Obtaining certificates for complete synchronisation of coupled oscillators

In this paper, we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable. To this end, we use semidefinite programming techniques. For the first time, we can efficiently search for and obtain certificates for synchronisability and, additionally, also optimise associated cost functions. In this paper, a Lyapunov-like function (certificate) is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one, which implies synchronisation. Moreover, we establish new conditions for complete synchronisation, which are based on the so called Bendixson’s Criterion for higher dimensional systems. This leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation. Importantly, the certificates are obtained by analysing the connection network and the model representing an individual system only. In order to illustrate the strength of our method we apply it to a system of coupled identical Lorenz oscillators and to coupled van der Pol oscillators.     

Remarks on my paper: packing of incongruent circles on the sphere

The paper [3] contains an upper bound to the weighted density of a packing of circles on the unit sphere with radii from a given finite set. This bound is attained by many packings and has applications to problems of solidity. In the present note it is shown that a certain condition imposed on the set of admissible radii can be removed by modifying the original proof of the theorem.     

Sorption of cesium from water solutions on potassium nickel hexacyanoferrate-modified <Emphasis Type="Italic">Agaricus bisporus</Emphasis> mushroom biomass

In order to gain biosorbent that would have the ability to bind cesium ions from water solution effectively, potassium nickel hexacyanoferrate(II) (KNiFC) was incorporated into the mushroom biomass of Agaricus bisporus. Cesium sorption by KNIFC-modified A. bisporus biosorbent was observed in batch system, using radiotracer technique using ¹³⁷Cs radioisotope. Kinetic study showed that the cesium sorption was quite rapid and sorption equilibrium was attained within 1 h. Sorption kinetics of cesium was well described by pseudo-second order kinetics. Sorption equilibrium was the best described by Freundlich isotherm and the distribution coefficient was at interval 7,662–159 cm³ g⁻¹. Cesium sorption depended on initial pH of solution. Cesium sorption was very low at pH₀ 1.0–3.0. At initial pH 11.0, maximum sorption of cesium was found. Negative effect of monovalent (K⁺, Na⁺, NH₄ ⁺) and divalent (Ca²⁺, Mg²⁺) cations on cesium sorption was observed. Desorption experiments showed that 0.1 M potassium chloride is the most suitable desorption agent but the complete desorption of cesium ions from KNiFC-modifed biosorbent was not achieved.     

CH···π interactions do not contribute to hydrogen transfer catalysis by glycerol dehydratase

The role of the nonbonded CH···π interaction in the hydrogen abstraction from glycerol by the coenzyme B(12)-independent glycerol dehydratase (GDH) was examined using the QM/MM (ONIOM), MP2, and CCSD(T) methods. The studied CH···π interaction included the hydrogen atom of the -C(2)H(OH)- group of the glycerol substrate and the tyrosine-339 residue of the dehydratase. A contribution of this interaction to the stabilization of the transition state for the transfer of a hydrogen atom from the adjacent terminal C(1)H(2)(OH) group to cysteine 433 was determined by ab initio HF, MP2, and CCSD(T) calculations with the aug-cc-pvDZ basis set for the corresponding methane/benzene, methanol/phenol, and glycerol radical/phenol subsystems. The calculated CH···π distance, defined as the distance between the H atom and the center of the phenol ring, shortened from 2.62 to 2.52 ? upon going from the ground- to the transition-state of the GDH-catalyzed reaction. However, this shortening was not accompanied by the expected lowering of the CH···π interaction free energy. Instead, this interaction remained weak (about -1 kcal/mol) along the entire reaction coordinate. Additionally, the mutual orientation of the CH group and the phenol ring did not change significantly during the reaction. These results suggest that the phenol group of the tyrosine-339 does not contribute to lowering the activation barrier in the enzyme, but do not exclude the possibility that tyrosine 339 facilitates proper orientation of glycerol for the electrostatic catalysis, or inhibits side-reactions of the reactive glycerol radical intermediate.     

On a metric for the class of compact convex sets

A distance function, defined in [12], for the class of compact convex sets inn-space is introduced in a new way, and some of its properties are developed. This concept is compared with some traditional distance functions for convex sets.     

Kolloidmühlen

Ohne Zusammenfassung     

Notiz über eine regiospezifische Methode zur Herstellung von konjugierten Cyclohexadienen Über synthetische Methoden, 11. Mitteilung

β,γ-unsaturated δ-hydroxy-cyclohexene carboxylic acids undergo a smooth decarboxylative elimination when treated with DMF-dineopentylacetal in an unpolar solvent. The reaction provides a method for the regiospecific preparation of 1,3-cyclohexadiene derivatives under non-isomerizing conditions, starting from easily accessible and structurally variable intermediates.