Benzo‐Fused Double [7]Carbohelicene: Synthesis,Structures, and Physicochemical Properties

A benzo‐fused double [7]carbohelicene (D7H) was synthesized through a regioselective cyclodehydrogenation of a tetranaphthyl‐p ‐terphenyl‐based precursor. The twisted (D7H‐1) and anti ‐folded (D7H‐2) conformers of D7H were separated by recrystallization, and their double helicene structures with overlapping terminal benzene rings were unambiguously elucidated by X‐ray crystallography. A record‐high isomerization barrier (46.0 kcal mol⁻¹) in double helicenes was estimated based on density functional theory (DFT) calculation, which resulted in the excellent conformational stability of D7H. The physicochemical properties of D7H‐1 and D7H‐2 were investigated by UV/Vis absorption spectroscopy and cyclic voltammetry, displaying the variation of electronic structure upon conformational changes. The optical resolution of the racemic D7H‐1 was carried out by chiral HPLC, offering enantiopure D7H‐1‐(P ,P ) and D7H‐1‐(M ,M ), which were further characterized by circular dichroism spectroscopy.     

On primeness of general skew inverse Laurent series ring

Ever since the introduction, skew inverse Laurent series rings have kept growing in importance, as researchers characterized their properties (such as Noetherianness, Armendarizness, McCoyness, etc.) in terms of intrinsic properties of the base ring and studied their relations with other fields of mathematics, as for example quantum mechanics theory. The goal of our paper is to study the primeness and semiprimeness of general skew inverse Laurent series rings R((x^?1;σ,δ)), where R is an associative ring equipped with an automorphism σ and a σ-derivation δ.     

Interlacing of Hurwitz series

In this paper, we introduce the notion of interlacing of Hurwitz series. We begin by reviewing some important properties of the ring of Hurwitz series over a commutative ring A of arbitrary characteristic, and we introduce and investigate properties of the maps exp and log. We show that solutions of linear homogeneous differential equations with constant coefficients from the ring A can be described simply as interlacings of solutions of a first order system of differential equations. We give several examples to illustrate this result, and we conclude by defining and investigating properties of trigonometric functions using interlacings of Hurwitz series.     

On maximal subalgebras and a generalized Jordan–Hölder theorem for Lie algebras

The purpose of this paper is to continue the study of chief factors of a Lie algebra and to prove a further strengthening of the Jordan–Hölder theorem for chief series.     

Relationships between the canonical ascending and descending central series of ideals of an associative algebra

We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results.     

Generalized harmonic number summation formulae via hypergeometric series and digamma functions

By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae for generalized harmonic numbers.