The determination of the past and the future of a physical system in quantum mechanics

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using unsharp measurements.This work was partly supported by the Bundesministerium für Forschung und Technologie, Bonn, the Research Institute for Theoretical Physics, Helsinki, and the University of Turku Foundation, Turku.     

Eu- and Yb-induced reconstructions on a vicinal Si(1 0 0) surface

Early stages of rare-earth metal (Yb and Eu) growth on a vicinal, single-domain Si(1 0 0)2 × 1 surface have been studied in the coverage range of 0.1-0.3 monolayer (ML) by low energy electron diffraction, scanning tunneling microscopy, and synchrotron radiation photoemission spectroscopy. We show that Yb induces the 2 × 3 periodicity in the whole range of coverage studied. The 2 × 3 reconstruction coexists with the local 3 × 2/4 × 2 structure at about 0.2 ML of Yb. In contrast, Eu forms the 3 × 2 periodicity at 0.1-0.2 ML, whereas this structure is converted into the 2 × 3 phase at about 0.3 ML. The atomic arrangement and electronic properties of these reconstructions and the adsorbate-mediated modification of surface morphology are investigated.     

Coherent States and Number-Phase Uncertainty Relations

The number-phase uncertainty relations arerevisited in view of the recent discovery of a propercovariant phase observable. The high-amplitude limits ofthe coherent-state expectations of the moment operators of the phase observable are determined and thebehavior of the number-phase uncertainty product in thatlimit is investigated.     

Hardy's inequality and the boundary size

We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.

     

Molecular dynamics simulations of conserved Hox protein hexapeptides. I. Folding behavior in water solution

Molecular dynamics simulations of hexapeptides TFDWMK and LFPWMR; the highly conserved regions of Hox proteins Hox B1 and Hox B8, respectively, are carried out starting from extended structures to investigate their conformational space in water solution. In addition, we have studied TADWMK and TADAMK, where the aromatic residues Phenylalanine and Tryptophan were successively substituted for Alanine to investigate effects from the presence/absence of aromatic amino acids and interactions between them to folding behavior. The backbone of the hexapeptides in all simulations folds to a similar conformation found in experimental studies in solution. Intramolecular, hydrophobically driven interactions between the aromatic residues and internal hydrogen bonds are found to stabilize the conformations.     

Rapid determination of trace concentrations of lead in gasoline by anodic stripping voltammetry

Anodic stripping voltammetry can be used for the determination of g/l concentrations of lead in gasoline. A gasoline sample is extracted with iodine monochloride reagent solution. An aliquot of the aqueous phase is pipetted into the measuring cell of the voltammeter. The ease of this method makes it a good alternative to atomic absorption spectrophotometry.     

Synthesis and catalytic activity of new chiral unsymmetrical Mn(III)-Schiff-base complexes containing salicylaldehyde and 1-(2-hydroxyphenyl)ketone units

Two new chiral unsymmetrical (non-C₂-symmetric) Schiff-base ligands containing salicylaldehyde and 1-(2-hydroxyphenyl)ketone units were synthesized from (R,R)-1,2-diphenylethylenediamine as the chiral diamine using a stepwise approach. The Mn(III) complexes of the ligands were subsequently used as catalysts in asymmetric epoxidation of unfunctionalized alkenes and the results were compared with those obtained using typical C₂-symmetric Mn(III)–salen complexes. Possible reasons for the differences in reactivity and selectivity between the two types of catalysts are briefly discussed.