A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Molecular structure,vibrational spectroscopic and chemical reactivity of nematogenic p-n-alkylbenzoic acids: A comparative computational analysis

Molecular structure and vibrational spectroscopic studies of higher homologous series nematogenic p-n-alkylbenzoic acids (nBAC) that have 6 (6BAC) and 7 (7BAC) carbon atoms in the alkyl chain have been investigated using the Density Functional Becke3-Lee-Yang-Parr (B3LYP) level with the basis set 6-31++G (d.p) and Hartree Fock (HF) with the same basis set. The observed vibrational spectra has been resolved and assigned in detail for comparision with both the molecules. These results indicate that DFT and HF values are slightly different at both the levels. A comparision of chemical reactivity such as HOMO (E_H), LUMO (E_L) energies, energy gap (E_g), ionization energy (I), electron affinity (A), electro negativity (χ), chemical hardness (η), electronic chemical potential (μ), electrophilicity index (ω), and softness (S) has been made. It has been observed that the decrement has occurred in the energy band gap value of isolated molecule with increment in alkyl chain length. This provides valuable information regarding enhancing the stability of liquid crystal materials by maintaining the conductivity.     

Catalyst-Free Arylation of Tertiary Phosphines with Diaryliodonium Salts Enabled by Visible Light

The visible-light-induced arylation of tertiary phosphines with aryl(mesityl)iodonium triflates to produce the quaternary phosphonium salts occurs under mild, metal, and catalyst-free conditions. Photo-excited EDA complexes between diaryliodonium salts and phosphines supposedly enable this transformation, which is difficult to achieve through the traditional ground-state reactions. Demonstrating high functional group tolerance, broad scope, and complete selectivity of the aryl group transfer, the method is particularly compatible with sterically congested phosphines, which are challenging under metal-based catalytic methods.     

Separation and purification of scandium: From industry to medicine

Scandium and its compounds are used in many modern industrial fields due to its unique chemical and physical properties. It is mainly recovered from residues and wastes in the production of other metals. The exploitation of the ores and wastes could contaminate water and soil creating environmental problems. This paper discusses recent developments and tendencies in scandium separation, purification and preconcentration from different wastes, residues, environmental samples as well as in the production of radiopharmaceuticals for nuclear medicine, both in the laboratory and on the industrial scale. The period reviewed here mainly includes publications that have appeared, since 2010.     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理，本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件，并通过数值算例验证了理论结果的有效性.