A scaling property in critical spectra of discrete systems

Power spectra of discrete dynamical systems at the threshold of chaos contain line series obeying S_ω ∞ ω$\text{μ}$ for small ω. We explain $\text{μ}$ in terms of the Feigenbaum rescaling parameter α. Another parameter β related to the noise strength of states of periodic chaos and recently numerically determined by Huberman and Zisook is related to α as well.     

Relativistic mean-field parametrization of effective interaction in nuclear matter

The results of the modern relativistic Dirac-Brueckner calculations of nuclear matter are parametrized in terms of the relativistic- mean-field theory with scalar and vector nonlinear selfinteractions. It is shown that the inclusion of the isoscalar vector-meson quartic selfinteraction is essential for obtaining a proper density dependence of the vector potential in the mean-field model. The obtained mean-field parameters represent a simple parametrization of effective interaction in nuclear matter. This interaction may be used in the mean-field studies of the structure of finite nuclei without the introduction of additional free parameters.This work was supported in part by the Grant Agency of the Slovak Academy of Sciences under Grant No. GA SAV-517/1991.     

Parallel information-based complexity

We develop the theory of information-based complexity from a parallel point of view. For a model of computation with p processors, each being capable of arithmetic operations and decisions, we analyze the complexity of function approximation, numerical integration, and solution of Fredholm integral equations. We obtain tight bounds on the complexity, considered as a function of three variables simultaneously: the number of processors, the required precision, and (in the case of approximation and integral equations) the number of points, in which the approximate solution is to be determined.     

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937–940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix’s radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.     

An upper gradient approach to weakly differentiable cochains

The aim of the present paper is to define a notion of weakly differentiable cochain in the generality of metric measure spaces and to study basic properties of such cochains. Our cochains are (sub)additive functionals on a subspace of chains, and a suitable notion of chains in metric spaces is given by Ambrosio–Kirchheim?s theory of metric currents. The notion of weak differentiability we introduce is in analogy with Heinonen–Koskela?s concept of upper gradients of functions. In one of the main results of our paper, we prove continuity estimates for cochains with p-integrable upper gradient in n-dimensional Lie groups endowed with a left-invariant Finsler metric. Our result generalizes the well-known Morrey–Sobolev inequality for Sobolev functions. Finally, we prove several results relating capacity and modulus to Hausdorff dimension.     

The influence of electrospray ion source design on matrix effects

This study investigates to which extent the design of electrospray ion sources influences the susceptibility to matrix effects (MEs) in liquid chromatography-tandem mass spectrometry (LC-MS/MS). For this purpose, MEs were measured under comparable conditions (identical sample extracts, identical LC column, same chromatographic method and always positive ion mode) on four LC-MS/MS instrument platforms. The instruments were combined with five electrospray ion sources, viz. Turbo Ion Spray, Turbo V(TM) Source, Standard ESI, Jet Stream ESI and Standard Z-Spray Source. The comparison of MEs could be made at all retention times because the method of permanent postcolumn infusion was applied. The MEs ascertained for 45 pesticides showed for each electrospray ion source the same pattern, i.e. the same number of characteristic signal suppressions at equivalent retention times in the chromatogram. The Turbo Ion Spray (off-axis geometry), Turbo V(TM) Source (orthogonal geometry) and the Standard Z-Spray Source (double orthogonal geometry) did not differ much in their susceptibility to MEs. The Jet Stream ESI (orthogonal geometry) reaches a higher sensitivity by an additional heated sheath gas, but suffers at the same time from significantly stronger signal suppressions than the comparable Standard ESI (orthogonal geometry) without sheath gas. No relation between source geometry and extent of signal suppression was found in this study.     

Fast and Reliable Automated Synthesis of RNA and Partially 2′-O- Protected Precursors (`Caged RNA') Based on Two Novel,Orthogonal 2′-O-Protecting Groups,Preliminary Communication

Two sets of RNA phosphoramidites, carrying the (fluoride-labile) 2′-O-[(triisopropylsilyl)oxy]methyl (=tom) group and the (photolabile) [(R)-1-(2-nitrophenyl)ethoxy]methyl (=(R)-npeom) group, were prepared (see 1 – 4 and 5 – 8 , resp.). The two protecting groups were completely orthogonal to each other. Three ribozyme-substrate constructs, protected each by a (R)-npeom group, were synthesized; on photolysis, efficient cleavage of this remaining protecting group occurred (Scheme 3). It could be demonstrated that the presence of one (R)-npeom group within a RNA strand has only a minor influence on the pairing properties of corresponding duplexes.     

(NH4)4Na2[V10O28]·10H2O

Tetra­ammonium disodium decavanadate decahydrate crystallizes in the triclinic system in space group P. The structure contains typical centrosymmetric OV₆ double octahedra and centrosymmetric pairs of edge‐shared NaO₆ double octahedra forming a layered structure. In contrast to other monovalent cationic decavanadates, the NaO₆ double octahedra are integrated in the layer.