No description available.

Thesis (Dr. rer. nat.)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2001. / Includes bibliographical references (p. 87-90).

A group whose co-word problem is a context free language is called coCF. Lehnert's conjecture states that a group G is coCF if and only if G embeds as a finitely generated subgroup of R. Thompson's group V. In this thesis we explore a class of groups, Faug, proposed by Berns-Zieze, Fry, Gillings, Hoganson, and Mathews to contain potential counterexamples to Lehnert's conjecture. We create infinite and finite presentations for such groups and go on to prove that a certain subclass of Faug consists of groups that do embed into V. By Anisimov a group has regular word problem if and only if it is finite. It is also known that a group G is finite if and only if there exists an embedding of G into V such that its natural action on C₂:= {0,1}^w is free on the whole space. We show that the class of groups with a context free word problem, the class of CF groups, is precisely the class of finitely generated demonstrable groups for V. A demonstrable group for V is a group G which is isomorphic to a subgroup in V whose natural action on C₂ acts freely on an open subset. Thus our result extends the correspondence between language theoretic properties of groups and dynamical properties of subgroups of V. Additionally, our result also shows that the final condition of the four known closure properties of the class of coCF groups also holds for the set of finitely generated subgroups of V.

This thesis studies subsemigroups of groups from three perspectives: automatic structures, ordinary semigroup presentations, and Malcev presentaions. [A Malcev presentation is a presentation of a special type for a semigroup that can be embedded into a group. A group-embeddable semigroup is Malcev coherent if all of its finitely generated subsemigroups admit finite Malcev presentations.] The theory of synchronous and asynchronous automatic structures for semigroups is expounded, particularly for group-embeddable semigroups. In particular, automatic semigroups embeddable into groups are shown to inherit many of the pleasant geometric properties of automatic groups. It is proved that group- embeddable automatic semigroups admit finite Malcev presentations, and such presentations can be found effectively. An algorithm is exhibited to test whether an automatic semigroup is a free semigroup. Cancellativity of automatic semigroups is proved to be undecidable. Study is made of several classes of groups: virtually free groups; groups that satisfy semigroup laws (in particular [virtually] nilpotent and [virtually] abelian groups); polycyclic groups; free and direct products of certain groups; and one-relator groups. For each of these classes, the question of Malcev coherence is considered, together with the problems of whether finitely generated subsemigroups are finitely presented or automatic. This study yields closure and containment results regarding the class of Malcev coherent groups. The property of having a finite Malcev presentation is shown to be preserved under finite Rees index extensions and subsemigroups. Other concepts of index are also studied.

We begin our study of amalgamations by examining some ideas which are well-known for the category of R-modules. In particular we look at such notions as direct limits, pushouts, pullbacks, tensor products and flatness in the category of S-sets. Chapter II introduces the important concept of free extensions and uses this to describe the amalgamated free product. In Chapter III we define the extension property and the notion of purity. We show that many of the important notions in semigroup amalgams are intimately connected to these. In Section 2 we deduce that 'the extension property implies amalgamation' and more surprisingly that a semigroup U is an amalgamation base if and only if it has the extension property in every containing semigroup. Chapter IV revisits the idea of flatness and after some technical results we prove a result, similar to one for rings, on flat amalgams. In Chapter V we show that the results of Hall and Howie on perfect amalgams can be proved using the same techniques as those used in Chapters III and IV. We conclude the thesis with a look at the case of rings. We show that almost all of the results for semi group amalgams examined in the previous chapters, also hold for ring amalgams.

The lattice of equational classes of idempotent semigroups is completely described. It is shown that every equational class of idempotent semigroups is determined by a single equation (in addition to the associative and idempotent equations). A method is presented for finding which class a given equation determines, and when the class determined by one equation is contained in the class determined by a second equation. / Thesis / Doctor of Philosophy (PhD)

We consider the problem of controlling a thermal convection flow by feedback. The system is governed by the Boussinesq approximation of the coupled set of Navier-Stokes and heat equations. The control is applied through Dirichlet boundary conditions. We concentrate on a two-dimensional mode and use a semidiscrete Galerkin scheme for numerical computations. We construct both a linear control and a non-linear quadratic control and apply them to the full non-linear model. First, we test these controllers on a one-mode approximation. The convergence of the numerical scheme is analyzed. We also consider LQR control for a two-dimensional heat equation. / Ph. D.

Geometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure. One such property is finite presentability. In geometric group theory, the geometric structure of choice is the Cayley graph of the group. It is known that in group theory finite presentability is an invariant under quasi-isometry of Cayley graphs. We choose to associate a metric space to a semigroup based on a Cayley graph of that semigroup. This metric space is constructed by removing directions, multiple edges and loops from the Cayley graph. We call this a skeleton of the semigroup. We show that finite presentability of certain types of direct products, completely (0-)simple, and Clifford semigroups is preserved under isomorphism of skeletons. A major tool employed in this is the Švarc-Milnor Lemma. We present an example that shows that in general, finite presentability is not an invariant property under isomorphism of skeletons of semigroups, and in fact is not an invariant property under quasi-isometry of Cayley graphs for semigroups. We give several skeletons and describe fully the semigroups that can be associated to these.

Neste trabalho introduzimos brevemente o formalismo matemático da Mecânica Quântica e analisamos em detalhe a classe dos operadores completamente positivos (e sua conhecida representação de Kraus). Seguindo [10], definimos que chamamos de semigrupos dinâmicos quânticos (QDS) e semigrupos markovianos quânticos (QMS), em analogia aos semigrupos clássicos da teoria de processos estocásticos com t real e t ≥ 0. Explorando a relação entre o semigrupo e seu gerador infinitesimal, encontramos condições necessárias e suficientes para que um operador seja o gerador infinitesimal de um destes semigrupos quânticos com t real e t ≥ 0. Um operador que satisfaz esta condição é chamado de operador condicionalmente completamente positivo. O tópico mais importante nesta dissertação é o seguinte: seguindo [10] descrevemos uma representação destes geradores originalmente devida à Lindblad [23]. / In this work we briey introduce the mathematical formalism of the theory of Quantum Mechanics and we we analyze in great details the class of completely positive operators (and also their well-known Kraus representation). Following [10], we define what we call quantum dynamical semigroups (QDS) and quantum markov semigroups (QMS), in analogy with classical semigroups arrising from stochastic processes theory where t is real and t ≥ 0. Exploring the relation between a semigroup and his infinitesimal generator, we find necessary and suficient conditions to an operator become an infinitesimalgenerator of one of those quantum semigroups where t is real and t ≥ 0. An operator which satisfies this condition is called conditionally completely positive. We present (following [10]) a representation for those generators originally due to Lindblad [23].

<p>We are study the spaces of convolutors and multipliers in the spaces of<br />tempered ultradistributions. There given theorems which gives us the characteri-zation of all the elements which belongs to spaces of convolutors and multipliers.<br />Structural theorem for ultradistribution semigroups and exponential ultradistri-bution semigroups is given. Fourier hyperfunction semigroups and hyperfunction<br />semigroups with non-densely dened generators are analyzed and also structural<br />theorems and spectral characterizations give necessary and sucient conditions<br />for the existence of such semigroups generated by a closed not necessarily densely<br />dened operator A. The abstract Cauchy problem is considered in the Banach<br />valued weighted Beurling ultradistribution setting and given some applications on<br />particular equations.</p> / <p>U disertaciji se proučavaju prostor konvolutora i multiplikatora na prostorima temperiranih ultradistribucija. Dokazane su&nbsp;teoreme koji karakteri&scaron;u elemente prostora konvolutora i multiplikatora. Date su strukturne teoreme za ultradistribucione &nbsp;polugrupe&nbsp;i eksponenecijalne polugrupe. Furijeve huperfunkciske polugrupe i&nbsp;hiperfunkciske polugrupe sa generatorima koji su negusto definisani&nbsp;<br />su analizirani, takođe su date strukturne teoreme i spektralne karakterizacije kao i dovoljni uslovi za postojenje na takvih polugrupa&nbsp;za operator A koji ne mora biti gust. Apstraktni Ko&scaron;ijev problem je&nbsp;proučavan za težinske Banahove prostore kao i za odgovarujuće prostora ultradistribucija. Takođe su date i primene za određene klase<br />jednačina.</p>