Inorganic Esters of Ethylene Glycol as Macrocyclic Ligands

Six different inorganic esters of ethylene glycol: B(OR)₃, P(OR)₃, OS(OR)₂, OP(OR)₃, OPH(OR)₂ and As(OR)₃, where R = CH₂CH₂OCH₃ were obtained. Their structures were studied by multinuclear NMR. These compounds can complex metal cations and behave like macrocyclic ligands. The influence of metal cation complexation on spectra were investigated by ¹, ¹³C, ¹⁷O, ¹¹B, ⁷Li, ⁸⁷Rb and ³¹P NMR.     

The Incompressible Navier-Stokes Equations in Vacuum

We are concerned with the existence and uniqueness issue for the inhomogeneous incompressible Navier-Stokes equations supplemented with H¹ initial velocity and only bounded nonnegative density. In contrast to all the previous works on those topics, we do not require regularity or a positive lower bound for the initial density or compatibility conditions for the initial velocity and still obtain unique solutions. Those solutions are global in the two-dimensional case for general data, and in the three-dimensional case if the velocity satisfies a suitable scaling-invariant smallness condition. As a straightforward application, we provide a complete answer to Lions' question in his 1996 book Mathematical Topics in Fluid Mechanics, vol. 1, Incompressible Models, concerning the evolution of a drop of incompressible viscous fluid in the vacuum. © 2018 Wiley Periodicals, Inc.     

Linear and Nonlinear Phenomena in Large Interacting Systems

We present recent results on construction and ergodicity properties of linear and nonlinear Markov semigroups for large interacting systems and discuss phenomena arising from interplay of nonlinearity and entropy.     

A transverse electric current in triglycine sulphate ferroelectric crystal

The application of a prolonged transverse electric field at a temperature T_A < T_C leads to unexpected qualitative changes in dielectric and thermal properties of the uniaxial ferroelectric triglycine sulphate (TGS) crystal, where T_C is the critical temperature of the paraelectric-ferroelectric phase transition. The new properties can be still observed even after the transverse field has ceased to be applied as long as the temperature of the sample does not exceed T_A. However, annealing the sample above T_C leads to the restoration of the original state of the crystal. An electric current flowing along the direction perpendicular to the polar axis of the uniaxial TGS ferroelectric crystal was measured below the temperature T_A at which the prolonged transverse electric field had been formerly applied to the crystal for a few hours. The experimental data resemble the classic pyroelectric current flowing along the polar axis.     

The chromatographic assay of 4‐hydroxynonenal as a biomarker of diseases by means of MEPS and HPLC technique

The aim of this study was to develop and validate a new analytical method for the determination of 4‐hydroxy‐2‐nonenal (4‐HNE) in biological samples while applying microextraction by packed sorbent as a sample preparation method and HPLC with UV–vis detection. Various microextraction by packed sorbent (MEPS) sorbents like C₂, C₈, C₁₈, M1 (80% C₈ and 20% SCX) and silica were used to separate 4‐HNE from biological samples. The highest affinity of 4‐HNE was observed for sorbents like C₁₈. The extraction efficiency was in the range from 47.4 to 89.2% dependent on the concentration of 4‐HNE. Lower efficiency of 4‐HNE extraction was obtained with use of MEPS packings such as C₈ and M1. The extraction efficiency was in the range from 35.2 to 66.3% for packing C8 and from 34.2 to 64.3% for packing M1, respectively. The limit of detection and lower limit of quantitation for UV–vis detection were respectively 4.5 and 9.0 nmol/mL. The proposed method can be used for the evaluation of extraction efficiency of 4‐HNE in biological sample because the values of lower limit of quantitation are lower than the determined amounts of the analyte in samples. The method yields excellent performance of quantification and identification in analysis of inflammation biomarkers. Copyright © 2014 John Wiley & Sons, Ltd.     

Compressible Navier-Stokes equations with ripped density

We are concerned with the Cauchy problem for the two-dimensional compressible Navier-Stokes equations  supplemented with general H¹ initial velocity and bounded initial density not necessarily strictly positive: it may be the characteristic function of any set, for instance. In the perfect gas case, we establish global-in-time existence and uniqueness, provided the volume (bulk) viscosity coefficient is large enough. For more general pressure laws (like e.g., $P={\rho }^{\gamma }$ with $\gamma >1$), we still get global existence, but uniqueness remains an open question. As a by-product of our results, we give a rigorous justification of the convergence to the inhomogeneous incompressible Navier-Stokes equations when the bulk viscosity tends to infinity. In the three-dimensional case, similar results are proved for short time without restriction on the viscosity, and for large time if the initial velocity field is small enough.