A new extension of Hermite matrix polynomials and its applications

In this paper, an extension of the Hermite matrix polynomials is introduced. Some relevant matrix functions appear in terms of the two-variable Hermite matrix polynomials. Furthermore, in order to give qualitative properties of this family of matrix polynomials, the Chebyshev matrix polynomials of the second kind are introduced.     

Electrochemical water splitting using nano-zeolite Y supported tungsten oxide electrocatalysts

Zeolites are often used as supports for metals and metal oxides because of their well-defined microporous structure and high surface area. In this study, nano-zeolite Y (50–150 nm range) and micro-zeolite Y (500–800 nm range) were loaded with WO₃, by impregnating the zeolite support with ammonium metatungstate and thermally decomposing the salt thereafter. Two different loadings of WO₃ were studied, 3 wt.% and 5 wt.% with respect to the overall catalyst. The prepared catalysts were characterized for their morphology, structure, and surface areas through scanning electron microscope (SEM), XRD, and BET. They were further compared for their electrocatalytic activity for hydrogen evolution reaction (HER) in 0.5 M H₂SO₄. On comparing the bare micro-zeolite particles with the nano-form, the nano-zeolite Y showed higher currents with comparable overpotentials and lower Tafel slope of 62.36 mV/dec. WO₃ loading brought about a change in the electrocatalytic properties of the catalyst. The overpotentials and Tafel slopes were observed to decrease with zeolite-3 wt.% WO₃. The smallest overpotential of 60 mV and Tafel slope of 31.9 mV/dec was registered for nano-zeolite with 3 wt.% WO₃, while the micro-zeolite gave an overpotential of 370 mV and a Tafel slope of 98.1 mV/dec. It was concluded that even with the same metal oxide loading, nano-zeolite showed superior performance, which is attributed to its size and hence easier escape of hydrogen bubbles from the catalyst.     

Stereodivergent Transformation of Azepino[3,4,5-cd]indoles En Route to Nature-Inspired Scaffolds

Azepino[3,4,5-cd]indole derivatives represent the core scaffold of important natural products and biologically relevant compounds. Therefore, the establishment of step- and atom-economic strategies to access this class of compounds is of paramount importance. To this end, complexity-to-diversity (CtD) strategy has become one of the most important tools that transforms complex molecules into diverse skeleta. However, many of the reactions that could be employed in CtD are restricted by the functional handles exist in these molecules. This limits the achievement of the desired skeletal diversity. Herein, an efficient and step-economic strategy to access a diverse collection of azepino-[3,4,5-cd]indole architectures through a cascade that combines Pictet-Spengler with Michael addition, is described. This was achieved by reacting cyclohexadienone acetaldehydes 2 a – 2 d with indolyl-4-ethyl amine 1 . Employing a CtD strategy on the developed azepino-[3,4,5-cd]indoles, a rapid rearrangement reaction that provided a modular, chemo- and diastereoselective access to diverse collection of spiro azepinocarbazole nature-inspired frameworks, was encountered.