A Cauchy kernel for slice regular functions

In this article, we show how to construct a regular, non-commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present several other consequent results.     

Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties

We define Enriques varieties as a higher dimensional generalization of Enriques surfaces and construct examples by using fixed point free automorphisms on generalized Kummer varieties. We also classify all automorphisms of generalized Kummer varieties that come from an automorphism of the underlying abelian surface.     

Front Cover: One-Pot Catalytic Synthesis of Optically Active Drug (S)-Clopidogrel (Eur. J. Org. Chem. 40/2023)

A first catalytic preparation of the popular antiplatelet drug (S)-clopidogrel, known with the tradename of Plavix, has been developed in a one-pot and innovative approach. The synthesis can be performed using commercially available ortho-chlorobenzaldehyde, 1-naphthylsulfonyl acetonitrile, tert-butyl hydroperoxide (TBHP), 4,5,6,7-tetrahydrothieno[3,2-c]pyridine and 20 mol % of a quinidine derived organocatalyst in a single solvent. A Knoevenagel/asymmetric epoxidation/domino ring-opening esterification (DROE) sequence enabled to obtain (S)-clopidogrel in 61 % overall yield and 62 % ee. Fine optimization of the reaction conditions proved to be crucial to set up a selective and efficient process.     

Open tubular liquid chromatography: Recent advances and future trends

Nano-liquid chromatography (nanoLC) is gaining significant attention as a primary analytical technique across various scientific domains. Unlike conventional high-performance LC, nanoLC utilizes columns with inner diameters (i.ds.) usually ranging from 10 to 150 μm and operates at mobile phase flow rates between 10 and 1000 nl/min, offering improved chromatographic performance and detectability. Currently, most exploration of nanoLC has focused on particle-packed columns. Although open tubular LC (OTLC) can provide superior performance, optimized OTLC columns require very narrow i.ds. (< 10 μm) and demand challenging instrumentation. At the moment, these challenges have limited the success of OTLC. Nevertheless, remarkable progress has been made in developing and utilizing OTLC systems featuring narrow columns (< 2 μm). Additionally, significant efforts have been made to explore larger columns (10–75 μm i.d), demonstrating practical applicability in many situations. Due to their perceived advantages, interest in OTLC has resurged in the last two decades. This review provides an updated outlook on the latest developments in OTLC, focusing on instrumental challenges, achievements, and advancements in column technology. Moreover, it outlines selected applications that illustrate the potential of OTLC for performing targeted and untargeted studies.     

The low-lying electronic states of YCu

The spectroscopic constants for the singlet and tripletstates of YCu below about 15 000 cm⁻¹ are determined using an internally contracted multireference configuration-interaction approach. These calculations are calibrated by studies of fewer states using higher levels of correlation treatment and/or basis sets. The computed T_c values and radiative lifetimes are in reasonable agreement with experiment. The calculations confirm the previous experimental assignment for all but one state, where theory helps resolve between two possible assignments.     

Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

Nonlinear Dynamics - The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes&nbsp;(dNNMs). Because of the non-conservative...