Small Periodic Solutions Generated by Sublinear Terms

The paper is concerned with Hopf bifurcations in systems of autonomous ordinary differential equations with a parameter. The principal distinction between usual theorems on Hopf bifurcations and our results is that here the linearized equation is degenerate and independent of the parameter. We present sufficient conditions for a parameter value to be a bifurcation point and analyze properties of small cycles arising in the vicinity of the equilibrium. Sublinear nonlinearities play the main role in the results obtained.     

A linearized Eulerian sound propagation model for studies of complex meteorological effects

Outdoor sound propagation is significantly affected by the topography (including ground characteristics) and the state of the atmosphere. The atmosphere on its part is also influenced by the topography. A sound propagation model and a flow model based on a numerical integration of the linearized Euler equations have been developed to take these interactions into account. The output of the flow model enables the calculation of the sound propagation in a three-dimensionally inhomogeneous atmosphere. Rigid, partly reflective, or fully absorptive ground can be considered. The linearized Eulerian (LE) sound propagation model has been validated by means of four different scenarios. Calculations of sound fields above rigid and grass-covered ground including a homogeneous atmosphere deviate from analytic solutions by < or = 1 dB in most parts of the computed domain. Calculations of sound propagation including wind and temperature gradients above rigid ground agree well with measured scale model data. Calculations of sound propagation over a screen including ground of finite impedance show little deviations to measured scale model data which are probably caused by an insufficient representation of the complex ground impedance. Further calculations included the effect of wind on shading by a screen. The results agree well with the measured scale model data.     

Tripeptides adopt stable structures in water. A combined polarized visible Raman,FTIR, and VCD spectroscopy study

We have measured the band profile of amide I in the infrared, isotropic, and anisotropic Raman spectra of L-alanyl-D-alanyl-L-alanine, acetyl-L-alanyl-L-alanine, L-vanyl-L-vanyl-L-valine, L-seryl-L-seryl-L-serine, and L-lysyl-L-lysyl-L-lysine at acid, neutral, and alkaline pD. The respective intensity ratios of the two amide I bands depend on the excitonic coupling between the amide I modes of the peptide group. These intensity ratios were obtained from a self-consistent spectral decomposition and then were used to determine the dihedral angles between the two peptide groups by means of a recently developed algorithm (Schweitzer-Stenner, R. Biophys. J. 2002, 83, 523-532). The validity of the obtained structures were checked by measuring and analyzing the vibrational circular dichroism of the two amide I bands. Thus, we found two solutions for all protonation states of trialanine. Assuming a single conformer, one obtains a very extended beta-helix-like structure. Alternatively, the data can be explained by the coexistence of a 3(1)(PII) and a beta-sheet-like structure. Acetyl-L-alanyl-L-alanine exhibits a structure which is very similar to that obtained for trialanine. The tripeptide with the central D-alanine adopts an extended structure with a negative psi and a positive phi angle. Trivaline and triserine adopt single beta(2)-like structures such as that identified in the energy landscape of the alanine dipeptide. Trilysine appears different from the other investigated homopeptides in that it adopts a left-handed helix which at acid pD is in part stabilized by hydrogen bonding between the protonated carboxylate (donor) and the N-terminal peptide carbonyl. Our result provides compelling evidence for the capability of short peptides to adopt stable structures in an aqueous solution, which at least to some extent reflect the intrinsic structural propensity of the respective amino acids in proteins. Furthermore, this paper convincingly demonstrates that the combination of different vibrational spectroscopies provides a powerful tool for the determination of the secondary structure of peptides in solution.     

Landau fragmentation and deformation effects in dipoSe response of sodium clusters

Recent experimental data on the dipole plasmon in axial sodium clusters Na _N ⁺ with 11 ≤ N ≤ 57 are analyzed within a self-consistent separable random-phase approximation (SRPA) based on the deformed Konh-Sham functional. Good agreement with the data is achieved. The calculations show that, while in light clusters plasmon properties (gross structure and width) are determined mainly by deformation splitting, in medium clusters with N τ 50 the Landau fragmentation becomes decisive. Moreover, in medium clusters shape isomers come to play with contributions to the plasmon comparable with the ground state one. As a result, commonly used methods of the experimental analysis of cluster deformation become useless and correct treatment of cluster shape requires microscopic calculations.     

Engineering Aspects of Preparation of Nanocrystalline Particles in Microemulsions

Engineering aspects of the preparation of palladium nanoparticles in non-ionic w/o-microemulsions are examined. In order to achieve reproducible synthesis conditions a semi-batch reactor with a standardized design is used. Influences of the stirring rate and of different ways of concentration control on the product properties are observed. For reproducible synthesis it is important to establish appropriate and defined preparation conditions. Monodisperse palladium particles of around 5nm size are obtained by adding the microemulsion containing the palladium salt at a constant feed rate to the precharged microemulsion containing the reducing agent. A quantitative kinetic model is proposed to describe particle formation in microemulsions. Unknown parameters of the model have been estimated by independent examinations or can be achieved by fitting to the experimental data.     

A proof of the bounded graph conjecture

Summary An infinite graph is called bounded if for every labelling of its vertices with natural numbers there exists a sequence of natural numbers which eventually exceeds the labelling along any ray in the graph. We prove an old conjecture of Halin, which characterizes the bounded graphs in terms of four forbidden topological subgraphs.Oblatum 17-IV-1991 & 25-X-1991     

Initial boundary value problems in one-dimensional non-linear thermoelasticity

The local existence of classical smooth solutions to the equations of homogeneous non-linear thermoelasticity in one space dimension is proved for the physically reasonable Dirichlet boundary conditions for both bounded and unbounded domains assuming smooth data.