Free-standing smectic liquid crystal elastomer films

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2010

Correction of non-period motion in computed tomography

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2010

Geometric distortion correction in EPI at ultra high field

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2012

Comparative morphology of the tongue in free-tailed bats (Chiroptera, Molossidae)

Descriptive and comparative studies on tongue of nineteen Molossidae, one Mystacinidae, and four Vespertilionidae bats species were carried out. Analysis was restricted to the external morphology, covering general shape of the tongue and its papillae. Types of papillae and their distribution presented considerable intergeneric variation, considering the strictly insectivorous feeding habits of these bats. Distribution of the data of tongue morphology is analyzed and compared with the phylogenetic schemes proposed previously and comments about evolutionary relationships among taxa were done.

Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

The automorphism group of a free-by-cyclic group in rank 2

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Polynomial-time complexity for instances of the endomorphism problem in free groups

We say the endomorphism problem is solvable for an element W in a free group F if it can be decided effectively whether, given U in F, there is an endomorphism Φ of F sending W to U. This work analyzes an approach due to C. Edmunds and improved by C. Sims. Here we prove that the approach provides an efficient algorithm for solving the endomorphism problem when W is a two- generator word. We show that when W is a two-generator word this algorithm solves the problem in time polynomial in the length of U. This result gives a polynomial-time algorithm for solving, in free groups, two-variable equations in which all the variables occur on one side of the equality and all the constants on the other side.

Distortion of surface groups in Cat (0) free-by-cyclic groups

Given a non-positively curved 2-complex with a circle-valued Morse function satisfying some extra combinatorial conditions, we describe how to locally isometrically embed this in a larger non- positively curved 2-complex with free-by-cyclic fundamental group. This embedding procedure is used to produce examples of CAT(0) free-by-cyclic groups that contain closed hyperbolic surface subgroups with polynomial distortion of arbitrary degree. We also produce examples of CAT(0) hyperbolic free-by-cyclic groups that contain closed hyperbolic surface subgroups that are exponentially distorted.

Free and fragmenting filling length

The filling length of an edge-circuit η in the Cayley 2-complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial null-homotopy of η down to a base point through loops of length at most L. We introduce similar notions in which the full-homotopy is not required to fix a base point, and in which the contracting loop is allowed to bifurcate. We exhibit a group in which the resulting filling invariants exhibit dramatically different behaviour to the standard notion of filling length. We also define the corresponding filling invariants for Riemannian manifolds and translate our results to this setting.

Excreção urinária de 17-Cetoesteroides neutros no cavalo normal e no cavalo castrado

Total urinary neutral 17-steroids were determined in normal and in castrated horses. One liter of a 15-26 hours urine collection was hydrolysed by refluxing with 10% HC1 (v/v) for ten minutes and extracted with peroxyde-free ethyl ether. The extract was purified by washing with saturated NaHCO³ and KOH solutions. One half of the crude neutral fraction was fractionated with Girard's "T" reagent . The Zimmermann reaction was performed both in the ketonic and in the crude neutral extracts, using alcoholic 2.5N KOH and a 60 minutes period for the colour development in the dark. Optical density measuments were made in a grating Coleman Universal Spectrophotometer at 420 mµ and 520mµ; for the crude neutral fraction a colour correction equation was applied. The aliquot fraction used for colorimety was adjusted for keeping optical density measurements within the range 0.2 to 0.7. Androsterone (mp. 184-184.5°C) with an absorption maximum at 290.5 mµ (Beckman Model DU Spectrophotometer) was used as a reference standard. Table I, ilustrates the results obtained. At the 0.05 probability level there is a significant difference among castrated and normal group means (Fischer's "t" test.) when were used the data obtained from the ketonic fractions; in spite of the use of a colour correction applied for inespecific chromogens, the same results could not be obtained with the crude neutral fractions, Since Girard's reagent fractionation is generaly accepted as the best method for correcting the inespecific chromogen interference in the determination of the 17-ketosteroids by the Zimmermann reaction, we emphasize the value of the results obtained with the ketonic fractions. From these results it appears, as occurs in others mammals, that castrated horses show a lower level of urinary 17-ketosteroids excretion than the normal horses. The significance of the horse testis contribution for the neutral urinary steroid metabolites is discussed. Since horse urine has a low androgenic activity, the fractionation of the neutral 17-ketosteroids must be studied more accurately.

Free triples, large indifference classes and the majority rule

We present a new domain of preferences under which the majority relation is always quasi-transitive and thus Condorcet winners always exist. We model situations where a set of individuals must choose one individual in the group. Agents are connected through some relationship that can be interpreted as expressing neighborhood, and which is formalized by a graph. Our restriction on preferences is as follows: each agent can freely rank his immediate neighbors, but then he is indifferent between each neighbor and all other agents that this neighbor "leads to". Hence, agents can be highly perceptive regarding their neighbors, while being insensitive to the differences between these and other agents which are further removed from them. We show quasi-transitivity of the majority relation when the graph expressing the neighborhood relation is a tree. We also discuss a further restriction allowing to extend the result for more general graphs. Finally, we compare the proposed restriction with others in the literature, to conclude that it is independent of any previously discussed domain restriction.

Cat(0) and Cat (-1) dimensions of torsion free

We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical fieldt heoretic notions, and we discuss in detail the notion of algebraic closure. We apply that theory to the study and the computation of certain algebraic properties of subgroups (e.g. being malnormal, pure, inert or compressed, being closed in certain profinite topologies) and the corresponding closure operators. We also analyze the closure of a subgroup under the addition of solutions of certain sets of equations.

The density of injective endomorphisms of a free group

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