Feynman maps without improper integrals

The Feynman maps introduced first by Truman are examined. The domain considered here consists of the Fresnel-integrable functions in the sense of Albeverio and Hoegh-Krohn; extensions to wider classes of functions will be studied in the following paper. The original definition of the F-maps is slightly modified: we start from the underlying measures on the Hilbert space of paths in order to avoid use of improper integrals. Some new properties of the F-maps are derived. In particular, the dominated convergence theorem is shown to be not valid for the F₁-map (or Feynman integral); this fact is of a certain importance for the classical limit of quantum mechanics.Dedicated to Professor Ivan Úlehla on the occasion of his sixtieth birthday.On leave from theNuclear Centre, Faculty of Mathematics and Physics of Charles University, Areál Troja, Povltavská ul., 180 00 Prague 8, Czechoslovakia.     

The Chemistry of Hydroxamic Acids and N-Hydroxyimides

This progress report is concerned primarily with problems relating to the structure and reactions of hydroxamic acids and N-hydroxyimides, and also surveys some of the biological activities of these compounds. Particular significance attaches to the Lossen rearrangement of O-acylated hydroxamic acids, which leads to isocyanates or their reaction products.     

Steric effects of polar substituents evaluated in terms of energy by means of isodesmic reactions

Steric effects of various polar and some charged groups were estimated on sterically crowded cyclopropane cis-1,2-bis derivatives 2 or 3, in which the variable substituent is in the proximity of a t-butyl group or of a methyl group. The steric energy was evaluated with reference to the pertinent mono derivatives, that is as reaction energy of an isodesmic reaction, in which the crowded compound is formally synthesized from simple derivatives. Energies were calculated within the framework of the density functional theory at level B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) for 11 dipolar and 5 charged substituents. Interaction of charged substituents is not only steric (destabilizing) but also inductive (stabilizing). The steric effects evaluated in this way differ distinctly from the standard steric constants derived purely from the van der Waals radii of the substituents.     

Synthesis and photoswitching studies of difurylperfluorocyclopentenes with extended π-systems

In an attempt to design molecular optoelectronic switches functioning in molecular junctions between two metal tips, we synthesized a set of photochromic compounds by extending the π-system of 1,2-bis-(2-methyl-5-formylfuran-3-yl)perfluorocyclopentene through suitable coupling reactions involving the formyl functions, thereby also introducing terminal groups with a binding capacity to gold. Avoiding the presence of gold-binding sulphur atoms in the photoreactive centre, as they are present in the frequently used analogous thienyl compounds, the newly synthesized compounds should be more suitable for the purpose indicated. The kinetics of reversible photoswitching of the new compounds by UV and visible light was quantitatively investigated in solution. The role of conformational flexibility of the π-system for the width of the UV/Vis spectra was clarified by using quantum chemical calculations with time-dependent (TD)-DFT. As a preliminary test of the potential of the new compounds to serve as optoelectronic molecular switches, monolayer formation and photochemical switching on gold surfaces was observed by using surface plasmon resonance.     

On Semi-weakly n-Hyponormal Weighted Shifts

Semi-weak n-hyponormality is defined and studied using the notion of positive determinant partition. Several examples related to semi-weakly n-hyponormal weighted shifts are discussed. In particular, it is proved that there exists a semi-weakly three-hyponormal weighted shift W _α with α ₀ = α ₁ < α ₂ which is not two-hyponormal, which illustrates the gaps between various weak subnormalities.     

Structure of weak laminar hydraulic jumps in single layer and two layer fluids

We consider the occurrence of hydraulic jumps in near critical single layer and two layer flows under the assumption that viscous effects are confined to a thin laminar boundary layer adjacent to the solid boundary. In the limit of large Reynolds number this leads to a structure problem formed by the classical triple deck equations supplemented with a novel nonlinear coupling condition which allows for the passage through the critical state. In the case of positive hydraulic jumps this passage is achieved by the local thickening of the boundary layer which acts as a viscous hump. Conversely, the pressure drop at the wall associated with negative hydraulic jumps causes the boundary layer to decrease locally thereby forming a local indentation required for the Froude number to pass through one in this case.