Counting all bent functions in dimension eight 99270589265934370305785861242880

Based on the classification of the homogeneous Boolean functions of degree 4 in 8 variables we present the strategy that we used to count the number of all bent functions in dimension 8. There are $$99270589265934370305785861242880 \approx 2^{106}$$ such functions in total. Furthermore, we show that most of the bent functions in dimension 8 are nonequivalent to Maiorana?CMcFarland and partial spread functions.     

Macroscopic investigation of the transient hydrodynamic memory behavior of preparative packed chromatography beds

The goal of the present work was to examine the hydrodynamic behavior of preparative scale packed chromatography beds during long-term cyclical operation at high loads using an experimental set-up with a high resolution measuring device of bed height. One agarose-based resin and one methacrylic-based resin were examined in a 140 mm column. Both resins exhibited hysteresis behavior during compression/relaxation cycles. The hystereses were less pronounced with decreasing hydrodynamic stress rate. The occurrence of hystereses was an indication for hydrodynamic memory behavior of the chromatography packing. During long-term cyclical operation at high loads of the column filled with methacrylic resin, oscillations of the steadily with time decreasing flow rate were observed for the first time. These oscillations were attributed to the viscoelasticity of the polymer particles network representing a system with materials with fading memory. Such nonlinear systems with feed-back are known to exhibit inherent self-oscillations. A decoupling of the two processes of bed compression and decrease of bed permeability was observed. The presented results explain why preparative packed-bed chromatography often yields unsatisfactory reproducible data and why unwanted phenomena like medium wall detachment or other symptoms of deteriorated chromatography beds are frequently observed.     

Solution synthesis of nanoparticular binary transition metal antimonides

The preparation of nanoengineered materials with controlled nanostructures, for example, with an anisotropic phase segregated structure or a regular periodicity rather than with a broad range of interparticle distances, has remained a synthetic challenge for intermetallics. Artificially structured materials, including multilayers, amorphous alloys, quasicrystals, metastable crystalline alloys, or granular metals, are mostly prepared using physical gas phase procedures. We report a novel, powerful solution-mediated approach for the formation of nanoparticular binary antimonides based on presynthesized antimony nanoparticles. The transition metal antimonides M-Sb (M = Co, Ni, Cu(2), Zn) were obtained with sizes ranging from 20 and 60 nm. Through careful control of the reaction conditions, single-phase nanoparticular antimonides were synthesized. The nanophases were investigated by powder X-ray diffraction and (high resolution) electron microscopy. The approach is based on activated metal nanoparticles as precursors for the synthesis of the intermetallic compounds. X-ray powder diffraction studies of reaction intermediates allowed monitoring of the reaction kinetics. The small particle size of the reactants ensures short diffusion paths, low activation barriers, and low reaction temperatures, thereby eliminating solid-solid diffusion as the rate-limiting step in conventional bulk-scale solid-state synthesis.     

Freezing of Lennard-Jones-type fluids

We put forward an approximate method to locate the fluid-solid (freezing) phase transition in systems of classical particles interacting via a wide range of Lennard-Jones-type potentials. This method is based on the constancy of the properly normalized second derivative of the interaction potential (freezing indicator) along the freezing curve. As demonstrated recently it yields remarkably good agreement with previous numerical simulation studies of the conventional 12-6 Lennard-Jones (LJ) fluid [S.A.Khrapak, M.Chaudhuri, G.E.Morfill, Phys. Rev. B 134, 052101 (2010)]. In this paper, we test this approach using a wide range of the LJ-type potentials, including LJ n-6 and exp-6 models, and find that it remains sufficiently accurate and reliable in reproducing the corresponding freezing curves, down to the triple-point temperatures. One of the possible application of the method--estimation of the freezing conditions in complex (dusty) plasmas with "tunable" interactions--is briefly discussed.     

The stoichiometry of single nanoparticles of copper zinc tin selenide

Cu(2)ZnSnSe(4) nanoparticles have high potential to be used as ink for printable solar cells. Using transmission electron microscopy we show that these nanoparticles exhibit a broad range of chemical heterogeneity. These results are contrary to the interpretation of previous experimental work and will have considerable impact on the development of these nanoparticles.     

Beitr?ge zur Harnanalyse

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