Thinking wants to be organized

Can the describable complexity of test problems concerning mathematical thinking and the empirical results of their dealing with be put into a relation? Can graded test problems be constructed which lead to results which can basically be predicted? Empirical studies give interesting and helpful answers which lead to didactically important consequences, just like the evaluation of the PISA results.     

Universal Algorithm for Simulating and Evaluating Cyclic Voltammetry at Macroporous Electrodes by Considering Random Arrays of Microelectrodes

An algorithm for the simulation and evaluation of cyclic voltammetry (CV) at macroporous electrodes such as felts, foams, and layered structures is presented. By considering 1D, 2D, and 3D arrays of electrode sheets, cylindrical microelectrodes, hollow-cylindrical microelectrodes, and hollow-spherical microelectrodes the internal diffusion domains of the macroporous structures are approximated. A universal algorithm providing the time-dependent surface concentrations of the electrochemically active species, required for simulating cyclic voltammetry responses of the individual planar, cylindrical, and spherical microelectrodes, is presented as well. An essential ingredient of the algorithm, which is based on Laplace integral transformation techniques, is the use of a modified Talbot contour for the inverse Laplace transformation. It is demonstrated that first-order homogeneous chemical kinetics preceding and/or following the electrochemical reaction and electrochemically active species with non-equal diffusion coefficients can be included in all diffusion models as well. The proposed theory is supported by experimental data acquired for a reference reaction, the oxidation of [Fe(CN)₆]⁴⁻ at platinum electrodes as well as for a technically relevant reaction, the oxidation of VO₂⁺ at carbon felt electrodes. Based on our calculation strategy, we provide a powerful open source tool for simulating and evaluating CV data implemented into a Python graphical user interface (GUI).     

Zeaxanthin Production by Novel Marine Isolates from Coastal sand of India and its Antioxidant Properties

Zeaxanthin carotenoids are class of commercially important natural products and diverse biomolecules produced by plants and many microorganisms. Bacteria often produce a cocktail of polar and nonpolar carotenoids limiting their industrial applications. Marine members of the family Flavobacteriaceae are known to produce potential carotenoids such as astaxanthin and zeaxanthin. A few bacterial species have been reported for the predominant production zeaxanthin. Here, we report the molecular identification of the zeaxanthin as a major carotenoid produced by two novel bacteria (YUAB-SO-11 and YUAB-SO-45) isolated from sandy beaches of South West Coast of India and the effect of carbon sources on the production of zeaxanthin. The strains were identified based on the 16S rRNA gene sequencing as a member of genus Muricauda. The closest relatives of YUAB-SO-11 and YUAB-SO-45 were Muricauda aquimarina (JCM 11811^T) (98.9 %) and Muricauda olearia (JCM 15563^T) (99.2 %), respectively, indicating that both of these strains might represent a novel species. The highest level of zeaxanthin production was achieved (YUAB-SO-11, 1.20?±?0.11 mg g^?1) and (YUAB-SO-45, 1.02?±?0.13 mg g^?1) when cultivated in marine broth supplemented with 2 % NaCl (pH 7) and incubated at 30 °C. Addition of 0.1 M glutamic acid, an intermediate of citric acid cycle, enhanced the zeaxanthin production as 18 and 14 % by the strains YUAB-SO-11 and YUAB-SO-45 respectively. The zeaxanthin showed in vitro nitric oxide scavenging, inhibition of lipid peroxidation, and 2,2-diphenyl-1-picryl hydrazyl scavenging activities higher than the commercial zeaxanthin. The results of this study suggest that two novel strains YUAB-SO-11 and YUAB-SO-45 belonging to genus Muricauda produce zeaxanthin as a predominant carotenoid, and higher production of zeaxanthin was achieved on glutamic acid supplementation. The pigment showed good in vitro antioxidant activity, which can be exploited further for commercial applications.     

Synthesis,Crystal Structures,Thermal and Magnetic Properties of New Selenocyanato Coordination Polymers with Pyrazine as Co‐Ligand

Reaction of iron(II), cobalt(II) and nickel(II) selenocyanate with pyrazine in water at room temperature leads to the formation of the isotypic new ligand‐rich 1:2 (1:2 = ratio between metal and co‐ligand) compounds [M(NCSe)₂(pyrazine)₂]_n (M = Fe ( 1 ), Co ( 2 ), Ni ( 3 )). The crystal structure of 2 was determined by X‐ray single crystal analysis and those of 1 and 3 were refined from X‐ray powder data with the Rietveld method. In their crystal structure the metal(II) cations are coordinated by four pyrazine co‐ligands, which connect them into layers, and two terminally N‐bonded selenocyanato anions in a distorted octahedral arrangement. The terminal coordination mode of the selenocyanato anions was further emphasized by IR spectroscopic investigations. On heating, all compounds decompose in a single heating step without the formation of ligand‐deficient intermediates like previously reported for related thiocyanato compounds. Magnetic measurements of compound 1 show a long‐range antiferromagnetic ordering with an ordering temperature of T_N = 6.7 K, which must be mediated by the aromatic π‐system of the pyrazine ligand, whereas 2 and 3 show only Curie–Weiss behavior with antiferromagnetic exchange interactions.     

Quantitative Evaluation of Infrared Absorbance Spectra – Lorentz Profile versus Lorentz Oscillator

We present the theoretical basis for a profound upgrade of the method of absorbance band fitting (“band deconvolution”), which requires only minute changes in the code of corresponding spectrometer software. This upgrade is based on a (re-)connection of the damped harmonic oscillator model (“Lorentz oscillator”) and the Lorentz profile used for band fitting. Based on this reconnection, we provide a proper extension to multiple oscillators. As a result, band fitting allows directly obtaining all oscillator parameters with very good accuracy, at least for the not too strong oscillators present in organic and biological matter. Accordingly, this could be the initial spark to open the way to a long-awaited paradigm shift in infrared spectroscopy: Away from a mere oscillator position-based, towards an also intensity-based quantitative interpretation of spectra. As an extra, absorbance band fitting (“Poor Man's Dispersion Analysis”), allows to obtain the index of refraction function in one go.     

$^{2}_{\infty}\rm [Tb(Tz\ast)_{3}]$, A Homoleptic 2‐Dimensional Framework from a Solvent Free Synthesis of Terbium Metal with 1H‐1,2,3‐Triazole

Single crystalline , (Tz*)^– = 1,2,3‐triazolate anion, C₂H₂N₃^–, was obtained by the reaction of terbium metal with the amine 1H‐1,2,3‐triazole. As no additional solvent was used, the formation of a homoleptic framework without additional co‐ligands is accessible. Furthermore molecular hydrogen is produced. is a 2‐dimensional framework with a (6,6) topology including (Tz*)^– double bridges. The structure can be deduced from a basic structure type as it adopts the AlCl₃ structure with the triazolate ligands establishing the package. (Tz*)^– thus function as μ‐η¹:η²/μ‐η²:η¹ linkers between trivalent terbium ions that have a C.N. of nine. The framework exhibits an exceptional thermal stability up to 380 °C considering the three neighbouring nitrogen atoms of the triazolate ligands. At this point the framework decomposes in one single exothermic step under release of N₂.     

Ein neuartiger Zugang zu reduzierten Polyoxomolybdaten mit komplexen Gegenionen – Synthese und Struktur von [Mn(CH3OH)6][Mo8O16(OCH3)8(C2O4)]

The tetranuclear compound [Mo₂(O₂C‐tBu)₃]₂(μ‐C₂O₄) ( 1 ) that is prepared from [Mo₂(O₂C‐tBu)₃]₄ and oxalic acid, was reacted with MnI₂ · 2THF to form the polyoxomolybdate compound [Mn(CH₃OH)₆] [Mo₈O₁₆(OCH₃)₈(C₂O₄)] ( 2 ) in a complex redox reaction. Crystals of 2 were analyzed by single‐crystal X‐ray diffraction showing a octanuclear polyoxomolybdate dianion in which the Mo=O moieties are alternately connected through μ‐oxo and μ‐methoxo units. Charge balance in 2 is realized by a manganese(II) cation that is octahedrally coordinated by methanol ligands. The crystal structure is dominated by strong hydrogen bond interactions of the O–H ··· O type of methanol molecules coordinated to manganese as well as additional methanol molecules in the crystal lattice.     

In situ Neutron Powder Diffraction on Intermediate Hydrides of MgPd3 in a Novel Sapphire Gas Pressure Cell

A novel gas pressure cell for in situ neutron powder diffraction has been developed. It is based on a single crystal sapphire tube as a sample holder, allows a 360° unobstructed access by the neutron beam and has little background contribution. This device was used to study the hydrogenation of α‐MgPd₃, which undergoes a hydrogen driven rearrangement from a ZrAl₃ to a AuCu₃ type structure. Deuterium could be located and a strong preference of [Pd₆] voids was found in α‐MgPd₃D_0.79 under 5 bar and in α‐MgPd₃D_0.94 under 20 bar deuterium pressure. The crystal structure may be described as a new defect superstructure variant of the NaCl type. In situ thermal analysis under 5 bar hydrogen pressure showed that both the hydrogen uptake of α‐MgPd₃, which is complete at temperatures below 450 K, and the transformation to the hydride of cubic β‐MgPd₃, starting around 550 K, are exothermic. This completion of the hydrogenation‐dehydrogenation series of MgPd₃ suggests, that the rearrangement of the metal structure proceeds by a hydrogen assisted gliding mechanism with a shift vector of [110]. This is also supported by quantum chemical calculations, which show a decohesion of the intermetallic structure upon hydrogenation accompanied by the appearance of Pd–H bonding interactions.