247 research outputs found
New examples of small Polish structures
We answer some questions from a paper of Krupi\'nski by giving suitable
examples of small Polish structures. First, we present a class of small Polish
group structures without generic elements. Next, we construct a first example
of a small non-zero-dimensional Polish -group
On \omega-categorical, generically stable groups
We prove that each \omega-categorical, generically stable group is
solvable-by-finite.Comment: 11 page
Left-ordered inp-minimal groups
We prove that any left-ordered inp-minimal group is abelian, and we provide
an example of a non-abelian left-ordered group of dp-rank 2
Locally finite profinite rings
We investigate the structure of locally finite profinite rings. We classify
(Jacobson-) semisimple locally finite profinite rings as products of complete
matrix rings of bounded cardinality over finite fields, and we prove that the
Jacobson radical of any locally finite profinite ring is nil of finite
nilexponent. Our results apply to the context of small compact -rings, where
we also obtain a description of possible actions of on the underlying ring.Comment: 17 page
The Lascar groups and the 1st homology groups in model theory
Let be a strong type of an algebraically closed tuple over
B=\acl^{\eq}(B) in any theory . Depending on a ternary relation \indo^*
satisfying some basic axioms (there is at least one such, namely the trivial
independence in ), the first homology group can be introduced,
similarly to \cite{GKK1}. We show that there is a canonical surjective
homomorphism from the Lascar group over to . We also notice that
the map factors naturally via a surjection from the `relativised' Lascar group
of the type (which we define in analogy with the Lascar group of the theory)
onto the homology group, and we give an explicit description of its kernel. Due
to this characterization, it follows that the first homology group of is
independent from the choice of \indo^*, and can be written simply as
. As consequences, in any , we show that
unless is trivial, and we give a criterion for the equality of stp and
Lstp of algebraically closed tuples using the notions of the first homology
group and a relativised Lascar group. We also argue how any abelian connected
compact group can appear as the first homology group of the type of a model.Comment: 30 pages, no figures, this merged with the article arXiv:1504.0772
Topologies induced by group actions
We introduce some canonical topologies induced by actions of topological
groups on groups and rings. For being a group [or a ring] and a
topological group acting on as automorphisms, we describe the finest group
[ring] topology on under which the action of on is continuous. We
also study the introduced topologies in the context of Polish structures. In
particular, we prove that there may be no Hausdorff topology on a group
under which a given action of a Polish group on is continuous.Comment: 13 page
Sets, groups, and fields definable in vector spaces with a bilinear form
We study definable sets, groups, and fields in the theory of
infinite-dimensional vector spaces over an algebraically closed field equipped
with a nondegenerate symmetric (or alternating) bilinear form. First, we define
an ()-valued dimension on definable
sets in enjoying many properties of Morley rank in strongly minimal
theories. Then, using this dimension notion as the main tool, we prove that all
groups definable in are (algebraic-by-abelian)-by-algebraic, which,
in particular, answers a question of Granger. We conclude that every infinite
field definable in is definably isomorphic to the field of scalars
of the vector space. We derive some other consequences of good behaviour of the
dimension in , e.g. every generic type in any definable set is a
definable type; every set is an extension base; every definable group has a
definable connected component.
We also consider the theory of vector spaces over a real
closed field equipped with a nondegenerate alternating bilinear form or a
nondegenerate symmetric positive-definite bilinear form. Using the same
construction as in the case of , we define a dimension on sets
definable in , and using it we prove analogous results about
definable groups and fields: every group definable in is
(semialgebraic-by-abelian)-by-semialgebraic (in particular, it is
(Lie-by-abelian)-by-Lie), and every field definable in is
definable in the field of scalars, hence it is either real closed or
algebraically closed.Comment: v2: The particular bounds on dimension obtained in Section 3 were
corrected, and a number of minor corrections has been made throughout the
pape
Trans reentrant loop structures in secondary transporters
Biologische membranen hebben een belangrijke rol in het beschermen van de cel tegen schadelijke condities van de omgeving en moeten tegelijkertijd de opname van verschillende stoffen, zoals voedingstoffen, alsook de uitscheiding van afvalproducten mogelijk maken. Transportfuncties worden uitgevoerd door transporteiwitten, die de verplaatsing van een substraat van de ene naar de andere kant van het membraan katalyseren. Het werk dat in dit proefschrift beschreven wordt, richt zich op structurele overeenkomst tussen families van transporteiwitten, en in het bijzonder tussen de glutamaat-transporter GltS van Escherichia coli en de citraat-transporter CitS van Klebsiella pneumoniae. Deze twee transporteiwitten, en andere leden van de families waartoe zij behoren, vertonen geen overeenkomst in aminozuurvolgorde, maar wel in hun hydropathie-profielen. Dit suggereert dat ze een overeenkomstige eiwitvouwing en mechanisme van transport hebben. Met de bioinformatische data verkregen uit het MemGen classificatie systeem en een eerder uitgevoerde topologie studie van CitS, waren we in staat om de membraantopologie van GltS te voorspellen en deze experimenteel te verifiëren. Hiermee is aangetoond dat, bij afwezigheid van een kristalstructuur, analyse van hydropathie-profielen van membraaneiwitten een goede methode is om de structuur van membraaneiwitten te bestuderen. De verkregen data suggereren dat beide eiwitten opgebouwd zijn uit twee homologe domeinen die beide een zogenaamde “trans reentrant loop” hebben, en aan elkaar verbonden zijn met een lange cytoplasmatische loop. De reentrant loops zijn belangrijk voor de activiteit van de transporters: ze staan in interactie met elkaar daar waar de twee domeinen aan elkaar grenzen en vormen een translocatiekanaal voor de substraten en co-ionen. (translated by Hein Trip
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