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Herein, a rational design of a biohybrid catalyst is described, consisting of Pd nanoparticles and a cross-linked network of aggregated lipase B enzyme of Candida antarctica (CalB CLEA) functioning as an active support for the Pd nanoparticles. Both entities of the hybrid catalyst showed good catalytic activity. The applicability was demonstrated in a one-pot reaction where Pd-catalyzed cycloisomerization of 4-pentynoic acid afforded a lactone that serves as acyl donor in a subsequent selective enzymatic kinetic resolution of a set of sec-alcohols. The catalyst proved to be robust and could be recycled five times without significant loss of activity.

A deformation of the classical trigonometric BC n Sutherland system is derived via Hamiltonian reduction of the Heisenberg double of SU(2n). We apply a natural Poisson-Lie analogue of the Kazhdan-Kostant-Sternberg type reduction of the free particle on SU(2n) that leads to the BC n Sutherland system. We prove that this yields a Liouville integrable Hamiltonian system and construct a globally valid model of the smooth reduced phase space wherein the commuting flows are complete. We point out that the reduced system, which contains 3 independent coupling constants besides the deformation parameter, can be recovered (at least on a dense submanifold) as a singular limit of the standard 5-coupling deformation due to van Diejen. Our findings complement and further develop those obtained recently by Marshall on the hyperbolic case by reduction of the Heisenberg double of SU(n, n).

We present a new case of duality between integrable many-body systems, where two systems live on the action-angle phase spaces of each other in such a way that the action variables of each system serve as the particle positions of the other one. Our investigation utilizes an idea that was exploited previously to provide group-theoretic interpretation for several dualities discovered originally by Ruijsenaars. In the grouptheoretic framework one applies Hamiltonian reduction to two Abelian Poisson algebras of invariants on a higher dimensional phase space and identifies their reductions as action and position variables of two integrable systems living on two different models of the single reduced phase space. Taking the cotangent bundle of U(2n) as the upstairs space, we demonstrate how this mechanism leads to a new dual pair involving the BC n trigonometric Sutherland system. Thereby we generalize earlier results pertaining to the A n trigonometric Sutherland system as well as a recent work by Pusztai on the hyperbolic BC n Sutherland system.

We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the 'Ruijsenaars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BC n generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.

In this paper, we construct a Lax pair for the classical hyperbolic van Diejen system with two independent coupling parameters. Built upon this construction, we show that the dynamics can be solved by a projection method, which in turn allows us to initiate the study of the scattering properties. As a consequence, we prove the equivalence between the first integrals provided by the eigenvalues of the Lax matrix and the family of van Diejen's commuting Hamiltonians. Also, at the end of the paper, we propose a candidate for the Lax matrix of the hyperbolic van Diejen system with three independent coupling constants.

Herein, we report on the use a biohybrid catalyst consisting of palladium nanoparticles immobilized on cross‐linked enzyme aggregates of lipase B of Candida antarctica (CalB CLEA) for the dynamic kinetic resolution (DKR) of benzylic amines. A set of amines were demonstrated to undergo an efficient DKR and the recyclability of the catalysts was studied. Extensive efforts to further elucidate the structure of the catalyst are presented.

Tertiary alcohols are known to be challenging substrates for applications in asymmetric synthesis due to their complexity and steric hinderance. The occurrence of tertiary alcohols and their esters in nature indicates the presence of natural biocatalytic synthetic routes for their preparation. Lipase A from Candida antarctica (CalA) is a hydrolase that has previously been shown to catalyze the transesterification of racemic 2‐phenylbut‐3‐yn‐2‐ol at a low rate. In this work, the activity of that enzyme was improved by protein engineering through a semi‐rational design strategy. An enzyme library was created and screened for transesterification activity towards racemic 2‐phenylbut‐3‐yn‐2‐ol in an organic solvent. One successful enzyme variant (L367G) showed a tenfold increased reaction rate compared to the wild‐type enzyme, while maintaining a high enantioselectivity.