Zeno Product Formula Revisited

We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive assumptions even operator-norm convergence is verified. The mentioned formula can be used to describe Zeno dynamics in the situation when the usual non-decay measurement is replaced by a particular generalized observables in the sense of Davies.     

Weakly Coupled States on Braching graphs,Lett. Math. Phys. 38(3) (1996), 313–320

Letters in Mathematical Physics -     

Unstable systems and repeated measurements

Behaviour of an unstable system over which repeated randomly distributed measurements are performed is studied. In the first part of the paper the problem is formulated and basic properties of its solution are found. In the following parts a special attention will be paid to the case of periodically structured measuring devices when the measured decay law is expected to decrease in some sense exponentially in the asymptotic region.     

Herstellung radioaktiv markierter Äthylen/Propylen-Copolymerer. Berechnung der Primärstruktur aus kinetischen Daten

Ohne Zusammenfassung     

Evaluation of the intramolecular basis set superposition error in the calculations of larger molecules: [n]helicenes and Phe-Gly-Phe tripeptide

Correlated ab initio calculations on large systems, such as the popular MP2 (or RI-MP2) method, suffer from the intramolecular basis set superposition error (BSSE). This error is typically manifested in molecules with folded structures, characterized by intramolecular dispersion interactions. It can dramatically affect the energy differences between various conformers as well as intramolecular stabilities, and it can even impair the accuracy of the predictions of the equilibrium molecular structures. In this study, we will present two extreme cases of intramolecular BSSE, the internal stability of [n]helicene molecules and the relative energies of various conformers of phenylalanyl-glycyl-phenylalanine tripeptide (Phe-Gly-Phe), and compare the calculated data with benchmark values (experimental or high-level theoretical data). As a practical and cheap solution to the accurate treatment of the systems with large anticipated value of intramolecular BSSE, the recently developed density functional method augmented with an empirical dispersion term (DFT-D) is proposed and shown to provide very good results in both of the above described representative cases.