On weak–strong uniqueness for the compressible Navier–Stokes system with non-monotone pressure law

We show the weak–strong uniqueness property for the compressible Navier–Stokes system with general non-monotone pressure law. A weak solution coincides with the strong solution emanating from the same initial data as long as the latter solution exists.     

2,9-Diazadibenzoperylene and 2,9-Dimethyldibenzoperylene-1,3,8,10-tetratriflates: Key to Functionalized 2,9-Diazaperopyrenes

The synthesis of 2,9-diaza-1,3,8,10-tetratriflato-dibenzoperylene (DDP 3 a ) and corresponding 2,9-dimethyl-1,3,8,10-tetratriflato-dibenzoperylene (DBP 3 b ) has been developed at multigram scale via reduction of one of the industrially most important high-performance dyes, perylene-3,4,9,10-tetracarboxylic diimide (PTCDI), and of the corresponding dihydroxy peropyrenequinone precursor. The focus of this paper is on the reactivity pattern of 3 a as key intermediate towards highly functionalized 2,9-diazadibenzopyrelenes (DDPs) obtained via catalytic substitution of four triflate by aryl, heteroaryl, alkynyl, aminyl, and O-phosphanyl substituents. The influence of electron-donating substituents (OSiMe₃, OPt-Bu₂, N-piperidinyl), electron-withdrawing (OTf, 3,5-bis-trifluoromethyl-phenyl), and of electron-rich π-conjugated (2-thienyl, 4-tert-butylphenyl, trimethylsilyl-ethynyl) substituents on optoelectronic and structural properties of these functionalized DDPs has been investigated via XRD analyses, UV/Vis, PL spectroscopy, and by electroanalytical CV. These results were correlated to results of DFT and TD-DFT calculations. Thus, functionalized DPPs with easily tunable HOMO and LUMO energies and gap became available via a new and reliable synthetic strategy starting from readily available PTCDI.     

On the Vanishing Electron-Mass Limit in Plasma Hydrodynamics in Unbounded Media

We consider the zero-electron-mass limit for the Navier?CStokes?CPoisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier?CStokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier?CStokes system.     

Furanose Bicyclophosphites as Synthons of Modified Nucleoside Diphosphates

Abstract

Previously we synthesized and examined in detail 1,2- alkylideneglucofuanose 3,5,6-bicyclophosphites; mono- and bicyclophosphates with peculiar chemical and physiological activity were obtained on their base [1]. During the study of their structural dependence, we modified the hydrocarbonic moiety, synthesiz-ed 1,2,3- and 3,5,6-bicyclophosphites and cyclophosphates of gulofuanose, and correlated their features with those of glucose analogues. Furthermore, an additional phosphonate moiety (obtained by a stereoselective reaction of an appropriate ketonic sugar with silylphosphites) was introduced into the glucofuranose 3,5,6-bicyclophosphite molecule to the third carbon atom. As a result, the monosaccharide matrix gained two functional groups containing tri- and fourcoordinated phosphorus.     

Electron spin resonance (ESR/EPR) of free radicals observed in human red hair: a new,simple empirical method of determination of pheomelanin/eumelanin ratio in hair

The definition of the concentration of pheomelanin in the skin is an issue of great interest because in the case of being influenced by UV radiation, it manifests itself as a prooxidant, causing various skin disorders including melanoma that might help to explain the relatively high incidence of skin cancer among individuals with red hair. The ESR spectra of red hair samples were investigated. It was found that at low microwave power, they are characterized by two types of spectra. Red hair ESR signals result from a superposition of two spectral shapes, a singlet spectrum as a result of the existence of eumelanin and a triplet spectrum as a result of the existence of pheomelanin. At high microwave power, only triplet spectra shape was detected, caused by saturation of the eumelanin singlet. Using different concentration ratios of black to red hair, we measured ESR spectra and plotted the ratio values in each sample against a measured ‘g‐factor’ (experimental). We found that there is a linear relationship between these two parameters. So, it is evident that using these results, the concentration ratio of pheomelanin to eumelanin in a sample of hair can be easily determined by an almost noninvasive method. This can be considered a potential advantage for many practical activities compared with other invasive methods. The concentration dependence curve of pheomelanin (µg/mg) on g_exp‐factor in an ESR spectrum of hair has been designed, which allows the determination of the amount of pheomelanin in hair of any color. Copyright © 2014 John Wiley & Sons, Ltd.     

QSAR modelling and structural aspects concerning synthetic heterocycles with larvicidal activity against Aedes aegypti

Structural Chemistry - In this paper, we present a quantitative structure–activity relationships modelling for two series of heterocyclic synthetic compounds with larvicidal activity against...     

On reactive solute transport through a curved pipe

The transport of a reactive solute by diffusion and convection in a thin (or long) curved pipe is considered. Using asymptotic analysis with respect to the pipe’s thickness, the effective model for solute concentration is formally derived. A simple approximation is computed, showing explicitly the effects of the pipe’s geometry in nature and magnitude.     

Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems

We consider a general Euler-Korteweg-Poisson system in R ³, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics equations with capillarity are recovered as particular examples. We show that the system admits infinitely many global-in-time weak solutions for any sufficiently smooth initial data including the case of a vanishing initial density - the vacuum zones. Moreover, there is a vast family of initial data, for which the Cauchy problem possesses infinitely many dissipative weak solutions, i.e. the weak solutions satisfying the energy inequality. Finally, we establish the weak-strong uniqueness property in a class of solutions without vacuum. In this paper we show that, even in presence of a dispersive tensor, we have the same phenomena found by De Lellis and Székelyhidi.