Effects of complex-valued electronic wave functions on nuclear motions

Moleculer species and colliding groups of atoms are considered for which the electronic wave functions are complex-valued, having arguments that depend parametrically on the nuclear coordinates. The effective Hamiltonian for nuclear motions in the adiabatic approximation that arises in the present case differs from the ordinary Born–Oppeneheimer Hamiltonian, the latter being obtained when restriction to real-valued electronic functions is made. The asymptotic boundary conditions imposed in collision theory lead to in- and out- states [8], and hence to complex-valued wave functions in the coordinate representation. The study of the influence of electron–molecule scattering on nuclear motions therefore necessitates the use of the new effective Hamiltonian, which leads to results differing from those predicted on the basis of the Born–Oppenheimer operator. It is shown that momentum-dependent potentials occurring in the new Hamiltonian might cause “distortions” to the vibrational patterns of some electron–molecule metastable states. Also, these terms can give rise to non-Born–Oppenheimer resonances when motions in an internuclear coordinate become unbounded. We derive expressions for the relevant level widths and line shapes, showing them to be subject to an isotope effect. Even when real-valued electronic functions may be used, the selections of complex-valued functions in their linear span is still optional. Although exact treatments lead to the same results in both real and complex cases we show how the choice of the argument of the electronic function to be non-zero and dependent on nuclear coordinates may be useful for the application of certain approximation schemes. It is demonstrated that for certain systems a suitable choice of the argument assures convergence when the related Lippmann–Schwinger Equation is iterated. It is also shown that in this way an nth order term in the series expansion of the T matrix [8] for moleculer systems can be made negligibly small.     

Determination of the diastereomers of vitamin K1

A method is described for the gas-chromatographic determination of the diastereomers of vitamin K₁ (phylloquinone) in the form of their dihydro dimethyl ethers. The reported method of derivatization and chromatographic analysis in conjunction with optical rotation measurements are useful approaches for characterization of vitamin K₁ samples with respect to their origin.     

Structural basis for recognition of bacterial cell wall teichoic acid by pseudo-symmetric SH3b-like repeats of a viral peptidoglycan hydrolase

Endolysins are bacteriophage-encoded peptidoglycan hydrolases targeting the cell wall of host bacteria via their cell wall-binding domains (CBDs). The molecular basis for selective recognition of surface carbohydrate ligands by CBDs remains elusive. Here, we describe, in atomic detail, the interaction between the Listeria phage endolysin domain CBD500 and its cell wall teichoic acid (WTA) ligands. We show that 3′O-acetylated GlcNAc residues integrated into the WTA polymer chain are the key epitope recognized by a CBD binding cavity located at the interface of tandem copies of beta-barrel, pseudo-symmetric SH3b-like repeats. This cavity consists of multiple aromatic residues making extensive interactions with two GlcNAc acetyl groups via hydrogen bonds and van der Waals contacts, while permitting the docking of the diastereomorphic ligands. Our multidisciplinary approach tackled an extremely challenging protein–glycopolymer complex and delineated a previously unknown recognition mechanism by which a phage endolysin specifically recognizes and targets WTA, suggesting an adaptable model for regulation of endolysin specificity.

Combining genetic, biochemical and computational approaches, we elucidated the molecular mechanisms underlying the recognition of Listeria wall teichoic acid by bacteriophage-encoded SH3b repeats.     

Kantorovich’s Fixed Point Theorem and Coincidence Point Theorems for Mappings in Vector Metric Spaces

Set-Valued and Variational Analysis - The fixed points and coincidence points of mappings of v-metric spaces, i.e., sets on which a vector metric is defined, are investigated. The values of such a...     

Four modes competition and chaos in a shell

Steady-state chaotic vibrations of a shallow shell as a system with a nonsymmetrical restoring force and one equilibrium state are considered. Mode interaction and its effect on a chaotic behavior of the shell is studied. The terms "natural" and "imposed" chaos are introduced for the response of resonant and nonresonant modes. It is shown that such a qualitative difference is important for better understanding of chaos in systems with distributed parameters, and may be very useful for numerical investigations. Some qualitative comparisons with previous papers on chaos in distributed mechanical systems are also made. (c) 1994 American Institute of Physics.     

Ultraviolet emission spectra of sunbeds

It is well known that UV radiation contributes to the development of skin cancer. Exposure to solar radiation is predominantly responsible for the high incidence rate of skin cancer, but there are also indications that sunbeds are involved. The aim of the present investigation was to determine the UV emission spectra of sunbeds. It included the most common sunbed models, which cover more than 50% of the Swiss market. The UV emission spectra of sunbeds have special characteristics and are different from the sun spectrum, which can be seen in high-resolution spectral measurements. Sunbed emission spectra are similar to the sun spectrum in the UVB (280-320 nm) range but reach values 10 to 15 times higher in the UVA (320-400 nm) range. An average erythema-effective irradiance of 0.33 W/m2 was determined for sunbeds. This corresponds to a UV index of 13, which is significantly higher than the UV index of 8.5 of the high summer sun at noon at intermediate latitudes. The measurements were spread over the whole effective area of the sunbeds, and an inhomogeneous distribution of the irradiances with variations of up to 30% from the average value was found.