Multiple Recurrence in Quasirandom Groups

We establish a new mixing theorem for quasirandom groups (finite groups with no low-dimensional unitary representations) G which, informally speaking, asserts that if g, x are drawn uniformly at random from G, then the quadruple (g, x, gx, xg) behaves like a random tuple in G ⁴, subject to the obvious constraint that gx and xg are conjugate to each other. The proof is non-elementary, proceeding by first using an ultraproduct construction to replace the finitary claim on quasirandom groups with an infinitary analogue concerning a limiting group object that we call an ultra quasirandom group, and then using the machinery of idempotent ultrafilters to establish the required mixing property for such groups. Some simpler recurrence theorems (involving tuples such as (x, gx, xg)) are also presented, as well as some further discussion of specific examples of ultra quasirandom groups.     

Acid-induced rearrangement of cycloadducts from N-aryl itaconimides and 1,3-diphenylisobenzofuran

Treatment of several Diels–Alder adducts of N-aryl itaconimides and 1,3-diphenylisobenzofuran with a strong acid triggers a skeletal rearrangement resulting in 2-aryl-6,10b-diphenylbenzo[h]isoquinoline-1,3(2H,10bH)-diones.     

Large Few-Body Systems

Signatures of large few-body systems were recently observed in experiments with ultracold gases. This paper presents a brief introductory review of related theoretical concepts and recent experimental advances.     

An Unusal Case of Facile Non‐Degenerate P?C Bond Making and Breaking

Oxidation of Li/X phosphinidenoid complex 2 , obtained via selective deprotonation from the P‐H precursor 1 , with [Ph₃C]BF₄ led to the formation of two P‐F substituted diorganophosphane complexes 6 , 7 ; the latter tautomer 7 formed via H‐shift from 6 . In contrast, oxidation of 2 with [(p‐Tol)₃C]BF₄ led to three major and one minor intermediates at low temperature, which we tentatively assign to two pairs of P‐C atropisomers 10a , a′ and 10c , c′ and which differ by the relative orientations of their CH(SiMe₃)₂ and W(CO)₅ groups. Conversion of all isomers led finally to complex 11 having a ligand with a long P? C bond to the central trityl* carbon atom, firmly established by single‐crystal X‐ray analysis. DFT calculations at the B3LYP/def2‐TZVPP//BP86/def2‐TZVP level of theory on real molecular entities revealed the structures of the in situ formed combined singlet diradicals ( 4 + 5 and 5 + 9 ) and the nature of intermediates on the way to the final product, complex 11 . Remarkable is that all isomers of 11 possess relative energies in the narrow energy regime of about 20 kcal mol^?1. A preliminary study revealed that complex 11 undergoes selective P? C bond cleavage at 75 °C in toluene solution.     

Protein Phosphatase Activity and Acidic/Alkaline Balance as Factors Regulating the State of Phytochrome A and its Two Native Pools in the Plant Cell

Phytochrome A (phyA), the most versatile plant phytochrome, exists in the two isoforms, phyA′ and phyA′′, differing by the character of its posttranslational modification, possibly, by phosphorylation at the N‐terminal extension [Sineshchekov, V. (2010) J. Botany 2010, Article ID 358372]. This heterogeneity may explain the diverse modes of phyA action. We investigated possible roles of protein phosphatases activity and pH in regulation of the phyA pools' content in etiolated seedlings of maize and their extracts using fluorescence spectroscopy and photochemistry of the pigment. The phyA′/phyA′′ ratio varied depending on the state of development of seedlings and the plant tissue/organ used. This ratio qualitatively correlated with the pH in maize root tips. In extracts, it reached a maximum at pH ≈ 7.5 characteristic for the cell cytoplasm. Inhibition of phosphatases of the PP1 and PP2A types with okadaic and cantharidic acids brought about phyA′ decline and/or concomitant increase of phyA′′ in coleoptiles and mesocotyls, but had no effect in roots, revealing a tissue/organ specificity. Thus, pH and phosphorylation status regulate the phyA′/phyA′′ equilibrium and content in the etiolated (maize) cells and this regulation is connected with alteration of the processes of phyA′ destruction and/or its transformation into the more stable phyA′′.     

Correction to: Complementary pairing of o-quinone methides with 3-(N,N-diethylamino)acrolein – synthesis of 1H-benzo[f]chromene-2-carbaldehydes

In the online version electronic supplementary material was mistakenly included.

     

The NTB phase in an achiral asymmetrical bent-core liquid crystal terminated with symmetric alkyl chains

ABSTRACT

The characteristics of the twist-bend nematic (N_TB) phase of an achiral asymmetrical rigid bent-core liquid crystal (LC), the ends of which are terminated by symmetric alkyl chains, are reported. The nematic–nematic phase transition and its properties are studied by differential scanning calorimetry (DSC), polarising microscopy and the electro-optic techniques. Large domains of opposite handedness are observed in the absence of the external field in the N_TB phase. Another set of periodic striped pattern consisting of domains with sharp boundaries is formed when a high-frequency electric field with a magnitude above its threshold is applied across a planarly aligned cell. The neighbouring domains are of opposite chirality. The temperature dependence of the heliconical angle θ₀ is determined from the birefringence measurements using Haller’s extrapolation technique. This material shows lower values of the heliconical angle (~9.3° at a temperature of 155°C within the N_TB phase) when compared with the previously reported dimer-based twist-bend nematic LCs (31°±3°).