On the 3D Steady Flow of a Second Grade Fluid Past an Obstacle

We study steady flow of a second grade fluid past an obstacle in three space dimensions. We prove existence of solution in weighted Lebesgue spaces with anisotropic weights and thus existence of the wake region behind the obstacle. We use properties of the fundamental Oseen tensor together with results achieved in Koch (Quad Mat 15:59?C122, 2004) and properties of solutions to steady transport equation to get up to arbitrarily small ?? the same decay as the Oseen fundamental solution.     

Dynamic properties of an individual wheelset drive of a railway vehicle

Spatial vibrations of an individual wheelset drive supported by rubber silent blocks in a two–axle bogie's frame of a railway vehicle are studied. The method, used for a creation of a mathematical model, is based on a decomposition of the wheelset drive into subsystems — a drive assembled from an engine and a gear transmission, a flexible composite hollow shaft and a flexible wheelset. Subsystems are modeled in local configuration spaces and they are mutually connected by deformable couplings. An adhesive characteristic in a wheel–rail contact is described using the Kalker's theory. The nonlinear mathematical model respects spatial vibrations of the drive's components and the flexible wheelset, a deformable rail ballast and it is used for investigating transient dynamic responses on different types of excitations. Experimentally investigated spatial bogie's frame displacements or displacements derived from a total model of the bogie caused by spatial irregularities of the rail track are main sources of excitations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new Banach space with Valdivia dual unit ball

We give an example of a Banach space which admits no projectional resolution of the identity but whose dual unit ball in weak* topology is a Valdivia compact. This answers a question asked by M. Fabian, G. Godefroy and V. Zizler. Partially supported by Research grants GAUK 277/2001, GAUK 160/1999 and MSM 113200007.     

Einsatz von rechenanlagen in der emissionsspektrochemie für aufstellung,bewertung und linearisierung der analytischen eichgeradenThe use of computers in emission spectrometry for the establishment,evaluation and linearization of analytical calibration curves

(The use of computers in emission spectrometry for the establishment, evaluation and linearization of analytical calibration curves)The problems of establishing optimum linear calibration lines for atomic emission spectrometry are discussed, with emphasis on use of photographic recording techniques. The calculation procedure, which is based on the least-squares method, generates additional statistical values which permit the linearity to be checked. As the desired linearity is not always achieved at the first attempt, the process is repeated after unreliable input data have been removed.     

Light scattering characterization of thermodynamic interaction of polymers in dilute solution. Effect of experimental error and temperature

Interaction between non-identical polymer molecules in a dilute solution of a mixture of two polymers is quantitatively characterized by the interaction parameter A₂₄, which is the second virial coefficient for interaction of unlike species. The value of A₂₄ may be experimentally obtained by light scattering. The determination of A₂₄ is very sensitive to experimental error in the input data, particularly for mixtures in which one polymer is greatly in excess, and for mixtures of polymers having molecular weights differing by orders of magnitude. A slight rise in A₂₄ with temperature has been observed for solutions of mixtures of polystyrene and poly(methyl methacrylate) in diethyl malonate in the range 25–100 C. This change in A₂₄ reflects the increased mutual miscibility of the polymers in solution at elevated temperatures.     

On Markushevich bases in preduals of von Neumann algebras

We prove that the predual of any von Neumann algebra is 1-Plichko, i.e., it has a countably 1-norming Markushevich basis. This answers a question of the third author who proved the same for preduals of semifinite von Neumann algebras. As a corollary we obtain an easier proof of a result of U. Haagerup that the predual of any von Neumann algebra enjoys the separable complementation property. We further prove that the selfadjoint part of the predual is 1-Plichko as well.     

Effect of atomic vibrations in XANES: polarization‐dependent damping of the fine structure at the Cu K‐edge of (creat)2CuCl4

Polarization‐dependent damping of the fine structure in the Cu K‐edge spectrum of creatinium tetrachlorocuprate [(creat)₂CuCl₄] in the X‐ray absorption near‐edge structure (XANES) region is shown to be due to atomic vibrations. These vibrations can be separated into two groups, depending on whether the respective atoms belong to the same molecular block; individual molecular blocks can be treated as semi‐rigid entities while the mutual positions of these blocks are subject to large mean relative displacements. The effect of vibrations can be efficiently included in XANES calculations by using the same formula as for static systems but with a modified free‐electron propagator which accounts for fluctuations in interatomic distances.     

Analytical and semipreparative chiral separation of cis‐itraconazole on cellulose stationary phases by high‐performance liquid chromatography

cis‐Itraconazole is a chiral antifungal drug administered as a racemate. The knowledge of properties of individual cis‐itraconazole stereoisomers is vital information for medicine and biosciences as different stereoisomers of cis‐itraconazole may possess different affinity to certain biological pathways in the human body. For this purpose, either chiral synthesis of enantiomers or chiral separation of racemate can be used. This paper presents a two‐step high‐performance liquid chromatography approach for the semipreparative isolation of four stereoisomers (two enantiomeric pairs) of itraconazole using polysaccharide stationary phases and volatile organic mobile phases without additives in isocratic mode. The approach used involves the separation of the racemate into three fractions (i.e. two pure stereoisomers and one mixed fraction containing the remaining two stereoisomers) in the first run and consequent separation of the collected mixed fraction in the second one. For this purpose, combination of cellulose tris‐(4‐methylbenzoate) and cellulose tris‐(3,5‐dimehylphenylcarbamate) columns with complementary selectivity for cis‐itraconazole provided full separation of all four stereoisomers (with purity of each isomer > 97%). The stereoisomers were collected, their optical rotation determined and their identity confirmed based on the results of a previously published study. Pure separated stereoisomers are subjected to further biological studies.