Fractals Corresponding to Subsets of Sequence Spaces

Recursion can generate a fractal limit set from a sequence of finite families of functions, even if every possible sequence does not converge to a limit point. Conditions, which make limit sets compact, are discussed. A construction giving an unbounded fractal is presented, together with an open question and an application of recursive compositions of contractions to sums of present values.     

Beitrag zur Theorie des Poissonschen Integrals über Endlichen Gruppen

 The Poisson kernel over odd order cyclic groups and truncated to height two is studied for hypercontractivity. A relevant multiplier inequality is verified. The corresponding convolution operator maps into with norm one for all parameters and all integers l. (Received 26 April 2001)     

Determination and prediction of transfer ratios for anions in capillary zone electrophoresis with indirect UV detection

Transfer ratios (i.e. the number of moles of the UV-absorbing probe anion displaced by one mole of analyte anion) were determined for the separation of inorganic and organic anions by capillary zone electrophoresis using indirect UV absorbance detection. When the electrolyte was buffered and contained only the probe anion and a single counter-cation, transfer ratios calculated from Kohlrausch theory were found to agree well with values obtained experimentally from accurately determined mobility data. However, these electrolyte systems gave long analysis times and were therefore considered impractical. More useful electrolytes were obtained by the addition of surfactants to suppress or reverse the electroosmotic flow but the co-anion introduced with the surfactant can reduce the value of the measured transfer ratio and hence adversely affect sensitivity. This problem was overcome by the use of a surfactant in the hydroxide from such as cetyltrimethylammonium hydroxide combined with a suitable buffering counter-cation such as protonated 1,3-bis[tris(hydroxymethyl)-methylamino]-propane or tris(hydroxymethyl)aminoethane. Four buffered electrolytes consisting of chromate, benzoate, phthalate, or trimellitate as probes and a suitable surfactant were used to determine transfer ratios. These systems were shown to give transfer ratios that were close to those calculated from Kohlrausch theory, thereby enabling prediction of experimental conditions giving maximum transfer ratios.     

Improved flow distribution in automotive monolithic converters

The flow distribution in a monolith is significantly improved by shaping the inlet face of the monolith to form a cone or a parabola. The improved flow distribution results in a more efficient catalyst.     

Tracking a single fluorescent molecule with a confocal microscope

We consider the problem of tracking a single fluorescent molecule in both two and three dimensions using a confocal laser scanning microscope. An estimate of the position of the molecule is generated from the measured fluorescence signal through the use of parameter estimation theory. This estimate is used in a nonlinear controller designed both to track the position of the molecule and to provide good measurements for use in the estimation algorithm. The performance of the approach is investigated through numerical simulation for molecules undergoing diffusion and directed transport and the capabilities of the controller relative to experimental limitations are discussed.     

Integrable factors in compact Schur multipliers

It is shown that a Schur multiplier is compact if and only if it is the Schur product of two multipliers, one of which is a Hankel-Schur multiplier generated by an integrable function. This is illuminated by factoring exotic, singular measures and is brought into relation with Paley set-based multipliers.

     

Large eddy simulations of the turbulent flow between a rotating and a stationary disk

Large eddy simulations of the flow between a rotating and a stationary disk have been performed using a dynamic and a mixed dynamic subgrid-scale model. The simulations were compared to direct numerical simulation results. The mixed dynamic model gave better overall predictions than the dynamic model. Modifications of the near-wall structures caused by the mean flow three-dimensionality were also investigated. Conditional averages near strong stress-producing events led to the same conclusions regarding these modifications as studies of the flow generated by direct numerical simulation, namely a distinct asymmetry of the vortices producing sweeps and ejections.     

Thermal conductivity of pressure polymerized C60

60 polymerization in the temperature interval at pressures below by measurements of the time dependence of the thermal conductivity. It has been found at that the polymerization process at is slower than the reverse transformation from “polymeric” to “monomeric” phase at . The thermal conductivity of polymerized C₆₀ was measured in the temperature range and found to increase with increasing temperature, which reflects strong phonon scattering. Both the presence of non-bonded C₆₀ molecules and a high degree of structural disorder in the crystalline lattice of the polymeric phase might be responsible for the behaviour of . The results for are qualitatively similar to those reported previously for C₆₀ polymerized at higher , but an order of magnitude smaller. Received: 20 September 1996/Accepted: 11 November 1996