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.     

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.

     

Studies on coordination compounds vii,chromatographic, thermoanalytical and spectroscopic studies on thermal decomposition of cadmium(II) and lead(II) salicyl-aldoximates

On the basis of decomposition temperatures and infrared spectra, cadmium(II) and lead(II) bissalicylaldoximates were considered to havetrans andcis structures, respectively.In the first stage bis(salicylaldoximato)cadmium(II) decomposes thermally like bis(salicylaldoximato)lead(II), with one ligand molecule leaving, but the intermediate is unstable and immediately decomposes further. The oxidation of the end- product is a rapid, exothermic reaction, probably catalyzed by cadmium metal. The mass spectrum of (C₇H₆O₂N)₂ Cd points to a different decomposition scheme than that elucidated through the pyrolysis decomposition products. This may be due to a catalytic effect of the ionization chamber. The thermal properties of (C₇H₅O₂N) Cd support the preceding views.TG curves showed the decompositions of mono(salicyl-aldoximato) lead(II) and the intermediate of bis(salicyl-aldoximato) lead(II) to be similar. The mass spectra of the chelates confirmed the formation of the same polymer (m/e 222) in both decompositions. Only the mass spectrum of (C₇H₅O₂N)Pb exhibited the molecular peakm/e 343. The decomposition schemes of the lead(II) salicylaldoximates were therefore elucidated more exactly. The metallic lead seems not to catalyze the oxidation of the organic part.

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Zusammenfassung Aufgrund der Zersetzungstemperatur und der Infrarotspektrum werden Cadmium(II)- und Blei(II)-bisalicylaldoximate als Verbindungen mit trans- bzw. cis-Struktur angesehen. Im ersten Schritt wird Bis-(salicylaldoximato)-blei(II) unter Abspaltung eines Ligandmoleküls zersetzt, die Zwischenverbindung ist jedoch nicht stabil und zersetzt sich sofort weiter. Die Oxydation des Endproduktes ist eine schnelle exotherme, wahrscheinlich durch metallisches Cadmium katalysierte Reaktion. Das Massenspektrum von (C₇H₆O₂N)₂ Cd weist auf ein Zersetzungsschema hin, das sich von dem aus den pyrolytischen Zersetzungsprodukten abgeleiteten unterscheidet. Dies ist möglicherweise auf einen katalytischen Effekt der Ionisationskammer zurückzuführen. Die thermischen Eigenschaften von (C₇H₅O₂N)Cd unterstützen diese Auffassungen. Aus den TG-Kurven ist zu ersehen, dass die Zersetzungen von Mono(salicylaldoximato)-blei(II) und des Zwischenproduktes von Bis(salicylaldoximato)-blei(II) ähnlich sind. Massenspektren der Chelate bestätigen die Bildung des gleichen Polymers (m/e 222) bei der Zersetzung beider Verbindungen. Nur im Massenspektrum von (C₇H₅O₂N)Pb tritt der Molekularpeak (m/e343) auf. Die Zersetzungsschemata der Salicylaldoximate von Blei(II) sind deshalb genauer aufgeklärt. Metallisches Blei scheint die Oxydation der organischen Komponente nicht zu katalysieren.

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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.     

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.     

Structure and dynamics of liquid water with different long-range interaction truncation and temperature control methods in molecular dynamics simulations

We have used molecular dynamics simulations to study the physical properties of modified TIP3P water model included in the CHARMM program, using four different methods-the Ewald summation technique, and three different spherical truncation methods-for the treatment of the long-range interactions. Both the structure and dynamics of the liquid water model were affected by the methods used to truncate the long-range interactions. For some of the methods artificial structuring of the model liquid was observed around the cutoff radius. The model liquid properties were also affected by the commonly applied temperature control methods. Four different methods for controlling the temperature of the system were studied, and the effects of these methods on the bulk properties for liquid water were analyzed. The system size was also found to change the dynamics of the model liquid water. Two control simulations with the SPC/E water model were carried out. The self-diffusion coefficient (D), the radial distribution function (g(OO)), the distance dependent Kirkwood G-factor [G(k)(r)] and the intermolecular potential energy (E(pot)) were determined from the different trajectories and compared with the experimental data.