Modeling of drift-diffusion systems

We derive drift-diffusion systems describing transport processes starting from free energy and equilibrium solutions by a unique method. We include several statistics, heterostructures and cross diffusion. The resulting systems of nonlinear partial differential equations conserve mass and positivity, and have a Lyapunov function (free energy). Using the inverse Hessian as mobility, non-degenerate diffusivity matrices turn out to be diagonal, or – in the case of cross diffusion – even constant.     

The ratio of decay constants ƒB/ƒD

The result ƒ_B≈ƒ_D which had been obtained from sum rules and lattice calculations, and which contradicts the naïve prediction ƒ_p1/√M_p, is rederived using a simple argument based on semilocal parton-hadron duality. Is is argued that both here and in sum rules the key point is the use of semilocal duality instead of the bound-state wave functions.     

Flow of oil and water in a porous medium

The flow of two immiscible and incompressible fluids in a porous medium is described by a system of quasilinear degenerate partial differential equations. In this paper the existence of a weak solution by regularization is shown.     

Supplier switching decisions

In order to maximize profit, a buying firm should continuously search for and access sources which offer more favorable prices. While the literature is replete with works on the formation and development of buyer–supplier relationships, there is surprisingly only scarce research on the termination of such relationships and supplier switching. Using the concept of switching costs in a principal-agent framework, we at first analyze whether a firm switches the entire or a partial quantity to an alternative supplier when there is either symmetric or asymmetric information about the alternative supplier’s cost structure. Information asymmetry results in inert supplier switching decisions. Subsequently, we extend our model and take competitive reactions of the incumbent supplier and economies of scale effects into consideration. We find conditions under which ‘no’, ‘partial’ and ‘complete’ switching occurs, which depend on the buying firm’s beliefs about the alternative supplier’s unit costs, switching costs, the price offered by the incumbent supplier, and refinements of the price offered by the incumbent supplier due to competitive reactions and economies of scale. Broader implications for supplier relationship management and sourcing strategy decisions are also provided.     

Complex symmetric operators and applications

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.

     

(R)-Oxynitrilase catalyzed synthesis of (R)-ketone cyanohydrins

(R)-Oxynitrilase from almonds (Prunus amygdalus) catalyzes the enantioselective addition of HCN to ethyl alkyl ketones 1 in diisopropyl ether yielding (R)-ethyl alkyl ketone cyanohydrins (R)-2, which are hydrolyzed under acid catalysis to give the -hydroxy acids (R)-3. This (R)-oxynitrilase also catalyzes the enantioselective addition in aqueous citrate buffer (50 mM, pH 4.0), as demonstrated for the preparation of (R)-methyl alkyl ketone cyanohydrins (R)-5 which are obtained in high enantiomeric excesses comparable to those in diisopropyl ether as solvent.