On the generators of the kernels of hyperbolic group presentations

In this paper we prove that if R is a (not necessarily finite) set of words satisfying certain small cancellation condition in a hyperbolic group G then the normal closure of R is free. This result was first presented (for finite set R) by T. Delzant [Delz] but the proof seems to require some additional argument. New applications of this theorem are provided

Cognitive functions and mental performance of team sports athletes

Objective: to study cognitive functions and mental performance of team sports athletes’ and persons who are not involved in sports. Materials and methods: The study has 141 participants (23,2 ± 1,7 years), 76 female (23,4 ± 1,8 years) and 64 male (23,0 ± 1,6 years). Group of team sports athletes (main group) consisted of 61 participants: 31 male (22,3 ± 1,3 years), 30 female (23,1 ± 2,1 years). Control group consisted of persons who were not involved in sports, and included 80 people, (23,6 ± 1.5 years):men - 34 (23,7 ± 1,5 years), women - 46 (23,6 ± 1,5 years). Diagnostics of mental health included psychophysical tests focused on memory, attention and mental productivity assessment. Results: athletes have demonstrated higher level of visual memory, volume and switching of attention, mental productivity and mental performance in comparison with persons who were not involved in sports. Male athletes had higher rates of visual memory, volume and switching attention, mental performance in comparison with men who were not involved in sports. Female athletes and women who are not involved in sports have similar level of aural, visual memory, attention but mental productivity and mental capacity are higher in the group of female athletes. Male athletes had higher level of volume and switching of attention, mental productivity and mental performance in comparison to female athletes. Men and women who are not involved in sports differ only in terms of visual memory upwards at women side. Conclusions: high rates of cognitive functions of athletes comparing with persons who are not involved in sports confirm positive impact physical activities on central nervous system. Findings may be used as baseline data for testing cognitive functions and mental performance of athletes in different time segments of sports activity

Spin-polarized electronic structure of the core-shell ZnO/ZnO:Mn nanowires probed by x-ray absorption and emission spectroscopy

The combination of x-ray spectroscopy methods complemented with theoretical analysis unravels the coexistence of paramagnetic and antiferromagnetic phases in the Zn_0.9Mn_0.1O shell deposited onto array of wurtzite ZnO nanowires. The shell is crystalline with orientation toward the ZnO growth axis, as demonstrated by X-ray linear dichroism. EXAFS analysis confirmed that more than 90% of Mn atoms substituted Zn in the shell while fraction of secondary phases was below 10%. The value of manganese spin magnetic moment was estimated from the Mn K{\beta} X-ray emission spectroscopy to be 4.3{\mu}B which is close to the theoretical value for substitutional Mn_Zn. However the analysis of L_2,3 x-ray magnetic circular dichroism data showed paramagnetic behaviour with saturated spin magnetic moment value of 1.95{\mu}B as determined directly from the spin sum rule. After quantitative analysis employing atomic multiplet simulations such difference was explained by a coexistence of paramagnetic phase and local antiferromagnetic coupling of Mn magnetic moments. Finally, spin-polarized electron density of states was probed by the spin-resolved Mn K-edge XANES spectroscopy and consequently analyzed by band structure calculations.Comment: Supplementary information available at http://www.rsc.org/suppdata/ja/c3/c3ja50153a/c3ja50153a.pdf J. Anal. At. Spectrom., 201

Normal subgroups in the Cremona group (long version)

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and algebraic geometry to produce elements in the Cremona group that generate non trivial normal subgroups.Comment: With an appendix by Yves de Cornulier. Numerous but minors corrections were made, regarding proofs, references and terminology. This long version contains detailled proofs of several technical lemmas about hyperbolic space