On the spectrum of certain noncommutative harmonic oscillators

Abstract Some spectral properties of certain 2×2 globally elliptic systems of ordinary differential operators, a class of vector-valued deformations of the classical harmonic oscillator here called noncommutative harmonic oscillators, will be described, with special emphasis on the Poisson relation and clustering properties of the eigenvalues. Keywords: Clustering theorems, Periodic trajectories, Poisson relations, Noncommutative harmonic oscillators     

Stereocomplementary Routes to Hydroxylated Nitrogen Heterocycles: Total Syntheses of Casuarine,Australine, and 7‐epi‐Australine

Addition of lithiated 1‐benzyloxyallene to a D ‐arabinose‐derived cyclic nitrone occurred with perfect diastereoselectivity furnishing a bicyclic 1,2‐oxazine derivative, which is an excellent precursor for pyrrolizidine alkaloids hydroxylated at C‐7 with optional configuration at this stereogenic center. Depending on the stage of the N? O bond cleavage and ring re‐closure, 7‐hydroxypyrrolizidines with 7R or 7S configuration were obtained, as a result of completely selective addition reactions occurring complementarily at the bottom or top face of the endocyclic C? C double bond in six‐ and five‐membered B rings, respectively. Applicability of these stereodivergent routes to obtain polyhydroxy pyrrolizidine alkaloids is demonstrated by the efficient syntheses of casuarine and australine as examples of the two classes of diversely configured 7‐hydroxypyrrolizidine alkaloids. An alternative synthesis of australine and two strategies for the preparation of 7‐epi‐australine are also reported, which demonstrate that the stereoselectivity of hydride reduction of an exocyclic C? O double bond is independent of the ring size, occurring preferentially from the top face either in a six‐ or five‐membered ring.     

Enzymatic Building-Block Synthesis for Solid-Phase Automated Glycan Assembly

Automated chemical oligosaccharide synthesis is an attractive concept that has been successfully applied to a large number of target structures, but requires excess quantities of suitably protected and activated building blocks. Herein we demonstrate the use of biocatalysis to supply such reagents for automated synthesis. By using the promiscuous NmLgtB-B β1-4 galactosyltransferase from Neisseria meningitidis we demonstrate fast and robust access to the LacNAc motif, common to many cell-surface glycans, starting from either lactose or sucrose as glycosyl donors. The enzymatic product was shown to be successfully incorporated as a complete unit into a tetrasaccharide target by automated assembly.     

An Enzymatic N-Acylation Step Enables the Biocatalytic Synthesis of Unnatural Sialosides

Chitin is one of the most abundant and cheaply available biopolymers in Nature. Chitin has become a valuable starting material for many biotechnological products through manipulation of its N-acetyl functionality, which can be cleaved under mild conditions using the enzyme family of de-N-acetylases. However, the chemoselective enzymatic re-acylation of glucosamine derivatives, which can introduce new stable functionalities into chitin derivatives, is much less explored. Herein we describe an acylase (CmCDA from Cyclobacterium marinum) that catalyzes the N-acylation of glycosamine with a range of carboxylic acids under physiological reaction conditions. This biocatalyst closes an important gap in allowing the conversion of chitin into complex glycosides, such as C5-modified sialosides, through the use of highly selective enzyme cascades.     

Phase coexistence in driven one-dimensional transport

We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte Carlo simulations, and we predict the phase diagram of this nonconserved dynamics in the thermodynamic limit.     

Enzyme-mediated synthesis of EEHP and EMHP,useful pharmaceutical intermediates of PPAR agonists

A new scaleable synthetic route to the title compounds has been developed. The reaction pathway is based on the α-chymotrypsin-catalysed hydrolysis of the racemic ethyl 2-ethoxy-3-(p-methoxyphenyl)propanoate or of the racemic ethyl 2-methoxy-3-(p-methoxyphenyl)propanoate to give the corresponding resolved (S)-esters with excellent ee. The acids were easily separated from the (S)-esters by a simple acid–base work-up. The overall yields of 1 and 2 were 16% and 17%, respectively.     

Totally asymmetric simple exclusion process on networks

We study the totally asymmetric simple exclusion process (TASEP) on complex networks, as a paradigmatic model for transport subject to excluded volume interactions. Building on TASEP phenomenology on a single segment and borrowing ideas from random networks we investigate the effect of connectivity on transport. In particular, we argue that the presence of disorder in the topology of vertices crucially modifies the transport features of a network: irregular networks involve homogeneous segments and have a bimodal distribution of edge densities, whereas regular networks are dominated by shocks leading to a unimodal density distribution. The proposed numerical approach of solving for mean-field transport on networks provides a general framework for studying TASEP on large networks, and is expected to generalize to other transport processes.     

An Exact Version of the Egorov Theorem for Schrödinger Operators in $$L^{2}({\mathbb {T}})$$ L 2 ( T )

Journal of Fourier Analysis and Applications - We provide an exact version of the Egorov Theorem for a class of Schrödinger operators in $$L^2({\mathbb {T}})$$ , where $${\mathbb {T}}={\mathbb...     

One-Pot Synthesis of Chiral N-Arylamines by Combining Biocatalytic Aminations with Buchwald–Hartwig N-Arylation

The combination of biocatalysis and chemo-catalysis increasingly offers chemists access to more diverse chemical architectures. Here, we describe the combination of a toolbox of chiral-amine-producing biocatalysts with a Buchwald–Hartwig cross-coupling reaction, affording a variety of α-chiral aniline derivatives. The use of a surfactant allowed reactions to be performed sequentially in the same flask, preventing the palladium catalyst from being inhibited by the high concentrations of ammonia, salts, or buffers present in the aqueous media in most cases. The methodology was further extended by combining with a dual-enzyme biocatalytic hydrogen-borrowing cascade in one pot to allow for the conversion of a racemic alcohol to a chiral aniline.     

Soluble (HN)2-groups

In this paper we investigate the class of finite soluble groups in which every subnormal subgroup has normal normalizer. In particular we prove that they areUN ₂U, whereU andN ₂denote finite abelian groups and of finite nilpotent groups of class at most 2 respectively.