Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

On Groups Whose Maximal Cyclic Subgroups Are Maximal

We consider the problem of classifying those groups whose maximal cyclic subgroups are maximal. We give a complete classification of those groups with this property and which are either soluble or residually finite.

Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Let M be a compact, connected non-orientable surface without boundary and of genus g >= 3. We investigate the pure braid groups P,(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 -> P(m)(M \ {x(1), ..., x(n)}) hooked right arrow P(n+m)(M) (P*) under right arrow P(n)(M) -> 1, where m, n >= 1, and p* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F(n+m)(M) -> F(n)(M) of configuration spaces, defined by p((x(1), ..., x(n), x(n+1), ..., x(n+m))) = (x(1), ..., x(n)). We show that p and p* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups. (C) 2009 Elsevier B.V. All rights reserved.

Group algebras of torsion groups and Lie nilpotence

Let * be an involution of a group algebra FG induced by an involution of the group G. For char F not equal 2, we classify the torsion groups G with no elements of order 2 whose Lie algebra of *-skew elements is nilpotent.

Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

We classify the ( finite and infinite) virtually cyclic subgroups of the pure braid groups P(n)(RP(2)) of the projective plane. The maximal finite subgroups of P(n)(RP(2)) are isomorphic to the quaternion group of order 8 if n = 3, and to Z(4) if n >= 4. Further, for all n >= 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of P(n)(RP(2)): Z, Z(2) x Z and the amalgamated product Z(4)*(Z2)Z(4).

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

Sensing hazardous metal ions using a fluoroionophore calix[4]arene species containing two 8-oxyquinoline groups

The interaction of a calix[4]arene-based species containing two 8-oxyquinoline chromophore pendants with hazardous metal ions has been investigated using optical absorption and fluorimetric techniques. In the presence of Hg(2+), Cd(2+), and Pb(2+) ions, there is only a small decrease of the calixarene absorption band at 283 nm. The main changes are associated with the absorption band of the 8-oxyquinoline group at 315 nm, undergoing a systematic bathochromic shift to above 350 nm. In addition, a systematic decrease of the oxyquinoline emission at lambda(em) = 392 nm (lambda(exc) = 315 nm) has been observed. These observations are consistent with the coordination of the metal ions to the quinoline groups attached to the calixarene ligand, providing a useful fluoroinophore species for analytical purposes.

Spectroscopic and electrochemical properties of iron(II) complexes of polydentate Schiff bases containing pyrazine, pyridine and imidazole groups

We report the synthesis and spectroscopic/electrochemical properties of iron(II) complexes of polydentate Schiff bases generated from 2-acetylpyridine and 1,3-diaminopropane, acetylpyrazine and 1,3-diaminopropane, and from 2-acetylpyridine and L-histidine. The complexes exhibit bis(diimine)iron(II) chromophores in association with pyrazine, pyridine or imidazole groups displaying contrasting pi-acceptor properties. In spite of their open geometry, their properties are much closer to those of macrocyclic tetraimineiron(II) complexes. An electrochemical/spectroscopic correlation between E degrees(Fe(III/II)) and the energies of the lowest MLCT band has been observed, reflecting the stabilization of the HOMO levels as a consequence of the increasing backbonding effects in the series of compounds. Mossbauer data have also confirmed the similarities in their electronic structure, as deduced from the spectroscopic and theoretical data. (C) 2008 Elsevier B.V. All rights reserved.

The Impact of the NIHERST/NGC National Science Centre, Trinidad and Tobago on Visiting Student Groups

The aim of this study was to asses the impact of a visit to the NIHERST/NGC National Science Centre in Trinidad on four different school-age visitor groups. The research was conducted through the administering of a post-visit questionnaire immediately upon completion of each visit by each group, and via visitor feedback obtained in post-visit or pre-visit activities conducted within two weeks of the visit for three groups. Teachers/instructors who accompanied the groups on their visit also completed post-visit questionnaires and provided additional information on follow-up activities via an interview. The results of this investigation suggest that the visit to this science centre provided entertainment/enjoyment value and potential educational value to most individuals. The nature of this enjoyment was noted for various age groups and genders in this study. Quantification of the educational impact was not possible within the constraints of this study, which was unable to capture long-term effects of the supply of ‘new knowledge’ to visitors which the visit to the science centre had provided.

Elitidrottsproblem? : En kvalitativ studie om elitidrottares karriäravslutning

This paper used a qualitative technique from a social scientific perspective, a model based on Hewitt and his theory of the self-concept. The purpose of this study was to investigate why some elite athletes experience troublesome periods after their career ending. Interviews were performed with five elite athletes with varying experiences after career ending. The length of the elite athlete careers vary between 7 to 17 years. Two groups were made based upon experiences after career ending. Group 1 had experienced problems, for example suicide tendency, and group 2 had not. The result shows that a troublesome period can come up independently of career ending. The self-concept was investigated during the career and further different kind of variables which could affect the self as training and competition, social relations both before and after termination from sport. Result indicates that an individual in group 2 who has a high complexity in the self-concept based upon significant others outside the elite sport during the career copes with the new situation after career ending much better than group 1 who have not. To build up the self based only upon significant others in the elite sport seems to give expression in a strengthen self. Intensity in training and competition did not have a connection with a troublesome period after retirement from sport but it could prevent establishing contact with others outside the elite sport and reduce a high complexity in the self-concept. The result further shows that elite athletes who practise an individual sport trains in to a greater extent than elite athletes in a seasonal sport. Result also shows that practising a sport with one day off a week, contributes to better opportunities for developing a higher complexity in the self-concept. Suspicions has also rouse that practising an elite sport on the highest level can lead to extensive focusing that further leads to social isolation from individuals outside elite sport. To build up the self upon significant others outside elite sport during the career and keep in touch with significant others from elite sport after the career seems to be the key to avoid problems after the career ending. Suggestions about further investigations are made to see if medial exposure and status can affect the self.

Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups

This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

Physiological demands of competitive elite cross-country skiing

Introduction Researchers have, for decades, contributed to an increased collective understanding of the physiological demands in cross-country skiing; however, almost all of these studies have used either non-elite subjects and/or performances that emulate cross-country skiing. To establish the physiological demands of cross-country skiing, it is important to relate the investigated physiological variables to the competitive performance of elite skiers. The overall aim of this doctoral thesis was, therefore, to investigate the external validity of physiological test variables to determine the physiological demands in competitive elite cross-country skiing. Methods The subjects in Study I – IV were elite male (I – III) and female (III – IV) cross-country skiers. In all studies, the relationship between test variables (general and ski-specific) and competitive performances (i.e. the results from competitions or the overall ski-ranking points of the International Ski Federation (FIS) for sprint (FISsprint) and distance (FISdist) races) were analysed. Test variables reflecting the subject’s general strength, upper-body and whole-body oxygen uptake, oxygen uptake and work intensity at the lactate threshold, mean upper-body power, lean mass, and maximal double-poling speed were investigated. Results The ability to maintain a high work rate without accumulating lactate is an indicator of distance performance, independent of sex (I, IV). Independent of sex, high oxygen uptake in whole-body and upper-body exercise was important for both sprint (II, IV) and distance (I, IV) performance. The maximal double-poling speed and 60-s double-poling mean power output were indicators of sprint (IV) and distance performance (I), respectively. Lean mass was correlated with distance performance for women (III), whereas correlations were found between lean mass and sprint performance among both male and female skiers (III). Moreover, no correlations between distance performance and test variables were derived from tests of knee-extension peak torque, vertical jumps, or double poling on a ski-ergometer with 20-s and 360-s durations (I), whereas gross efficiency while treadmill roller skiing showed no correlation with either distance or sprint performance in cross-country skiing (IV). Conclusion The results in this thesis show that, depending on discipline and sex, maximal and peak oxygen uptake, work intensity at the lactate threshold, lean mass, double-poling mean power output, and double-poling maximal speed are all externally valid physiological test variables for evaluation of performance capability among elite cross-country skiers; however, to optimally indicate performance capability different test-variable expressions should be used; in general, the absolute expression appears to be a better indicator of competitive sprint performance whereas the influence of body mass should be considered when evaluating competitive distance performance capability of elite cross-country skiers.

Optimal V. O2max-to-mass ratio for predicting 15 km performance among elite male cross-country skiers

The aim of this study was 1) to validate the 0.5 body-mass exponent for maximal oxygen uptake (V. O2max) as the optimal predictor of performance in a 15 km classical-technique skiing competition among elite male cross-country skiers and 2) to evaluate the influence of distance covered on the body-mass exponent for V. O2max among elite male skiers. Twenty-four elite male skiers (age: 21.4±3.3 years [mean ± standard deviation]) completed an incremental treadmill roller-skiing test to determine their V. O2max. Performance data were collected from a 15 km classicaltechnique cross-country skiing competition performed on a 5 km course. Power-function modeling (ie, an allometric scaling approach) was used to establish the optimal body-mass exponent for V . O2max to predict the skiing performance. The optimal power-function models were found to be race speed = 8.83⋅(V . O2max m-0.53) 0.66 and lap speed = 5.89⋅(V . O2max m-(0.49+0.018lap)) 0.43e0.010age, which explained 69% and 81% of the variance in skiing speed, respectively. All the variables contributed to the models. Based on the validation results, it may be recommended that V. O2max divided by the square root of body mass (mL⋅min−1 ⋅kg−0.5) should be used when elite male skiers’ performance capability in 15 km classical-technique races is evaluated. Moreover, the body-mass exponent for V . O2max was demonstrated to be influenced by the distance covered, indicating that heavier skiers have a more pronounced positive pacing profile (ie, race speed gradually decreasing throughout the race) compared to that of lighter skiers.