Non-commutative generalization of integrable quadratic ODE systems

Letters in Mathematical Physics - We find all homogeneous quadratic systems of ODEs with two dependent variables that have polynomial first integrals and satisfy the Kowalevski–Lyapunov test....     

Neutron scattering from PEEK

An alkali‐soluble polysaccharide, GM5‐1, from the mycelium of Ganoderma tsugae, was fractionated by the nonsolvent addition method. The weight‐average molecular mass (M _w) and intrinsic viscosity ([η]) of fractions were studied by laser light scattering and viscometry with dimethylsulfoxide (DMSO) containing 0.25M LiCl (0.25M LiCl/DMSO) as the solvent at 30°C. The dependences of [η] and the radius of gyration (?S ²?_z ^1/2) on M _w were found to be [η]=9.8×10^?2 M _w ^0.57 (cm³g^?1) and ?S ²?_z ^1/2=1.65×10^?2 M _w ^0.58 (nm) in the M _w range from 8.6×10⁵ to 2.6×10⁶. The analysis based on current theories for a wormlike chain showed that the chain conformational parameters of GM5‐1 were 4.2 nm for persistence length (q) and 833 nm^?1 for linear mass density (M_L) with an obvious excluded volume effect. The results suggested the alkali‐soluble polysaccharide behaves like a semiflexible chain in 0.25M LiCl/DMSO at 30°C.     

Unstable attractors induce perpetual synchronization and desynchronization

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.     

Finite Hamiltonian systems: Linear transformations and aberrations

Finite Hamiltonian systems contain operators of position, momentum, and energy, having a finite number N of equally-spaced eigenvalues. Such systems are under the æis of the algebra su(2), and their phase space is a sphere. Rigid motions of this phase space form the group SU(2); overall phases complete this to U(2). But since N-point states can be subject to U(N) ?U(2) transformations, the rest of the generators will provide all N ² unitary transformations of the states, which appear as nonlinear transformations—aberrations—of the system phase space. They are built through the “finite quantization” of a classical optical system.     

A convenient HPLC assay for the determination of fructosamine-3-kinase activity in erythrocytes

Fructosamine-3-kinase (FN3K) mediates the regeneration of lysine from fructosamines formed on proteins as a result of the ‘early’ Maillard reaction. As fructosamines and advanced glycation endproducts derived therefrom are supposed to play an adverse role in the development of diabetic complications, FN3K is discussed as a protein-repairing enzyme. In this study, a method for the determination of FN3K activity in erythrocyte lysate is described which overcomes the complexity of currently known assays. The assay is based on the FN3K-dependent conversion of the synthetic UV-active fructosamine N ^α-hippuryl-N ^ε-(1-deoxy-D-fructosyl)lysine (BzGFruK) to N ^α-hippuryl-N ^ε-(phosphofructosyl)lysine (BzGpFruK). The FN3K activity was quantified by measuring the formation of BzGpFruK using RP-HPLC with UV detection. Identification of the metabolite BzGpFruK was achieved by means of UV and mass spectroscopy. The results are related to the content of haemoglobin for standardisation. First activity measurements with a chosen number of normoglycaemic subjects confirmed the convenient applicability of the method and showed distinctly different individual activities, as already discovered recently. The new established assay needs only the equipment of a routine laboratory with HPLC instrumentation. This should facilitate further studies about a possible relationship between the FN3K activity and the development of diabetic complications.     

Suppressed Particle Formation by Kinetically Controlled Ozone Removal: Revealing the Role of Transient‐Species Chemistry during Alkene Ozonolysis

The new approach of kinetically controlled ozone removal suppresses particle formation in laboratory ozonolysis experiments for methylcyclohexene and methylenecyclohexane (MCHa) at excess alkene concentrations (see graph). The results support the hypothesis that peroxy radicals are involved in organic nucleation and particle‐growth mechanisms.

     

Negativer linearer thermischer Ausdehnungskoeffizient von verstrecktem Polyäthylen

Zusammenfassung Der lineare thermische Ausdehnungskoeffizient von linearem Polyäthylen hoher Dichte wurde im Temperaturbereich –20 °C bis + 40°C bestimmt. Bei isotropen Proben besteht eine lineare Beziehung zwischen Dichte bzw. Kristallisationsgrad _v und. Die gemessenen Koeffizienten liegen fürT ₀ = 20 °C im Bereich = 110 ... 130 · 10^–6 K^–1.Kalt verstreckte Proben mit Verstreckungsgraden = 8 ... 15 haben beiT ₀ = 20 °C in Verstreckrichtung den Koeffizienten _l = –24 · 10^–6 K^–1. Der negative Zahlenwert von _tl ist unabhängig von und weiteren Herstellungsparametern. Seine Ursache ist einerseits die Orientierung derc-Achsen der Kristallite in Verstreckrichtung mit _c = –12 · 10^–6 K^–1 und andererseits der negative Koeffizient _am * –50 · 10^–6 K^–1 der verspannten amorphen Phase, der auf dem gummielastischen Verhalten der tie-molecules beruht.Beim Tempern oberhalb von +40 °C schrumpfen die Proben irreversibel, wobei _| ansteigt und nach dem Aufschmelzen der Proben wieder den Wert des isotropen Materials annimmt. Nach dem Tempern wenig unterhalb der Schmelztemperatur der Kristallite wurden überhöhte Koeffizienten _| gemessen, die eine Rotation der Kristallite um dieb-Achsen erkennen lassen.

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Summary The linear thermal coefficient of expansion,, of high density linear polyethylene has been determined in the temperature range of –20 ° ... + 40 °C. For isotropic samples a linear relationship between density or crystallinity _v and is valid. Measured values of forT ₀ = 20 °C amount to = 110 ... 130 · 10^–6 K^–1.Cold drawn samples of draw ratios = 8 ... 15 yield _| = –24 · 10^–6 K^–1 atT ₀ = 20 °C parallel to the draw axis. The negative value of _| does not depend on draw ratio or other parameters of sample processing. It is caused byc-axis orientation of the crystallites in draw direction with _c = –12 · 10^–6 K^–1 and by a negative coefficient _am * = –50 · 10^–6 K^–1 of the stressed amorphous phase, which is due to rubber elastic behaviour of the tie molecules.When annealed above 40 °C the samples shrink irreversibly and _| is augmented. After melting the samples the value of isotropic material is restored. Annealing the samples little below the melting temperature of the crystallites leads to superelevated values all which reflect| rotation of the crystallites around theb-axis.

     

Sodium periodate as a primary oxidant for water-oxidation catalysts

Sodium periodate was characterized as a primary chemical oxidant for the catalytic evolution of oxygen at neutral pH using a variety of water-oxidation catalysts. The visible spectra of solutions formed from Cp*Ir(bpy)SO(4) during oxygen-evolution catalysis were measured. NMR spectroscopy suggests that the catalyst remains molecular after several turnovers with sodium periodate. Two of our [Cp*Ir(bis-NHC)][PF(6)](2) complexes, along with other literature catalysts, such as the manganese terpyridyl dimer, Hill's cobalt polyoxometallate, and Meyer's blue dimer, were also tested for activity. Sodium periodate was found to function only for water-oxidation catalysts with low overpotentials. This specificity is attributed to the relatively low oxidizing capability of sodium periodate solutions relative to solutions of other common primary oxidants. Studying oxygen-evolution catalysis by using sodium periodate as a primary oxidant may, therefore, provide preliminary evidence that a given catalyst has a low overpotential.     

Evaluation of a combination of local hybrid functionals with DFT-D3 corrections for the calculation of thermochemical and kinetic data

Due to their position-dependent exact exchange admixture, local hybrid functionals offer a higher flexibility and thus the potential for more universal and accurate exchange correlation functionals compared to global hybrids with a constant admixture, as has been demonstrated in previous work. Yet, the local hybrid constructions used so far do not account for the inclusion of dispersion-type interactions. As a first exploratory step toward a more general approach that includes van der Waals-type interactions with local hybrids, the present work has added DFT-D3-type corrections to a number of simple local hybrid functionals. Optimization of only the s(8) and s(r,6) parameters for the S22 set provides good results for weak interaction energies but deteriorates the excellent performance of the local hybrids for G3 atomization energies and for classical reaction barriers. A combined optimization of the two DFT-D3 parameters with one of the two parameters of the spin-polarized local mixing function (LMF) of a local hybrid for a more general optimization set provides simultaneously accurate dispersion energies, improved atomization energies, and accurate reaction barriers, as well as excellent alkane protobranching ratios. For other LMFs, the improvements of such a combined optimization for the S22 energies have been less satisfactory. The most notable advantage of the dispersion-corrected local hybrids over, for example, a B3LYP-D3 approach, is in the much more accurate reaction barriers.