Eigenvalue ratios of vibrating strings

Summary New results for the eigenvalue ratios of vibrating strings are presented partially in connection with previous results concerning Schr?dinger operators.     

Multiple Shocks in Bricklayers' Model

In bricklayers' model, which is a generalization of the misanthrope processes, we show that a nontrivial class of product distributions is closed under the time-evolution of the process. This class also includes measures fitting to shock data of the limiting PDE. In particular, we show that shocks of this type with discontinuity of size one perform ordinary nearest neighbor random walks only interacting, in an attractive way, via their jump rates. Our results are related to those of Belitsky and Schütz⁽⁴⁾ on the simple exclusion process, although we do not use quantum formalism as they do. The structures we find are described from a fixed position. Similar ones were found in Balázs,⁽²⁾ valak as seen from the random position of the second class particle.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Spectroscopic investigation of cyclodextrin monomers,derivatives, polymers and azo dyes (1)

Circular dichroism (CD) and visible spectra of inclusion compounds between Methyl Orange (MO) analogues and -, -, -cyclodextrin (cdx), 2,6-dimethyl-and 2,3,6-trimethyl--cdx, water soluble -, -, -cdx polymer products were investigated. In the CD-spectroscopic investigation, the complex with -cdx epichlorohydrin condensate showed a large amplitude and splitting of the induced ^* band. Fractions of glyceryl ether of less than 2000 and polymer of more than 10000 dalton molecular mass were separated. Complexes of above two fractions and MO showed the same splitting spectral pattern. Job's plots from visible spectra showed the formation of the 11 complex and CD-data suggested the co-existence of the 21 MO-cdx complex. This splitting pattern showed the reversal of the signs when -cdx-ethyleneglycol-bis(epoxypropyl) ether was used and disappeared when larger host molecules and azo dyes were used. The splitting was explained by exciton interaction.     

Neighboring amide group participation in ester aminolysis in aprotic solvents

The piperidinolysis of 8-quinolyl-, p-nitrophenyl-, o-, and p-piperidinocarbonylphenyl acetates in acetonitrile and in chlorobenzene was studied at 25°C. The strictly second order kinetic behaviour and the weaks solvent-dependence of the rate of the reaction of o-piperidinocarbonylphenyl acetate indicate anchimeric assistance by the o-amide group, and support the suggestion that amide groups of hydrophobic enzyme active sites may act as general base catalysts.

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Aromatic Foldamer Helices as α-Helix Extended Surface Mimetics

Helically folded aromatic oligoamide foldamers have a size and geometrical parameters very distinct from those of α-helices and are not obvious candidates for α-helix mimicry. Nevertheless, they offer multiple sites for attaching side chains. It was found that some arrays of side chains at the surface of an aromatic helix make it possible to mimic extended α-helical surfaces. Synthetic methods were developed to produce quinoline monomers suitably functionalized for solid phase synthesis. A dodecamer was prepared. Its crystal structure validated the initial design and showed helix bundling involving the α-helix-like interface. These results open up new uses of aromatic helices to recognize protein surfaces and to program helix bundling in water.     

Barriers to internal rotation in 1,3,5-trineopentylbenzenes—II: Unsymmetrically halogen-substituted compounds

The temperature dependence of the three different methylene AB spectra due to the 1-, 3- and 5-neopentyl groups in 2-chloro-4-iodo, 2-bromo-4-iodo and 2-bromo-4-chloro-1,3,5-trineopentyl-benzene was studied by proton magenetic resonance measurements at 60 MHz. The identification of the lines of the AB quartets at low temperature was carried out on an HA-100 spectrometer by means of the INDOR technique. The activation parameters for all three barriers in each compound were found to be approximately the same, which perhaps reflects the interdependence of the rotations, with the smaller of the two halogens determining the size of the barrier. An explanation in terms of magnetic nonequivalence induced in the 1- and 5-methylenes by the 3-neopentyl group is considered to be most plausible.     

Monitoring nanoparticle formation during laser ablation of graphite in an atmospheric-pressure ambient

Excimer laser ablation of highly oriented pyrolytic graphite (HOPG) was performed at atmospheric pressure in an N₂ and in an air ambient. During the ablation, nanoparticles condensed from the material ejecta, and their size distribution was monitored in the gas phase by a Differential Mobility Analyzer (DMA) in combination with a Condensation Particle Counter (CPC). Size distributions obtained at different laser repetition rates revealed that the interaction between subsequent laser pulses and formed particles became significant above 15 Hz. This interaction resulted in laser heating, leading to considerable evaporation and a decrease in the size of the particles. X-ray photoelectron spectroscopy revealed that approximately 8% nitrogen was incorporated into the CN_x particles generated in the N₂ ambient, and that the nitrogen was mostly bonded to sp³-hybridized carbon. Monodisperse particles were also deposited and were analyzed by means of Raman spectroscopy to monitor size-induced effects. PACS 81.07.-b; 61.46.+w; 79.70.+q     

Production of biologically inert Teflon thin layers on the surface of allergenic metal objects by pulsed laser deposition technology

Allergic-type diseases are current nowadays, and they are frequently caused by certain metals. We demonstrated that the metal objects can be covered by Teflon protective thin layers using a pulsed laser deposition procedure. An ArF excimer laser beam was focused onto the surface of pressed PTFE powder pellets; the applied fluences were 7.5–7.7 J/cm². Teflon films were deposited on fourteen-carat gold, silver and titanium plates. The number of ablating pulses was 10000. Post-annealing of the films was carried out in atmospheric air at oven temperatures between 320 and 500 °C. The thickness of the thin layers was around 5 μm. The prepared films were granular without heat treatment or after annealing at a temperature below 340 °C. At 360 °C a crystalline, contiguous, smooth, very compact and pinhole-free thin layer was produced; a melted and re-solidified morphology was observed above 420 °C. The adhesion strength between the Teflon films and the metal substrates was determined. This could exceed 1–4 MPa depending on the treatment temperature. It was proved that the prepared Teflon layers can be suitable for prevention of contact between the human body and allergen metals and so for avoidance of metal allergy. Received: 12 June 2002 / Accepted: 13 June 2002 / Published online: 4 November 2002 RID="*" ID="*"Corresponding author. E-mail: bhopp@physx.u-szeged.hu