A variational characterization of contact metric structures

Annals of Global Analysis and Geometry - On a manifold with a given nowhere vanishing vector field, we examine the squared $$L^2$$ -norm of the integrability tensor of the orthogonal complement of...     

Simulating the dynamic behavior of planetary gearbox based on improved Hanning function

Planetary gearboxes are widely used in industrial machines. They usually work in harsh environments giving rise to damages and high maintenance costs. Condition monitoring is a key action allowing one to detect the presence of such damage ensuring healthy running conditions. The knowledge of the dynamic behavior of such a gearbox can be achieved using modeling tools as a primary step before conditioning the monitoring subject. In addition, modeling a gear set can help in the stage of design in order to optimize physical and geometric parameters of the system. Therefore, in this work, a two-dimensional lumped parameter model is adopted to build all vibration sources. The time-varying mesh stiffness is approximated as a square wave form. A novel mathematical formulation is proposed to model the amplitude modulation phenomenon due to the rotational motion of the planets around the center of the gearbox. Finally, the overall vibration signal is concluded as a summation of all vibration components influenced by the modulation function.     

Stabilité analytique et convergence locale de translatées en dynamique homogène S-arithmétique

We present the main result of Richard and Zamojski [14] concerning, in homogeneous dynamics, the general problem of the dynamics of sequences of translates of a certain measure in a space of S-arithmetic lattices.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Synthesis,Characterisation and Crystal Structures of Two Bi‐oxadiazole Derivatives Featuring the Trifluoromethyl Group

The synthesis, characterisation, and crystal structure determination of the closely related compounds 3,3′‐bi‐(5‐trifluoromethyl‐1,2,4‐oxadiazole) and 5,5′‐bi‐(2‐ trifluoromethyl‐1,3,4‐oxadiazole) are reported. These two compounds are known for their bioactivity; however, in this study they serve as model compounds to evaluate the suitability of the heterocyclic oxadiazole ring system for energetic materials when the fluorine atoms in the exocyclic CF₃ groups are substituted successively by nitro groups. Quantum chemical calculations for the bi‐1,3,4‐ oxadiazole derivatives with difluoronitromethyl, fluorodinitromethyl, and trinitromethyl groups have been carried out and predict promising energetic performances for both explosive and propulsive applications.     

Properties of the Reactants and Their Interactions within and with the Enzyme Binding Cavity Determine Reaction Selectivities. The Case of Fe(II)/2-Oxoglutarate Dependent Enzymes

Fe(II)/2-oxoglutarate dependent dioxygenases (ODDs) share a double stranded beta helix (DSBH) fold and utilise a common reactive intermediate, ferryl species, to catalyse oxidative transformations of substrates. Despite the structural similarities, ODDs accept a variety of substrates and facilitate a wide range of reactions, that is hydroxylations, desaturations, (oxa)cyclisations and ring rearrangements. In this review we present and discuss the factors contributing to the observed (regio)selectivities of ODDs. They span from inherent properties of the reactants, that is, substrate molecule and iron cofactor, to the interactions between the substrate and the enzyme's binding cavity; the latter can counterbalance the effect of the former. Based on results of both experimental and computational studies dedicated to ODDs, we also line out the properties of the reactants which promote reaction outcomes other than the “default” hydroxylation. It turns out that the reaction selectivity depends on a delicate balance of interactions between the components of the investigated system.     

Reversible and Stepwise Single-Crystal-to-Single-Crystal Transformation of a Platinum(II) Complex with Vapochromic Luminescence

The vapochromic single-crystal-to-single-crystal (SCSC) transformation of a highly luminescent Pt^II complex bearing an N-heterocyclic carbene [Pt(CN)₂(tBu-impy)] (tBu-impyH⁺=1-tert-butyl-3-(2-pyridyl)-1H-imidazolium) is reported. The trihydrate form of the complex, which exhibits blue ³MMLCT emission owing to weak Pt⋅⋅⋅Pt interactions, changed its luminescence color from blue to yellowish-green upon the desorption of water molecules while keeping the high emission quantum yield of more than 0.45. Variable-temperature and continuous in-situ tracking of single-crystal X-ray diffraction measurements revealed that the SCSC transformation proceeds reversibly by the release and reabsorption of water molecules, thereby changing the stacked structure slightly. As a result, the dynamics of vapor-induced SCSC transformation were elucidated: that the anhydrous form returned to the original trihydrate form in a two-step process under a water vapor atmosphere. In addition, the Pt^II complex exhibited a similar SCSC response accompanied by a luminescence color change in the presence of methanol vapor, while being inactive toward ethanol vapor.