Asymmetry of Outer space

We study the asymmetry of the Lipschitz metric d on Outer space. We introduce an (asymmetric) Finsler norm \({\|\cdot\|^L}\) that induces d. There is an Out(F _n )-invariant “potential” Ψ defined on Outer space such that when \({\|\cdot\|^L}\) is corrected by dΨ, the resulting norm is quasi-symmetric. As an application, we give new proofs of two theorems of Handel-Mosher, that d is quasi-symmetric when restricted to a thick part of Outer space, and that there is a uniform bound, depending only on the rank, on the ratio of logs of growth rates of any irreducible \({f\in Out(F_n)}\) and its inverse.     

Contributed report: Flavor anarchy for Majorana neutrinos

We argue that neutrino flavor parameters may exhibit features that are very different from those of quarks and charged leptons. Specifically, within the Proggatt-Nielsen (FN) framework, charged fermion parameters depend on the ratio between two scales, while for neutrinos a third scale — that of lepton number breaking — is involved. Consequently, the selection rules for neutrinos may be different. In particular, if the scale of lepton number breaking is similar to the scale of horizontal symmetry breaking, neutrinos may become flavor-blind even if they carry different horizontal charges. This provides an attractive mechanism for neutrino flavor anarchy.     

High-resolution NMR spectroscopic trends and assignment rules of metal-free, metallated and substituted corroles

Major advances over the last few years have facilitated the synthesis of a large variety of meso-only substituted corroles that display interesting catalytic, therapeutic and photophysical properties. This work is the first to study extensively the NMR spectral characteristics of both metallated and non-metallated triarylcorroles in various organic solvents and provide guidelines for easy and reliable assignments of 1D 1H spectra from trends of J coupling constants and chemical shifts. An excellent correlation is found between C=C bond lengths derived from 3J(H,H) values and experimental lengths determined by x-ray crystallography of the same molecules. The nuclear Overhauser effect provides a robust 1D 1H NMR tool for determining the selectivity of electrophilic substitutions. Variable-temperature NMR and isotopic labelling reveal a single preferred tautomerization state and unsymmetric ring orientations at -70 degrees C. The beta-pyrrole protons demonstrate long-range heteronuclear couplings with the coordination core (15N) and with the ortho-19F nuclei of the meso-carbon aryl rings. In sum, application of multinuclear magnetic resonance to corroles and their metal complexes, through the compilation of chemical shifts and J couplings and the recognition of trends therein, provides basic information essential to reliable spectral assignments. Additionally, the conclusions drawn about the structures of corroles and the electron densities at various positions of the corrole macrocycle resulting from the application of high-resolution NMR techniques are of importance to an in-depth understanding of the molecular interactions and processes of this relatively new and rapidly expanding class of compounds.     

Formation and X-ray Structures of PCP Ligand Based Platinum(II) and Palladium(II) Macrocycles

The coordination behavior prior to C-M bond formation of the chelating aromatic PCP substrate DPPMH (3; DPPMH = 1,3-bis((diphenylphosphino)methylene)mesitylene) has been studied in order to determine the factors which control the complex formation of such ligands. Reacting 3 with (RCN)(2)MCl(2) (R = Me, Ph; M = Pd, Pt) and (COD)PtX(2) (X = Cl, Me; COD = 1,5-cyclooctadiene) resulted in the formation of several 8- and 16-membered mono- and binuclear palladium(II) and platinum(II) macrocycles: trans-[(DPPMH)PdCl(2)](2) (5), trans-[(DPPMH)PtCl(2)](2) (6), cis-(DPPMH)PtCl(2) (7), cis-(DPPMH)PtMe(2) (8), and cis-[(DPPMH)PtMe(2)](2) (9). Compounds 5-9 were fully characterized using NMR, FAB-MS, FD-MS, elemental analysis, and X-ray crystallography. Thermolysis of the bimetallic trans-[(DPPMH)PtCl(2)](2) (6) results in the formation of the monomeric cis-(DPPMH)PtCl(2) (7). The product formation depends on the neutral- (nitriles or COD) and anionic ligands (Cl and CH(3)) of the metal precursor. The molecular structures of trans-[(DPPMH)PdCl(2)](2) (5) and cis-[(DPPMH)PtMe(2)](2) (9) have been determined by complete single-crystal diffraction studies. Crystal data for 5: monoclinic, space group P2(1)/n with a = 14.547(3) ?, b = 17.431(4) ?, c = 27.839 (5) ?, beta = 99.56(2) degrees, V = 6961(3) ?(3), and Z = 4. The structure converged to R = 0.048 and R(w) = 0.049. Crystal data for 9: monoclinic, space group P2(1)/n with a = 19.187(4) ?, b = 19.189(4) ? c = 20.705(2) ?, beta = 103.41(3) degrees, V = 7415(3) ?(3), and Z = 4. The structure refinement converged to R = 0.0977 and R(w) = 0.2212.     

ON THE GENERATION OF THE HYDROXYLATION AGENT FROM SUPEROXIDE RADICAL. CAN THE HABER–WEISS REACTION BE THE SOURCE OF OH RADICALS?

Abstract— In many biological systems, the role of O₂^- in hydroxylation and toxic processes was assumed to be due to the formation of OH radicals. The Haber-Weiss reaction (Haber and Weiss, 1934)—(H₂O₂+ O₂^-→ OH + OH^-+ O₂) was suggested as the origin of this activity.
In this study it is shown that this reaction pathway is too slow, and that OH is probably formed from the reaction of complexed superoxide with H₂O₂ or/and from the reduction of Fe(III), bound to biological compounds, by O₂^-; the reduced Fe(II) can then react with H₂O₂ as a Fenton reagent, to yield OH.
It is also shown that singlet oxygen cannot be formed in these biological systems neither from the dismutation of OJ nor from the reaction of O₂^- with OH. Singlet oxygen may be formed from the reduction of metal complexes by O₂^-.     

Tensor functors between Morita duals of fusion categories

Given a fusion category \({\mathcal C}\) and an indecomposable \({\mathcal C}\)-module category \({\mathcal M}\), the fusion category \({\mathcal C}^*_{_{{\mathcal M}}}\) of \({\mathcal C}\)-module endofunctors of \({\mathcal M}\) is called the (Morita) dual fusion category of \({\mathcal C}\) with respect to \({\mathcal M}\). We describe tensor functors between two arbitrary duals \({\mathcal C}^*_{_{{\mathcal M}}}\) and \({\mathcal D}^*_{\mathcal N}\) in terms of data associated to \({\mathcal C}\) and \({\mathcal D}\). We apply the results to G-equivariantizations of fusion categories and group-theoretical fusion categories. We describe the orbits of the action of the Brauer–Picard group on the set of module categories and we propose a categorification of the Rosenberg–Zelinsky sequence for fusion categories.     

Selective dispersion of single-walled carbon nanotubes in the presence of polymers: the role of molecular and colloidal length scales

Dimensionality is known to play a key role in the solution behavior of nano- and mesoparticles. In particular, the shape and the range of the attractive van der Waals interparticle potential are determined by the number of microscopic versus mesoscopic dimensions. For single-walled nanotubes (SWNTs), where two of the dimensions are nanoscopic and one is mesoscopic, the intertube attraction is relatively short ranged, albeit very steep. The very large attraction (compared to the thermal energy, K(b)T) among long SWNTs leads to aggregation at different levels and constitutes a major barrier for manipulation and utilization of SWNTs. This study demonstrates that it is possible to shape the intertube potential by decorating SWNTs with end-tethered polymers. In good solvent conditions for the polymers, entropic repulsion among the tethered chains generates a free energy barrier that prevents SWNTs from approaching the attractive part of the intertube potential. Consequentially, stable dispersions of individual, well separated SWNTs can be prepared. Investigation of different chain lengths and tethering densities of the polymers as well as the interparticle potentials for nanometric versus mesoscopic particles suggests that polymer-induced steric stabilization provides a generic method for separation of SWNTs from mixtures of colloidal species, as demonstrated experimentally.     

Quantization of presymplectic manifolds and circle actions

We prove several versions of ``quantization commutes with reduction' for circle actions on manifolds that are not symplectic. Instead, these manifolds possess a weaker structure, such as a spin structure. Our theorems work whenever the quantization data and the reduction data are compatible; this condition always holds if we start from a presymplectic (in particular, symplectic) manifold.

     

Synthesis and Reactivity of Cationic Boron Complexes Distorted by Pyridine‐based Pincer Ligands: Isolation of a Photochemical Hofmann–Martius‐type Intermediate

A family of cationic boron complexes was synthesized, using a dianilidopyridine pincer ligand, which imposes in‐plane distortion of the geometry at boron towards T‐shaped. Reactivity of these cations toward hydride and base was investigated, and the utility of these cations as precursors to a variety of π‐conjugated BN heterocycles was demonstrated. 300 nm irradiation of a deprotonated pincer boron complex triggered a C?N cleavage/C?C formation yielding a dearomatized boryl imine, which has a structure akin to the long‐proposed intermediate in the photochemical Hofmann–Martius rearrangement. The photo‐rearrangement triggers relief of the distortion imposed by the pincer ligand.