Peripheral fillings of relatively hyperbolic groups

A group theoretic version of Dehn surgery is studied. Starting with an arbitrary relatively hyperbolic group $G$ we define a peripheral filling procedure, which produces quotients of $G$ by imitating the effect of the Dehn filling of a complete finite volume hyperbolic 3--manifold $M$ on the fundamental group $\pi_1(M)$. The main result of the paper is an algebraic counterpart of Thurston's hyperbolic Dehn surgery theorem. We also show that peripheral subgroups of $G$ 'almost' have the Congruence Extension Property and the group $G$ is approximated (in an algebraic sense) by its quotients obtained by peripheral fillings. Various applications of these results are discussed.Comment: The difference with the previous version is that Proposition 3.2 is proved for quasi--geodesics instead of geodesics. This allows to simplify the exposition in the last section. To appear in Invent. Mat

Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups

Given an automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-twisted conjugacy classes. One says that $\Gamma$ has the $R_\infty$-property if there are infinitely many $\phi$-twisted conjugacy classes for every automorphism $\phi$ of $\Gamma$. In this paper we show that SL$(n,\mathbb{Z})$ and its congruence subgroups have the $R_\infty$-property. Further we show that any (countable) abelian extension of $\Gamma$ has the $R_\infty$-property where $\Gamma$ is a torsion free non-elementary hyperbolic group, or SL$(n,\mathbb{Z})$, Sp$(2n,\mathbb{Z})$ or a principal congruence subgroup of SL$(n,\mathbb{Z})$ or the fundamental group of a complete Riemannian manifold of constant negative curvature

Dynamics and Heating of the Magnetic Network on the Sun: Efficiency of mode transformation

We aim to identify the physical processes which occur in the magnetic network of the chromosphere and which contribute to its dynamics and heating. Specifically, we study the propagation of transverse (kink) MHD waves which are impulsively excited in flux tubes through footpoint motions. When these waves travel upwards, they get partially converted to longitudinal waves through nonlinear effects (mode coupling). By solving the nonlinear, time-dependent MHD equations we find that significant longitudinal wave generation occurs in the photosphere typically for Mach numbers as low as 0.2 and that the onset of shock formation occurs at heights of about 600 km above the photospheric base. We also investigate the compressional heating due to longitudinal waves and the efficiency of mode coupling for various values of the plasma $\beta$, that parameterises the magnetic field strength in the network. We find that this efficiency is maximum for field strengths corresponding to $\beta\approx 0.2$, when the kink and tube wave speeds are almost identical. This can have interesting observational implications. Furthermore, we find that even when the two speeds are different, once shock formation occurs, the longitudinal and transverse shocks exhibit strong mode coupling.Comment: 8 pages, 3 figure

The pathology of familial breast cancer: Immunohistochemistry and molecular analysis

Extensive studies of BRCA1- and BRCA2-associated breast tumours have been carried out in the few years since the identification of these familial breast cancer predisposing genes. The morphological studies suggest that BRCA1 tumours differ from BRCA2 tumours and from sporadic breast cancers. Recent progress in immunohistochemistry and molecular biology techniques has enabled in-depth investigation of molecular pathology of these tumours. Studies to date have investigated issues such as steroid hormone receptor expression, mutation status of tumour suppressor genes TP53 and c-erbB2, and expression profiles of cell cycle proteins p21, p27 and cyclin D(1). Despite relative paucity of data, strong evidence of unique biological characteristics of BRCA1-associated breast cancer is accumulating. BRCA1-associated tumours appear to show an increased frequency of TP53 mutations, frequent p53 protein stabilization and absence of imunoreactivity for steroid hormone receptors. Further studies of larger number of samples of both BRCA1- and BRCA2-associated tumours are necessary to clarify and confirm these observations

Maintenance of <I>Francisella tularensis</I> 15 RIEH and <I>Brucella abortus</I> 19 BA Strains in a Viable State by Means of Deep Freezing

Assessed are the methods for storage of microorganisms in a viable state under various technological conditions for a period of two years. Compared is the survivability of the test-strains of tularemia and brucellosis agents (exemplified by Francisella tularensis 15 RIEH and Brucella abortus 19 BA) when stored on the nutrient media at temperatures raging 0 °C up +8 °C and at -70 °C for over a year. Made has been an estimate of survivability of the vaccine strains stored at -70 °C within two years term. It is determined that optimum media for storing the stated above microorganisms with no changes in their morphological characteristics at -70 °C are sucrose-gelatin agar and Albimi broth with 10 % glycerin. Demonstrated is the fact that it is more efficient to conserve microorganisms stored in working collections by way of deep freezing

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

Hydrazides of glycine-containing decasubstituted pillar[5]arenes: Synthesis and encapsulation of Floxuridine

© 2018 Elsevier Ltd Hydrazides of glycine-containing decasubstituted pillar[5]arenes were synthesized and characterized. Dynamic light scattering (DLS) and transmission electron microscopy (TEM) showed that self-assembly into monodisperse spherical nanoparticles (28 nm) was typical in water for pillarene hydrazides containing glycylglycide fragments (1 × 10−3 M). Binding of the antitumor drug Floxuridine in water by the substituents of the macrocycle was established by NMR spectroscopy. It was shown by DLS and TEM, that heating the macrocycle-Floxuridine system in a 1:1 ratio at 1 × 10−4 M led to its self-organization into monodisperse spherical particles 132 nm in diameter

Iminodiacetic derivatives of p-tert-butylthiacalix[4]arene: Synthesis and influence of conformation on the aggregation with bismarck brown Y

© ISUCT Publishing. Three conformers (cone, partial cone and 1,3-alternate) of tetrasubstituted at the lower rim p-tert-butylthiacalix[4] arene derivatives with iminodiacetic fragments were synthesized and characterized. It was shown by spectral methods (UV-Vis, 1 H NMR and DOSY spectroscopy, DLS) and TEM that the monodisperse nano-sized particles are formed by self-assembly of synthetic octaacids in water with azo dye Bismarck brown Y in the case of the partial cone and 1,3-alternate conformations. It was found that the dye associates with the acid binding sites of the macrocycle