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.

     

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.     

Determination of the Dissociation Constants of Urocanic Acid Isomers in Aqueous Solutions

Summary. (E)- and (Z)-Urocanic acids are endogenous chemicals in the normal mammalian skin. The first and the second thermodynamic dissociation constants (pK _a1 and pK _a2) of urocanic acid isomers were determined using UV spectrophotometry in aqueous solutions. The values with standard deviation (pK _a1 = 3.43 ± 0.12 and pK _a2 = 5.80 ± 0.04) and (pK _a1 = 2.7 ± 0.3 and pK _a2 = 6.65 ± 0.04) were obtained to (E)- and (Z)-urocanic acids, respectively. The second dissociations were studied also by potentiometric titration in aqueous sodium chloride solutions up to the isotonic salt concentration (0.154 mol dm⁻³), and the second thermodynamic dissociation constants as well as activity parameters for both isomers were determined at temperature 25°C and for (E)-urocanic acid also at 37°C. The obtained pK _a2 values were close to those found by UV spectrophotometry. The equations for the calculation of the second stoichiometric dissociation constants of urocanic acid isomers on molality and molarity scale in aqueous sodium chloride solutions were derived. The obtained pK _a1 and pK _a2 values for (Z)-urocanic acid appear to be essentially lower than some previously reported values in literature. An erratum to this article is available at .     

Alnumycins A2 and A3: new inverse-epimeric pairs stereoisomeric to alnumycin A1

Two new pairs of stereoisomeric alnumycin As, A2 {(2)-(1R,1′RS,4′SR,5′SR)} and A3 {(2)-(1R,1′RS,4′SR,5′RS)}, are described. Similar to alnumycin A1 {(2)-(1R,1′RS,4′RS,5′SR)}, each of these naturally occurring compounds is also a pair of C-1 inverse epimers. The relative configurations of the dioxane ring sidechains were assigned on the basis of ¹H NMR NOE contacts and molecular modeling using density functional theory (DFT) at the M06-2X/6-31G(d) level of theory. The absolute configurations of C-1 and the determination of inverse epimeric relationships were achieved by experimental electronic circular dichroism (ECD) measurements, with both aspects confirmed by using the chiral derivatizing agent (CDA) Mosher′s acid chloride {α-methoxy-α-trifluorophenylacetyl chloride (MTPACl)} to effect enantiodifferentiation. The absolute configurations of the dioxane ring using the CDA could only be effected in the case of alnumycin A1, the results of which were in agreement with previous assignments. The dioxane ring conformational mobility and the likely interaction between the MTPA groups coupled with the structural novelty of the diols in the dioxane ring with respect to CDA analysis precluded an absolute configuration assignment for alnumycins A2 and A3 based on empirical comparisons or by computational analysis of through-space NMR shieldings (TSNMRS) emanating from the phenyl groups of the MTPA moieties.     

Dimension gap under Sobolev mappings

We prove an essentially sharp estimate in terms of generalized Hausdorff measures for the images of boundaries of Hölder domains under continuous Sobolev mappings, satisfying suitable Orlicz–Sobolev conditions. This estimate marks a dimension gap, which was first observed in [2] for conformal mappings.     

Kinetics of bioconjugate nanoparticle label binding in a sandwich-type immunoassay

Nanoparticle labels have enhanced the performance of diagnostic, screening, and other measurement applications and hold further promise for more sensitive, precise, and cost-effective assay technologies. Nevertheless, a clear view of the biomolecular interactions on the molecular level is missing. Controlling the ratio of molecular recognition over undesired nonspecific adhesion is the key to improve biosensing with nanoparticles. To improve this ratio with an aim to disallow nonspecific binding, a more detailed perspective into the kinetic differences between the cases is needed. We present the application of two novel methods to determine complex binding kinetics of bioconjugate nanoparticles, interferometry, and force spectroscopy. Force spectroscopy is an atomic force microscopy technique and optical interferometry is a direct method to monitor reaction kinetics in second-hour timescale, both having steadily increasing importance in nanomedicine. The combination is perfectly suited for this purpose, due to the high sensitivity to detect binding events and the ability to investigate biological samples under physiological conditions. We have attached a single biofunctionalized nanoparticle to the outer tip apex and studied the binding behavior of the nanoparticle in a sandwich-type immunoassay using dynamic force spectroscopy in millisecond timescale. Utilization of the two novel methods allowed characterization of binding kinetics in a time range spanning from 50 ms to 4 h. These experiments allowed detection and demonstration of differences between specific and nonspecific binding. Most importantly, nonspecific binding of a nanoparticle was reduced at contact times below 100 ms with the solid-phase surface.

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Figure A single biofunctionalized nanoparticle was attached to the outer tip apex and the binding behavior of the nanoparticle in a sandwich-type immunoassay, A) without analyte, B) with analyte and C) saturating analyte concentration, was recorded using dynamic force spectroscopy in millisecond timescale. The setting allowed measurement of the association speed of nonspecific binding.

     

Acoustic detection and classification of river boats

We present a robust algorithm to detect the arrival of a boat of a certain type when other background noises are present. It is done via the analysis of its acoustic signature against an existing database of recorded and processed acoustic signals. We characterize the signals by the distribution of their energies among blocks of wavelet packet coefficients. To derive the acoustic signature of the boat of interest, we use the Best Discriminant Basis method. The decision is made by combining the answers from the Linear Discriminant Analysis (LDA) classifier and from the Classification and Regression Trees (CART) that is also accompanied with an additional unit, called Aisles, that reduces false alarms rate. The proposed algorithm is a generic solution for process control that is based on a learning phase (training) followed by an automatic real time detection while minimizing the false alarms rate.