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.     

Interpreting Observables in a Quantum World from the Categorial Standpoint

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime.     

A Rechargeable Hydrogen Battery Based on Ru Catalysis

Apart from energy generation, the storage and liberation of energy are among the major problems in establishing a sustainable energy supply chain. Herein we report the development of a rechargeable H₂ battery which is based on the principle of the Ru‐catalyzed hydrogenation of CO₂ to formic acid (charging process) and the Ru‐catalyzed decomposition of formic acid to CO₂ and H₂ (discharging process). Both processes are driven by the same catalyst at elevated temperature either under pressure (charging process) or pressure‐free conditions (discharging process). Up to five charging–discharging cycles were performed without decrease of storage capacity. The resulting CO₂/H₂ mixture is free of CO and can be employed directly in fuel‐cell technology.     

A Versatile Long‐Wavelength‐Absorbing Scaffold for Eu‐Based Responsive Probes

Coumarin‐sensitized, long‐wavelength‐absorbing luminescent Eu^III‐complexes have been synthesized and characterized. The lanthanide binding site consists of a cyclen‐based chelating framework that is attached through a short linker to a 7‐hydroxycoumarin, a 7‐B(OH)₂‐coumarin, a 7‐O‐(4‐pinacolatoboronbenzyl)‐coumarin or a 7‐O‐(4‐methoxybenzyl)‐coumarin. The syntheses are straightforward, use readily available building blocks, and proceed through a small number of high‐yielding steps. The sensitivity of coumarin photophysics to the 7‐substituent enables modulation of the antenna‐absorption properties, and thus the lanthanide excitation spectrum. Reactions of the boronate‐based functionalities (cages) with H₂O₂ yielded the corresponding 7‐hydroxycoumarin species. The same species was produced with peroxynitrite in a ×10⁶–10⁷‐fold faster reaction. Both reactions resulted in the emergence of a strong ≈407 nm excitation band, with concomitant decrease of the 366 nm band of the caged probe. In aqueous solution the methoxybenzyl caged Eu‐complex was quenched by ONOO^?. We have shown that preliminary screening of simple coumarin‐based antennae through UV/Vis absorption spectroscopy is possible as the changes in absorption profile translate with good fidelity to changes in Eu^III‐excitation profile in the fully elaborated complex. Taken together, our results show that the 7‐hydroxycoumarin antenna is a viable scaffold for the construction of turn‐on and ratiometric luminescent probes.     

Synthesis of functionalized analogs of pyochelin, a siderophore of Pseudomonas aeruginosa and Burkholderia cepacia

Using an improved synthesis of pyochelin, a siderophore common to several pathogenic Pseudomonas species, three functionalized pyochelin analogs were efficiently synthesized starting from appropriate 2-hydroxybenzonitriles.     

Determination of neutron flux parameters in PUSPATI TRIGA Mark II Research Reactor, Malaysia

In standardization NAA, it is necessary to characterize the neutron spectrum parameters such as epithermal neutron flux shape factor (α), thermal to epithermal neutron flux ratio (f), thermal neutron flux (φ _th) and epithermal neutron flux (φ _epi) in the irradiation facility to determine the concentration of an element in the sample using absolute and k ₀ standardization methods. The α and f were determined using Cd-ratio multi monitor method using experimental data obtained in PUSPATI TRIGA Mark II research reactor at four irradiation positions (10, 20, 30 and 40) of the rotary rack. The calculated values of α and f ranged from 0.006 to 0.0281 and 18.56 to 19.12 respectively. The average values of φ _th and φ _epi were found as 2.33 × 10¹² and 1.23 × 10¹¹ n cm^?2 s^?1 respectively. Moreover, a comparison of the neutron flux parameters in the present study shows an acceptable level of consistency with those of previous studies.     

Optically detected magnetic resonance study of the lowest excited triplet state of aromatic thioketones: Xanthione

The aromatic thioketone xanthione has been investigated by means of the optically detected magnetic resonance (ODMR) technique in a n-hexane matrix at ≈ 1.1 K. It was established that the short-lived red emission, which is characteristic for many thione molecules, is phosphorescence. At high temperatures (77 K) this phosphorescence originates mainly (>80%) from the T₁^z (n, π*) sublevel (k_z^(r) >k_x^(r), k_y^(r). At low temperature (1.1 K) the intersystem crossing following S₂ (π, π*) ← S₀ excitation is a highly spin-sublevel selective process which populates predominantly the T₁^x and T₁^y, levels. Hence, the slow spin—lattice relaxation phosphorescence at low temperature originates from these sublevels. A value of 0.0611 cm^?1 was obtained for the zero-field parameter |E|/hc. A lower limit of 0.66 cm^?1 has been found for the zero-field parameter |D|/hc. This value is considerably larger than those observed for ketones, and it is shown that spin—orbit coupling contributes strongly to the zero-field splitting.