Über Gruppen,insbesondere continuierliche Gruppen von Cremona-Transformationen der Ebene und des Raumes

Ohne ZusammenfassungVortrag, gehalten auf dem internationalen Mathematiker-Congress in Zürich den 10. August 1897.     

Sur les différentes espèces de complexes du 2e dégrè des droites qui coupent harmoniquement deux surfaces du second ordre

Sans résumé     

B-decay CP-asymmetries in SUSY with a U(2)3 flavour symmetry

We study CP asymmetries in rare B decays within supersymmetry with a U(2)³ flavour symmetry, motivated by the SUSY flavour and CP problems, the hierarchies in the Yukawa couplings and the absence so far of any direct evidence for SUSY. Even in the absence of flavour-blind phases, we find potentially sizable CP violating contributions to b→s decay amplitudes. The effects in the mixing-induced CP asymmetries in B→ϕK _S and B→η′K _S , angular CP asymmetries in B→K ^∗ μ ⁺ μ ⁻ and the direct CP asymmetry in B→X _s γ can be in the region to be probed by LHCb and next generation B factories. At the same time, these effects in B decays are compatible with CP violating contributions to meson mixing, including a non-standard B _s mixing phase hinted by current tensions in the CKM fit mostly between S_yKS, e_KS_{\psi K_{S}}, \epsilon_{K} and DM_Bs/DM_Bd\Delta M_{B_{s}}/\Delta M_{B_{d}}.     

Leptogenesis at the electroweak scale

In this Letter we propose a model of leptogenesis in which the scale for the mass of the necessary heavy neutral lepton is similar to the scale of electroweak symmetry breaking.     

Nanocomposites by melt intercalation based on polycaprolactone and organoclay

Nanocomposites based on biodegradable polycaprolactone (PCL) and organically modified layered silicates (organoclay) were prepared by melt mixing. Their structures and properties were characterized by wide‐angle X‐ray diffraction, thermal analysis, and rheological measurements. The exfoliation of the organoclay was achieved via a melt mixing process in an internal mixer and showed a dependence on the type of organic modifier, the organoclay contents, and the processing temperature. The addition of the organoclay to PCL increased the crystallization temperature of PCL, but a high content of the organoclay could show an inverse effect. The PCL/organoclay nanocomposites showed a significant enhancement in their mechanical properties and thermal stability due to the exfoliation of the organoclay. The nanocomposites showed a much higher complex viscosity than the neat PCL and significant shear‐thinning behavior in the low frequency range. The shear storage modulus and loss modulus of the nanocomposites also exhibited less frequency dependence than the pure PCL in the low frequency range, and this was caused by the strong interactions between the organoclay layers and PCL molecules and by the good dispersion of exfoliated organoclay platelets in the PCL. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 670–678, 2003     

Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability

We characterize the long‐time asymptotic behavior of the focusing nonlinear Schrödinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity by using a variant of the recently developed inverse scattering transform (IST) for such problems and by employing the nonlinear steepest‐descent method of Deift and Zhou for oscillatory Riemann‐Hilbert problems. First, we formulate the IST over a single sheet of the complex plane without introducing the uniformization variable that was used by Biondini and Kova?i? in 2014. The solution of the focusing NLS equation with nonzero boundary conditions is thereby associated with a matrix Riemann‐Hilbert problem whose jumps grow exponentially with time for certain portions of the continuous spectrum. This growth is the signature of the well‐known modulational instability within the context of the IST. We then eliminate this growth by performing suitable deformations of the Riemann‐Hilbert problem in the complex spectral plane. The results demonstrate that the solution of the focusing NLS equation with nonzero boundary conditions remains bounded at all times. Moreover, we show that, asymptotically in time, the xt ‐plane decomposes into two types of regions: a left far‐field region and a right far‐field region, where the solution equals the condition at infinity to leading order up to a phase shift, and a central region in which the asymptotic behavior is described by slowly modulated periodic oscillations. Finally, we show how, in the latter region, the modulus of the leading‐order solution, initially obtained as a ratio of Jacobi theta functions, can be reduced to the well‐known elliptic solutions of the focusing NLS equation. These results provide the first characterization of the long‐time behavior of generic perturbations of a constant background in a modulationally unstable medium. © 2017 Wiley Periodicals, Inc.     

Hydrogen atom abstraction selectivity in the reactions of alkylamines with the benzyloxyl and cumyloxyl radicals. The importance of structure and of substrate radical hydrogen bonding

A time-resolved kinetic study on the hydrogen abstraction reactions from a series of primary and secondary amines by the cumyloxyl (CumO(?)) and benzyloxyl (BnO(?)) radicals was carried out. The results were compared with those obtained previously for the corresponding reactions with tertiary amines. Very different hydrogen abstraction rate constants (k(H)) and intermolecular selectivities were observed for the reactions of the two radicals. With CumO(?), k(H) was observed to decrease on going from the tertiary to the secondary and primary amines. The lowest k(H) values were measured for the reactions with 2,2,6,6-tetramethylpiperidine (TMP) and tert-octylamine (TOA), substrates that can only undergo N-H abstraction. The opposite behavior was observed for the reactions of BnO(?), where the k(H) values increased in the order tertiary < secondary < primary. The k(H) values for the reactions of BnO(?) were in all cases significantly higher than those measured for the corresponding reactions of CumO(?), and no significant difference in reactivity was observed between structurally related substrates that could undergo exclusive α-C-H and N-H abstraction. This different behavior is evidenced by the k(H)(BnO(?))/k(H)(CumO(?)) ratios that range from 55-85 and 267-673 for secondary and primary alkylamines up to 1182 and 3388 for TMP and TOA. The reactions of CumO(?) were described in all cases as direct hydrogen atom abstractions. With BnO(?) the results were interpreted in terms of the rate-determining formation of a hydrogen-bonded prereaction complex between the radical α-C-H and the amine lone pair wherein hydrogen abstraction occurs. Steric effects and amine HBA ability play a major role, whereas the strength of the substrate α-C-H and N-H bonds involved appears to be relatively unimportant. The implications of these different mechanistic pictures are discussed.