétés des semi-groupes

The topic of this thesis is the class of weakly U-abundant semigroups. This class is very wide, containing inverse, orthodox, regular, ample, adequate, quasi-adequate, concordant, abundant, restriction, Ehresmann and weakly abundant semigroups. A semigroup $S$ with subset of idempotents U is weakly U-abundant if every $\art_U$-class and every $\elt_U$-class contains an idempotent of U, where $\art_U$ and $\elt_U$ are relations extending the well known Green's relations $\ar$ and $\el$. We assume throughout that our semigroups satisfy a condition known as the Congruence Condition (C). We take several approaches to weakly $U$-abundant semigroups. Our first results describe those that are analogous to completely simple semigroups. Together with an existing result of Ren this determines the structure of those weakly $U$-abundant semigroups that are analogues of completely regular semigroups, that is, they are superabundant. Our description is in terms of a semilattice of rectangular bands of monoids. The second strand is to aim for an extension of the Hall-Yamada theorem for orthodox semigroups as spined products of inverse semigroups and fundamental orthodox semigroups. To this end we consider weakly $B$-orthodox semigroups, where $B$ is a band. We note that if $B$ is a semilattice then a weakly $B$-orthodox semigroup is exactly an Ehresmann semigroup. We provide a description of a weakly $B$-orthodox semigroup $S$ as a spined product of a fundamental weakly $\overline{B}$-orthodox semigroup $S_B$ (depending only on $B$) and $S/\gamma_B$, where $\overline{B}$ is isomorphic to $B$ and $\gamma_B$ is the analogue of the least inverse congruence on an orthodox semigroup. This result is an analogue of the Hall-Yamada theorem for orthodox semigroups. In the case that $B$ is a normal band, or $S$ is weakly $B$-superabundant, we find a closed form $\delta_B$ for $\gamma_B$, which simplifies our result to a straightforward form. For the above to work smoothly in the case $S$ is weakly $B$-superabundant, we need to find a canonical fundamental weakly $B$-superabundant subsemigroup of $S_B$. This we do, and give the corresponding answers in the case of the Hall semigroup $W_B$ and a number of intervening semigroups. We then change our direction. A celebrated result of Nambooripad shows that regular semigroups are determined by ordered groupoids built over a regular biordered set. Our aim, achieved at the end of the thesis, is to extend Nambooripad's work to {\em weakly $U$-regular} semigroups, that is, weakly $U$-abundant semigroups with (C) and $U$ generating a regular subsemigroup whose set of idempotents is $U$. As an intervening step we consider weakly $B$-orthodox semigroups in this light. We take two approaches. The first is via a new construction of an inductive generalised category over a band. In doing so we produce a new approach to characterising orthodox semigroups, by using inductive generalised groupoids. We show that the category of weakly $B$-orthodox semigroups is isomorphic to the category of inductive generalised categories over bands. Our approach is influenced by that of Nambooripad, however, there are significant differences in strategy, the first being the introduction of generalised categories and the second being that it is more convenient to consider (generalised) categories equipped with pre-orders, rather than with partial orders. Our work may be regarded as extending a result of Lawson for Ehresmann semigroups. We also examine the trace of a weakly $B$-orthodox semigroup, which is a primitive weakly $B$-orthodox semigroup. We then take a more `traditional' approach to weakly $B$-orthodox semigroups via band categories and weakly orthodox categories over a band, equipped with two pre-orders. We show that the category of weakly $B$-orthodox semigroups is equivalent to the category of weakly orthodox categories over bands. To do so we must substantially adjust Armstrong's method for concordant semigroups. Finally, we consider the most general case of weakly $U$-regular semigroups. Following Nambooripad's theorem, which establishes a correspondence between algebraic structures (inverse semigroups) and ordered structures (inductive group-oids), we build a correspondence between the category of weakly $U$-regular semigroups and the category of weakly regular categories over regular biordered sets, equipped with two pre-orders.

In this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FA-presentable semigroups. We consider the properties of graph automatic semigroups, showing that they are independent of the choice of generating set, have decidable word problem, and that if we have a graph automatic structure for a semigroup then we can find one with uniqueness. Semigroup constructions and their effect on graph automaticity are considered. We show that finitely generated direct products, free products, finitely generated Rees matrix semigroup constructions, zero unions, and ordinal sums all preserve unary graph automaticity, and examine when the converse also holds. We also demonstrate situations where semidirect products, Bruck-Reilly extensions, and semilattice constructions preserve graph automaticity, and consider the conditions we may impose on such constructions in order to ensure that graph automaticity is preserved. Unary graph automatic semigroups, that is semigroups which have graph automatic structures over a single letter alphabet, are also examined. We consider the form of an automaton recognising multiplication by generators in such a semigroup, and use this to demonstrate various properties of unary graph automatic semigroups. We show that infinite periodic semigroups are not unary graph automatic, and show that we may always find a uniform set of normal forms for a unary graph automatic semigroup. We also determine some necessary conditions for a semigroup to be unary graph automatic, and use this to provide examples of semigroups which are not unary graph automatic. Finally we consider semigroup constructions for unary graph automatic semigroups. We show that the free product of two semigroups is unary graph automatic if and only if both semigroups are trivial; that direct products do not always preserve unary graph automaticity; and that Bruck-Reilly extensions are never unary graph automatic.

Cette thèse constitue un point de départ pour la programmation d'un système de calcul formel sur les automates, les semigroupes et les langages rationnels. On y trouve la caractérisation des automates construits selon l'algorithme de Glushkov. Des caractérisations de familles de langages testables à partir de leurs automates minimaux y sont également décrites. Le logiciel AGL regroupe un ensemble de packages Maple sur les automates, les semigroupes et les langages rationnels. L'ensemble des algorithmes déduits des caractérisations y est implémenté. Ce logiciel constitue un prototype pour un système de calcul formel dédié aux automates, aux semigroupes et aux langages rationnels.

Vollständig reguläre Halbgruppen weisen eine stark regelmäßige Struktur auf, die verschiedenste Zerlegungsmöglichkeiten gestatten. Ziel dieser Dissertation ist es, diese strukturelle Regelmäßigkeit auf Halbringe zu übertragen und die gewonnenen Algebren zu untersuchen. Mehrere Charakterisierungen werden herausgearbeitet, aufgrund derer es sich herausstellt, dass die Klasse aller vollständig regulären Halbringe eine Varietät bilden, deren Untervarietäten in der Folge untersucht werden. Zentrale Bedeutung haben dabei vollständig einfache Halbringe, deren Analyse einen der Schwerpunkte der Arbeit darstellt. Es zeigt sich, dass diese Bausteine vollständig regulärer Halbringe untereinander eine feste Struktur besitzen, selber aber auch als Zusammensetzung von isomorphen Halbringen aufgefasst werden können. Außerdem werden orthodoxe Halbringe, also Halbringe, deren idempotente Elemente einen Unterhalbring bilden, betrachtet. Zunächst wird dabei wieder auf mehrere Teilklassen eingegangen, bevor abschließend für beliebige vollständig reguläre Halbringe eine Beschreibung der kleinsten Kongruenz angegeben wird, deren Faktorhalbring orthodox ist.

Mestrado em Física Aplicada
O aproveitamento da energia gerada pelo Sol, inesgotável na escala terrestre de tempo, tanto como fonte de calor quanto de luz, é hoje, sem sombra de dúvida, uma das alternativas energéticas mais promissoras para enfrentar os desafios do novo milénio. E quando se fala em energia, deve-se lembrar que o Sol é responsável pela origem de praticamente todas as outras fontes de energia. Em outras palavras, as fontes de energia são derivadas da energia do Sol. Nesta tese é apresentado um estudo sobre o crescimento e caracterização de filmes finos de CuInSe2 de modo a desenvolver células fotovoltaicas. O semicondutor tipo-p (CuInSe2) é um material adequado para se utilizar como camada absorvente na preparação de uma célula solar de filme fino. Esse facto deve-se a possuir uma banda proibida de 1 e.V. e possuir um elevado coeficiente de absorção na zona do espectro solar. A sua dopagem do tipo-p é obtida tirando partido dos defeitos na estrutura cristalina resultantes de uma ligeira deficiência em Cu nos filmes. Assim pretendeu-se depositar filmes de CIS com uma razão entre os percursores de Cu:In~0.9. No Capítulo I é abordada a energia renovável como uma alternativa aos combustíveis fósseis, o mercado e a evolução da tecnologia fotovoltaica, o objectivo de trabalho desenvolvido e o estado da arte. No Capítulo II são abordados alguns conceitos teóricos fundamentais para compreender a preparação e o funcionamento de uma célula fotovoltaica baseada em silício. No Capítulo III é analisado o diagrama de fases do filme de CuInSe2 e a estrutura da calcopirite. São também abordadas as propriedades eléctricas e ópticas e a estrutura de CuInSe2 (CIS). No Capítulo IV são descritas as técnicas experimentais utilizadas na elaboração de células fotovoltaicas: a preparação do substrato, a elaboração da camada absorvente CIS (semicondutor tipo p), a deposição de CdS (semicondutor tipo n), a deposição de Óxido de Zinco (i-ZnO), para eliminar possíveis zonas de curto-circuito e, por fim, a deposição ITO que é a janela óptica da célula fotovoltaica. No Capítulo V são apresentados os resultados experimentais resultantes da caracterização dos filmes de CIS obtidos por selenização dos precursores Cu/In. Recorrendo às técnicas de SEM, EDS, Difracção de Raio-X e Espectroscopia Raman foi possível obter respostas sobre a morfologia da superfície/secção, composição e estrutura cristalina dos filmes. No Capítulo VI apresentam-se as principais conclusões do trabalho realizado. No Capítulo VII são sugeridos alguns estudos para um trabalho futuro. ABSTRACT: The use of the energy generated by the Sun, inexhaustible in the earth´s time scale, both as a source of heat and as a source of light, is today, without a shadow of a doubt, one of the more promising alternatives energy to face the challenges of the new millennium. It is also interesting to remember that the Sun is ultimately the source of most other sources of energy. In this thesis a study of the growth and characterization of thin films of CuInSe2 and the additional materials necessary for solar cell preparation is presented. In order to obtain CuInSe2 with p-type conductivity it is necessary to ensure some Cu deficiency to produce Cu vacancies in the chalcopyrite structure known to produce acceptor states. Therefore we aimed to achieve a precursor ratio of Cu:In~0.9. In the Chapter I the renewable energy as an alternative, the market and the evolution of the photovoltaic technology, the scope of this thesis and the state of art are presented. In the Chapter II the relevant concepts for the preparation and for the understanding of the operation of a silicon solar cell are presented. In the Chapter III the phase diagram of CuInSe2 film is analysed and the calcopirite structure. Also the optical and electrical properties are approached and the CuInSe2 (CIS) structure. In the Chapter IV the experimental techniques used in the course of the work were described. Different techniques were employed for each step of a cell preparation namely: the preparation of the substrate, the deposition of the CIS absorber layer, the deposition of CdS (n-type semiconductor), the deposition of intrinsic Zinc oxide (i-ZnO), to eliminate possible short circuit areas and, finally, the deposition of ITO that is the optical window of the solar cell. In the Chapter V the experimental results obtained through the analyses of CIS by SEM, EDS, X-ray diffraction and Raman Spectroscopy are presented and discussed. Important information on the morphology of the surface/crosssection, composition and crystalline structure of the films is thus obtained. In the Chapter VI the main conclusions of the work are presented. In the Chapter VII studies for a future work are suggested.

Nous étudions les semi-groupes de matrices avec des points de vue variés qui se re-coupent. Le point de vue de la croissance s'avère relié à un point de vue géométrique : nous avons partiellement généralisé aux semi-groupes un théorème de Patterson-Sullivan-Paulin sur les groupes, qui donne l'égalité entre exposant critique et dimension de Hausdorff de l'ensemble limite. Nous obtenons cela dans le cadre général des semi-groupes d'isométries d'un espace Gromov-hyperbolique, et notre preuve nous a permis d'obtenir également d'autres résultats nouveaux. Le point de vue informatique s'avère également relié à la croissance, puisque la notion de semi-groupe fortement automatique, que nous avons introduit, permet de calculer les exposants critiques exactes de semi-groupes de développement en base β. Et ce point de vue donne également beaucoup d'autres informations sur ces semi-groupes. Cette notion de croissance s'avère aussi reliée à des conjectures sur les fractions continues telles que celle de Zaremba. Et c'est en étudiant certains semi-groupes de matrices que nous avons pu démontrer des résultats sur les fractions continues périodiques bornées qui permettent de petites avancées dans la résolution d'une conjecture de McMullen.

As with groups, one can study the left regular representation of a semigroup. If one considers such representations, then it is natural to ask similar questions to the group case. We start by formulating several questions in the semigroup case and then work towards understanding the structure of the representations given. We present results describing what the elements of the image under the representation map can look like (the semigroup problem), whether or not two semigroups will give isomorphic representations (the isomorphism problem), and whether or not the representation of a semigroup is reflexive (the reflexivity problem). This research has been funded in part by a scholarship from the Natural Sciences and Engineering Research Council of Canada.

The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of suffix-, bifix-, and factor-free regular languages, star-free languages including three subclasses, and R- and J-trivial regular languages. We found upper bounds on the syntactic complexities of these classes of languages. For R- and J-trivial regular languages, the upper bounds are n! and ⌊e(n-1)!⌋, respectively, and they are tight for n >= 1. Let C^n_k be the binomial coefficient ``n choose k''. For monotonic languages, the tight upper bound is C^{2n-1}_n. We also found tight upper bounds for partially monotonic and nearly monotonic languages. For the other classes of languages, we found tight upper bounds for languages with small state complexities, and we exhibited languages with maximal known syntactic complexities. We conjecture these lower bounds to be tight upper bounds for these languages. We also observed that, for some subclasses C of regular languages, the upper bound on state complexity of the reversal operation on languages in C can be met by languages in C with maximal syntactic complexity. For R- and J-trivial regular languages, we also determined tight upper bounds on the state complexity of the reversal operation.

Ren Xueming.
"November 2001."
Thesis (Ph.D.)--Chinese University of Hong Kong, 2001.
Includes bibliographical references.
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Mode of access: World Wide Web.
Abstracts in English and Chinese.