Nonautonomous Hamiltonian quantum systems,operator equations,and representations of the Bender–Dunne Weyl-ordered basis under time-dependent canonical transformations

We solve the problem of integrating operator equations for the dynamics of nonautonomous quantum systems by using time-dependent canonical transformations. The studied operator equations essentially reproduce the classical integrability conditions at the quantum level in the basic cases of one-dimensional nonautonomous dynamical systems. We seek solutions in the form of operator series in the Bender–Dunne basis of pseudodifferential operators. Together with this problem, we consider quantum canonical transformations. The minimal solution of the operator equation in the representation of the basis at a fixed time corresponds to the lowest-order contribution of the solution obtained as a result of applying a canonical linear transformation to the basis elements.     

Wave packets and statistics concerned with SUSY-QM partners of Paul trap Hamiltonians

We consider time-dependent quadratic Hamiltonians in the supersymmetric quantum mechanical framework. We study the quantum mechanical properties of some basic states in the fermionic sector of the Hilbert space. To understand the differences between the bosonic and fermionic sectors better, we focus on periodic quadratic Hamiltonians of the Paul-trap type.     

Production of glucose and bioactive aglycone by chemical and enzymatic hydrolysis of purified oleuropein fromOlea Europea

Pure-grade oleuropein, a bitter, hypotensive, phenolic glucoside, was obtained from organic extracts of olive plant leaves by two Chromatographic steps. The purified compound was characterized by spectroscopic NMR and FAB-MS methods. The glucoside underwent chemical and enzymatic hydrolysis. Aglycone was characterized by spectroscopic methods (¹H-NMR and FAB-MS). Glucose was measured by enzymatic methods. The enzymatic hydrolysis of oleuropein was carried out by a soluble β-glucosidase. The reaction was characterized in terms of kinetic parameters, optimal pH value, activation energy, inhibition constant by glucose, and thermal stability. Preliminary experiments were also performed in a continuousflow ultrafiltration membrane reactor. The cut-off of the membrane was lower than the molecular-weight of the enzyme, thus determining β-glucosidase confinement within the reactor. Under these conditions, β-glucosidase had a good long-term stability. This is an encouraging result in view of possible industrial applications.     

Theoretical and experimental analysis of an immobilized enzyme membrane reactor

The unsteady state behavior of an immobilized enzyme membrane reactor has been analyzed both theoretically and experimentally. The reacting system considered is sucrose hydrolysis by invertase (EC 3.2.1.26). Enzyme immobilization has been obtained by ultrafiltering co-cross-linked invertase through a cellulose acetate asymmetric membrane. On the basis of the proposed mathematical model, the steady state behavior of the system can be dealt with in terms of a continuous stirred tank reactor