Polyfluoroorganotrifluoroborates and -difluoroboranes: interesting materials in fluoroorgano and fluoroorgano-element chemistry

The aimed introduction of the polyfluoroorgano groups (4-C₅F₄N), C₆F₁₃C₂H₄, and C₂F₅ into methoxy group-containing boron electrophiles is reported. The new compounds obtained after transformations K[(4-C₅F₄N)BF₃], (4-C₅F₄N)BF₂, K[C₆F₁₃C₂H₄BF₃], C₆F₁₃C₂H₄BF₂, K[(C₂F₅)₂B(OMe)₂], and K[(C₂F₅)₂BF₂] were isolated and characterised. Additionally some of their precursors as there are Li(4-C₅F₄N), Li[(4-C₅F₄N)B(OMe)₃], (4-C₅F₄N)B(OH)₂ and the by-products Li[(4-C₅F₄N)₂B(OMe)₂], (4-C₅F₄N)₂BOH, and K[(4-C₅F₄N)₂BF₂] are described. The usefulness of polyfluoroorganodifluoroboranes for introducing polyfluoroorgano groups into hypervalent FEF bonds is demonstrated by the synthesis of [C₆F₅(4-C₅F₄N)I][BF₄] and [p-FC₆H₄(trans-CF₃CFCF)I][BF₄].     

Structure of fully dispersed waves in dusty gases

The structure of one-dimensional fully dispersed waves in dusty gases is investigated using the Navier-Stokes equations for the gas phase and for the particle phase. The resulting system of six ordinary nonlinear differential equations is reduced to a system of four autonomous nonlinear differential equations which is solved analytically in phase space by expanding the variables of state in power series.

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Zusammenfassung Die Struktur eindimensionaler voll dispergierter Wellen in staubhaltigen Gasen wird untersucht indem die Navier-Stokesschen Gleichungen auf die Gas-Phase und auf die Partikel-Phase angewendet werden. Das sich ergebende System von sechs gewöhnlichen nichtlineren Differentialgleichungen wird auf ein System von vier autonomen nichtlinearen Differentialgleichungen zurückgeführt. Dieses System wird durch Reihenentwicklung der Zustandsgrößen im Phasenraum analytisch gelöst.

     

Modeling,Analysis, and Simulation of Biofilm Formation and Decay

In this article, we give a brief overview of our recent work on continuum mechanical modelling and simulation of microbial films. This comprises some classical tasks of applied mathematics such as computational fluid dynamics, analysis of partial differential equations, and mathematical biology.     

Subsampling effects in neuronal avalanche distributions recorded in vivo

Background  

Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma = 1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task.     

Three-dimensional resolution enhancement in fluorescence microscopy by harmonic excitation

A method for increasing lateral as well as axial resolution in fluorescence microscopy is presented. A passband with a high cutoff frequency throughout reciprocal space can be achieved by illumination of the object with spatially harmonic excitation patterns generated by the interference of two collimated laser beams. Theoretical calculations show an almost isotropic point-spread function with a FWHM near 100 nm.     

Physicochemical characterization of the endotoxins from Coxiella burnetii strain Priscilla in relation to their bioactivities

Background  

Coxiella burnetiiis the etiological agent of Q fever found worldwide. The microorganism has like other Gram-negative bacteria a lipopolysaccharide (LPS, endotoxin) in its outer membrane, which is important for the pathogenicity of the bacteria. In order to understand the biological activity of LPS, a detailed physico-chemical analysis of LPS is of utmost importace.