He's homotopy perturbation method for solving the shock wave equation

In this article, we discuss the analytic solution of the fully developed shock waves. The homotopy perturbation method is used to solve the shock wave equation, which describes the flow of gases. Unlike the various numerical techniques, which are usually valid for short period of time, the solution of the presented equation is analytic for 0 < t < ∞. The results presented converge very rapidly, indicating that the method is reliable and accurate.     

Weak and Strong Convergence of an Implicit Iteration Process in Uniformly Convex Banach Spaces

The purpose of this article is to introduce an implicit iteration process for approximating common fixed points of three finite families nonexpansive mappings and to prove weak and strong convergence theorems in uniformly convex Banach spaces.     

Interactions of Imidazolium Based Ionic Liquids with Water Studied by Density and Speed of Sound Measurements: Effect of the Chain Length of an Alkyl Substituent on the Imidazolium Ion

Densities and speeds of sound of three ionic liquids (ILs), 1-ethyl-3-methyl imidazoliumtetrafluoroborate (C₂mimBF₄), 1-butyl-3-methylimidazoliumtetrafluoroborate (C₄mimBF₄) and 1-hexyl-3-methylimidazoliumtetrafluoroborate (C₆mimBF₄) were measured in aqueous solutions at (288.15, 293.15, 298.15, 303.15 and 308.15) K. These data were used to calculate the volumetric properties apparent molar volume and apparent molar isentropic compression as a function of molality. Infinite dilution values for these properties were evaluated by an extrapolation procedure based on Redlich–Meyer type equations. Apparent molar isobaric expansions at infinite dilution were also obtained from the slopes of the apparent molar volume at infinite dilution versus temperature. All these properties are interpreted in terms of IL–water interactions. The hydrolysis of the \( {\text{BF}}_{4}^{ - } \) anion of the ILs and its effects on the results is discussed.     

Enhanced H2 adsorption in isostructural metal-organic frameworks with open metal sites: strong dependence of the binding strength on metal ions

Metal-organic frameworks (MOFs) with open metal sites exhibit a much stronger H2 binding strength than classical MOFs, due to the direct interaction between H2 and the coordinately unsaturated metal ions. Here we report a systematic study of the H2 adsorption on a series of isostructural MOFs, M2(dhtp) (M = Mg, Mn, Co, Ni, Zn). The experimental, initial isosteric heats of adsorption for H2 (Qst) of these MOFs range from 8.5 to 12.9 kJ/mol, with increasing Qst in the following order: Zn, Mn, Mg, Co, and Ni. The H2 binding energies derived from first-principles calculation follow the same trend as the experimental observation on Qst, confirming the electrostatic Coulomb attraction between the H2 and the open metals being the major interaction. We also found a strong correlation between the metal ion radius, the M-H2 distance, and the H2 binding strength, which provides a viable, empirical method to predict the relative H2 binding strength of different open metals.     

Alkali and alkaline-earth metal amidoboranes: structure, crystal chemistry, and hydrogen storage properties

Alkali- and alkaline-earth metal amidoboranes are a new class of compounds with rarely observed [NH2BH3](-) units. LiNH2BH3 and solvent-containing Ca(NH2BH3)2 x THF have been recently reported to significantly improve the dehydrogenation properties of ammonia borane. Therefore, metal amidoboranes, with accelerated desorption kinetics and suppressed toxic borazine, are of great interest for their potential applications for hydrogen storage. In this work, we successfully determined the structures of LiNH2BH3 and Ca(NH2BH3)2 using a combined X-ray diffraction and first-principles molecular dynamics simulated annealing method. Through detailed structural analysis and first-principles electronic structure calculations the improved dehydrogenation properties are attributed to the different bonding nature and reactivity of the metal amidoboranes compared to NH3BH3.     

Crystal structure analysis of Bis{(N,N′‐dimethylformamide)‐[μ‐bis‐N,N′‐(2‐oxybenzyl)‐1,3‐propanediaminato](μ‐asetato) nickel(II)}nickel(II)

The title compound, a homotrinuclear Ni^II complex has been synthesized from ONNO type Schiff base reduced with the help of NaBH₄. The structure of the complex, [Ni{Ni(CH₃CO₂) (C₁₇H₂₀N₂O₂) (C₃H₇NO)}₂], was identified using elemental analysis, thermal analysis, IR spectroscopy and x‐ray diffraction techniques. It was established that although some bond lengths and angles changed with respect to previous complexes, the Ni…Ni distance was approximately the same.