Cobalt promoted Ni/MgAl2O4 catalyst in lean methane catalytic oxidation

In the present research, magnesium aluminate spinel was prepared as catalyst support using a novel, facile, and efficient mechanochemical method. The Co-promoted catalysts with 20 wt.% of Ni were fabricated using an impregnation route and the samples were analyzed by the X-ray diffraction (XRD), N₂ adsorption/desorption (BET), temperature-programmed reduction and desorption (H₂-TPR and O₂-TPD), and field emission scanning electron microscopy (FESEM) tests. The results confirmed that all samples have a mesoporous structure with a high specific surface area and the presence of cobalt caused complete CH₄ oxidation at low temperatures, and no side reactions were observed. The results indicated that the 3%Co-20%Ni/MgAl₂O₄ catalyst was the optimal sample among the prepared catalysts, owing to the improvement of reduction features and oxygen mobility. The 50 and 90% of methane conversion was obtained at 530 and 600 °C, respectively. Also, the influence of calcination temperature, GHSV, and feed ratio was determined on the catalytic activity. The obtained outcomes revealed that the calcination temperature has a significant effect on the textural properties and catalytic efficiency. The sample calcined at 700 °C showed the weakest performance, which was related to the sintering of particles at high temperatures. The catalytic stability showed that the 3%Co-20%Ni/MgAl₂O₄ has acceptable stability during 600 min time of reaction.

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Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

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