Cambiarenes: Single-Step Synthesis and Selective Zwitterion Binding of a Clip-Shaped Macrocycle with a Redox-Active Core

A novel macrocyclic host molecule was synthesized that forms in a single step from commercially available starting materials. The core of the macrocycle backbone possesses two quinone rings and, thus, it is redox-active. Host–guest binding involving the clip-shaped cavity indicates selective binding of pyridine N-oxides based on the electron density of and steric bulk around the anionic oxygen.     

Fluorine-Induced Pseudo-Anomeric Effects in Methoxycyclohexanes through Electrostatic 1,3-Diaxial Interactions

We report counter-intuitive axial preferences in non-stereochemically biased, selectively fluorinated methoxycyclohexanes. These pseudo-anomeric effects are apparent when electronegative CF₂ groups are placed at the C-2, C-4 and C-6 positions of the cyclohexane ring to render the C-3/5 axial hydrogen atoms electropositive. The electrostatic interaction between these axial hydrogen atoms and the -OMe oxygen is stabilising. The effect is explored using high-level ab initio and DFT calculations in the framework of NBO, QTAIM and NCI analysis across a range of derivatives, and experimentally (¹⁹F{¹H}-NMR at −80 °C) for some illustrative examples. The effect is significant in energy terms for a weak interaction, and illustrates a new stereoelectronic aspect attributed to selective fluorine substitution in organic chemistry.     

On the Classification of Automorphic Lie Algebras

The problem of reduction of integrable equations can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of Automorphic Lie Algebras, beyond the context of integrable systems. In this paper it is shown that \mathfraksl₂(\mathbbC){\mathfrak{sl}_{2}(\mathbb{C})}–based Automorphic Lie Algebras associated to the icosahedral group \mathbb I{{\mathbb I}}, the octahedral group \mathbb O{{\mathbb O}}, the tetrahedral group \mathbb T{{\mathbb T}}, and the dihedral group \mathbb D_n{{\mathbb D}_n} are isomorphic. The proof is based on techniques from classical invariant theory and makes use of Clebsch-Gordan decomposition and transvectants, Molien functions and the trace-form. This result provides a complete classification of \mathfraksl₂(\mathbbC){\mathfrak{sl}_{2}(\mathbb{C})}–based Automorphic Lie Algebras associated to finite groups when the group representations are chosen to be the same and it is a crucial step towards the complete classification of Automorphic Lie Algebras.     

On the Geometric Distance Between Quantum States with Positive Partial Transposition and Private States

We prove an analytic positive lower bound for the geometric distance between entangled positive partial transpose (PPT) states of a broad class and any private state that delivers one secure key bit. Our proof holds for any Hilbert space of finite dimension. Although our result is proven for a specific class of PPT states, we show that our bound nonetheless holds for all known entangled PPT states with non-zero distillable key rates, irrespective of whether they are in our special class or not. Thus, our result naturally leads to the conjecture of impossibility of using PPT-bound entangled state in physical implementation of quantum key distribution.     

A footnote to The crisis in contemporary mathematics

We examine the preparation and context of the paper “The Crisis in Contemporary Mathematics” by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as ‘a debasement of meaning.’ The ‘debasement’ comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. We elucidate the context of the ‘debasement’ comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle.     

Delayed pulse referencing for cancellation of polychromatic beating noise in grating spectrometry

We use a grating spectrometer with a time resolution of 17.4 μs and a spectral resolution of 5 GHz to analyze a superluminescent source operating near 1350 nm. Polychromatic beating noise is shown to dominate single-shot measurements of the source spectrum; the observed noise level is within 19% of the theoretical beating noise level. By adopting a delayed pulse referencing scheme used previously with wavelength-swept sources, the beating noise is virtually eliminated, allowing spectral measurements limited only by shot noise and camera read noise.     

Reverse Mathematics and parameter-free Transfer

Recently, conservative extensions of Peano and Heyting arithmetic in the spirit of Nelson's axiomatic approach to Nonstandard Analysis, have been proposed. In this paper, we study the Transfer axiom of Nonstandard Analysis restricted to formulas without parameters. Based on this axiom, we formulate a base theory for the Reverse Mathematics of Nonstandard Analysis and prove some natural reversals, and show that most of these equivalences do not hold in the absence of parameter-free Transfer.