Further remarks on simple flows of fluids with pressure-dependent viscosities

Recently Suslov and Tran (2008) [1] claimed to have found an error in one of the solutions given in the paper by Hron (2001) et al. [2] concerning the flows of fluids with pressure-dependent viscosities. We show that their arguments are related to the question of the continuity of the pressure, and we show that the original solution, although it is not a classical one, can be interpreted as a solution in a generalized sense. Mathematical and physical implications of such generalizations are briefly discussed. The discussion in the paper highlights the importance of recognizing what is meant by a “solution” to a partial differential equation, whether by a solution we mean a classical solution, a weak solution, or a solution in some other sense.     

An Unusual β‐Oxidation of N‐Functionalized Alkyl Chains by 1H‐Imidazole

The 1H‐imidazole‐mediated condensation of primary aliphatic amines with perylene‐3,4 : 9,10‐tetracarboxylic bis‐anhydride resulted in by‐products where the aliphatic group was functionalized in the β‐position by imidazole units.     

Expansions in Series of Suitable Systems of Functions

The paper is devoted to the study of expansions of functions ?, which are holomorphic in a circle Ω around 0, in a series of the form where the given system of functions (f_k) _k=0 ^? has the property that each function f_k has a representation as a power series of the form with a ₀ ^(k) = 1. It is the question if and where an expansion of the form (*) holds. We present sufficient conditions for the sequence (a _n ^(k) ) _k,n=0 ^∞ , under which there exists a subset Ω₀ of Ω such that for arbitrary ? the expansion (*) holds on Ω₀ and the series converges absolutely uniformly on compact subsets of Ω₀. The obtained results can be applied to prove expansions of analytic functions in a series of a suitable system of m-fold products of Bessel functions. Expansions of this type have been treated by many authors in special cases, but we are able to state a general expansion theorem.     

Capillary zone electrophoresis of humic acids from the American continent

A multicomponent background electrolyte (BGE) was developed and its composition optimized using artificial neural networks (ANN). The optimal BGE composition was found to be 90 mM boric acid, 115 mM Tris, and 0.75 mM EDTA (pH 8.4). A separation voltage of 20 kV, 20 degrees C and detection at 210 nm were used. The method was applied to characterize several humic acids originating from various countries of the American continent: soil (Argentina), peat (Brazil), leonardite (Guatemala and Mexico) and coal (United States). Comparison with humic acids of International Humic Substances Society (IHSS) standard samples was also done. Well reproducible electropherograms showing a relatively high number of peaks were obtained. Characterization of the samples by elemental analysis and UV spectrophotometry was also done. In spite of the very different origins, the similarities between humic acids are high and by matrix assisted desorption/ionization-time of flight (MALDI-TOF)-mass spectrometry it was shown that most of the m/z patterns are the same in all humic acids. This means that humic acids of different origin have the same structural units or that they contain the same components.     

Prediction of an inverse heavy-atom effect in H-C-CH(2)Br: bromine substituent as a pi acceptor

A comparison of spin-orbit coupling calculated [CASSCF(6,6)/(cc-pVDZ on C,H and VDZ+P on Br] for bromomethylcarbene and methylcarbene predicts a highly unusual inverse heavy-atom effect by the Br substituent, particularly at geometries near the syn conformation. This behavior is due to a vacant 4d orbital on the Br atom acting as a weak pi-electron acceptor and overwhelming the even weaker effect of the pi-symmetry lone pair donor 4p orbital, which in itself would cause a small normal heavy-atom effect.     

Unimolecular Fragmentation of Energy Selected Allene Molecular Cations

The unimolecular fragmentations of internal energy selected allene molecular ions ( 1 ⁺) have been investigated by photoelectron-photoion coincidence spectroscopy. The energy dependence of the branching ratio between the two most important fragmentation channels is reported, together with values for the kinetic energy release during fragmentation. Loss of an hydrogen atom from 1 ⁺ is interpreted to proceed via two paths, yielding different isomeric forms of C₃H with different kinetic energy release values.