An estimator of the stable tail dependence function based on the empirical beta copula

The replacement of indicator functions by integrated beta kernels in the definition of the empirical tail dependence function is shown to produce a smoothed version of the latter estimator with the same asymptotic distribution but superior finite-sample performance. The link of the new estimator with the empirical beta copula enables a simple but effective resampling scheme.     

Numerical study of melting in an enclosure with discrete protruding heat sources

In order to explore the capability of a solid–liquid phase change material (PCM) for cooling electronic or heat storage applications, melting of a PCM in a vertical rectangular enclosure was studied. Three protruding generating heat sources are attached on one of the vertical walls of the enclosure, and generating heat at a constant and uniform volumetric rate. The horizontal walls are adiabatic. The power generated in heat sources is dissipated in PCM (n-eicosane with the melting temperature, T_m = 36 °C) that filled the rectangular enclosure. The advantage of using PCM is that it is able to absorb high amount of heat generated by heat sources due to its relatively high energy density. To investigate the thermal behaviour and thermal performance of the proposed system, a mathematical model based on the mass, momentum and energy conservation equations was developed. The governing equations are next discretised using a control volume approach in a staggered mesh and a pressure correction equation method is employed for the pressure–velocity coupling. The PCM energy equation is solved using the enthalpy method. The solid regions (wall and heat sources) are treated as fluid regions with infinite viscosity and the thermal coupling between solid and fluid regions is taken into account using the harmonic mean of the thermal conductivity method. The dimensionless independent parameters that govern the thermal behaviour of the system were next identified. After validating the proposed mathematical model against experimental data, a numerical investigation was next conducted in order to examine the thermal behaviour of the system by analyzing the flow structure and the heat transfer during the melting process, for a given values of governing parameters.     

Synthesis,Characterization and Properties of Two Novel E - and Z -Stilbenophanes: Their Lithium-selective Complexation and C-H⋯O Short Hydrogen Bonds in the X-ray Structure of the E -Isomer

Stilbenophanes 1c and 2c were synthesized in good yields. Among alkali ions, both isomers only formed 1:1 complexes with lithium selectively. An X-ray structure of 1c shows a statistical disorder which leads to two refined positions for the ethylene moiety. The existence of a weak intramolecular C-H > O hydrogen bond in its structure was confirmed by both X-ray analysis and theoretical calculation.     

Application of the Fe3O4@1,10‐phenanthroline‐5,6‐diol@Mn nano‐catalyst for the green synthesis of tetrazoles and its biological performance

The Fe₃O₄ magnetic particles were modified with 1,10‐phenanthroline‐5,6‐diol (Phen) and the related Mn complex (Fe₃O₄@Phen@Mn) synthesized as a heterogeneous catalyst to be used for the one‐pot three‐component synthesis of various tetrazoles. The catalysts were characterized by several methods, such as the elemental analysis, FT‐IR, X‐ray powder diffraction, dispersive X‐ray spectroscopy, scanning electron microscopy, transmission electron microscopy, dynamic light scattering, thermogravimetric‐differential thermal analysis, vibrating sample magnetometer and X‐ray photoelectron spectroscopy. In addition, the antioxidant and antibacterial activities of the catalyst and its Phen ligand were in vitro screened with 2,2‐diphenyl‐1‐picrylhydrazyl by free radical scavenging methods. Results showed that the synthesized compounds possess strong antioxidant activity (IC50; 0.172  ±  0.005 mg ml^?1) as well as a good antibacterial potential in comparison to standards.