Effect of multiple H‐bonding on the properties of polyimides containing the rigid rod groups

To investigate the influence of hydrogen bonding on the properties of polyimides (PIs) containing rigid rod‐like groups, five symmetrical diamines containing benzimidazole, benzoxazole, and hydroxy group were synthesized, and then a series of PIs were prepared. Results showed that hydroxyl‐containing poly(benzoxazole imide)s possess higher glass transition temperature (T_g) and dimensional stabilities than their corresponding poly(benzoxazole imide)s. Moreover, the corresponding poly(benzimidazole imide)s presented the best performances, such as the highest T_g, the highest char yield and the highest dimensional stabilities. The influence of hydrogen bonding of benzimidazole on the properties of PIs was stronger than that of hydroxyl groups. Hydroxyl‐containing poly(benzoxazole imide)s were formed in crosslinking structures after heat treatment at 400 °C. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 570–581     

C−H Acetoxylation‐Based Chemical Synthesis of 17 β‐Hydroxymethyl‐17 α‐methyl‐18‐norandrost‐13‐ene Steroids

Palladium‐catalyzed C?H acetoxylation has been proposed as a key transformation in the first chemical synthesis of steroids bearing a unique 17β‐hydroxymethyl‐17α‐methyl‐18‐nor‐13‐ene D ‐fragment. This C?H functionalization step was crucial for inverting the configuration at the quaternary stereocenter of a readily available synthetic intermediate. The developed approach was applied to prepare the metandienone metabolite needed as a reference substance in anti‐doping analysis to control the abuse of this androgenic anabolic steroid.     

Laguerre Polynomials, Restriction Principle, and Holomorphic Representations of SL(2,R)

The restriction principle is used to implement a realization of the holomorphic representations of SL(2,R) on L ² (R ⁺,t dt) by way of the standard upper half plane realization. The resulting unitary equivalence establishes a correspondence between functions that transform according to the character e^–i(2n++1); under rotations and the Laguerre polynomials. The standard recursion relations amongst Laguerre polynomials are derived from the action of the Lie algebra.     

The Ramifications of the Centres: Quantised Function Algebras at Roots of Unity

This paper continues the study of quantised function algebrasO[G] of a semisimple group G at an lth root of unity . Thesealgebras were introduced by De Concini and Lyubashenko in 1994,and studied further by De Concini and Procesi and by Gordon,amongst others. Our main purpose here is to increase understandingof the finite-dimensional factor algebras O[G](g), for g G.We determine the representation type and block structure ofthese factors, and (for many g) describe them up to isomorphism.A series of parallel results is obtained for the quantised Borelalgebras and . 2000 Mathematical Subject Classification: 16W35,17B37.     

Polynomial Dehn Functions and the Length of Asynchronously Automatic Structures

We extend the range of observed behaviour among length functionsof optimal asynchronously automatic structures. We do so bymeans of a construction that yields asynchronously automaticgroups with finite aspherical presentations where the Dehn functionof the group is polynomial of arbitrary degree. Many of thesegroups can be embedded in the automorphism group of a free group.Moreover, the fact that the groups have aspherical presentationsmakes them useful tools in the search to determine the spectrumof exponents for second order Dehn functions. We contributeto this search by giving the first exact calculations of groupswith quadratic and superquadratic exponents. 2000 Mathematical Subject Classification: 20F06, 20F65, 20F69.     

Abstract Commensurators of Groups Acting on Rooted Trees

We show that the abstract commensurator of a nearly level transitive weakly branch group H coincides with the relative commensurator of H in the homeomorphism group of the boundary of the tree on which H acts. It is also shown that the commensurator of an infinite group which is commensurable with its own nth direct power contains a Higman–Thompson group as a subgroup. Applying these results to the Grigorchuk 2-group G we show that the commensurator of G is a finitely presented infinite simple group.