Mechanistic aspects of aldehyde and imine electro-reduction in a liquid–liquid carbon nanofiber membrane microreactor

A simple and electrolyte-free ion-transfer electrosynthesis micro-reactor system (volume 100 μL, up to 10 mg batches) for processes at liquid–liquid interfaces is developed and demonstrated for the reduction of aldehydes and imines. These cathodic reactions occur at an amphiphilic carbon nanofiber membrane accompanied by proton cation transfer from an aqueous phase into an organic phase.     

Copper Causes Regiospecific Formation of C4F8‐Containing Six‐Membered Rings and their Defluorination/Aromatization to C4F4‐Containing Rings in Triphenylene/1,4‐C4F8I2 Reactions

The presence of Cu in reactions of triphenylene (TRPH) and 1,4‐C₄F₈I₂ at 360 °C led to regiospecific substitution of TRPH ortho C(β) atoms to form C₄F₈‐containing rings, completely suppressing substitution on C(α) atoms. In addition, Cu caused selective reductive‐defluorination/aromatization (RD/A) to form C₄F₄‐containing aromatic rings. Without Cu, the reactions of TRPH and 1,4‐C₄F₈I₂ were not regiospecific and no RD/A was observed. These results, supported by DFT calculations, are the first examples of Cu‐promoted 1) regiospecific perfluoroannulation, 2) preparative C?F activation, and 3) RD/A. HPLC‐purified products were characterized by X‐ray diffraction, low‐temperature PES, and ¹H/¹⁹F NMR.     

Noetherianity of some degree two twisted commutative algebras

The resolutions of determinantal ideals exhibit a remarkable stability property: for fixed rank but growing dimension, the terms of the resolution stabilize (in an appropriate sense). One may wonder if other sequences of ideals or modules over coordinate rings of matrices exhibit similar behavior. We show that this is indeed the case. In fact, our main theorem is more fundamental in nature: It states that certain large algebraic structures (which are examples of twisted commutative algebras) are noetherian. These are important new examples of large noetherian algebraic structures, and ones that are in some ways quite different from previous examples.     

Self-intersections in combinatorial topology: statistical structure

Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the minimum number of transversal self-intersection points of representatives of the class. We prove that if a class is chosen at random from among all classes of m letters, then for large m the distribution of the self-intersection number approaches the Gaussian distribution. The theorem was strongly suggested by a computer experiment with four million curves producing a very nearly Gaussian distribution.