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.     

Application of microcrystalline cellulose as an efficient and cheap sorbent for the extraction of metoprolol from plasma and wastewater before HPLC–MS/MS determination

A dispersive solid-phase extraction method based on a new sorbent has been performed on plasma and wastewater samples to determine metoprolol by high-performance liquid chromatography–tandem mass spectrometry. In this study, the analyte was adsorbed from the samples onto microcrystalline cellulose as a green and efficient sorbent and then eluted for use in the determination step. In the mass spectrometer, the analyte was detected in the positive mode and selectivity of the analysis was increased by sequential mass analysis through multiple reaction monitoring. All of the effective parameters in the extraction of metoprolol from plasma and wastewater were optimized. Under optimal conditions the method was linear in the ranges of 1–1,000 and 0.1–1,000 ng/ml in plasma and wastewater samples, respectively. The detection limits of the method were 0.30 and 0.03 ng/ml in plasma and wastewater samples, respectively. The data showed that the method provides low detection limit, wide linear range, good precision and high extraction recovery. Finally several plasma and wastewater samples were successfully analyzed using the method. The use of a small amount of a green and inexpensive sorbent and a low volume of plasma without the need for further pretreatment steps are the main advantages of the method.     

Carbohydrate-based nanostructured catalysts: applications in organic transformations

The requirement of green and sustainable materials to prepare heterogeneous catalysts has intensified for practical reasons over the past few decades. Carbohydrates are possibly the most plentiful and renewable organic materials in nature with inimitable physiochemical properties, plausible low-cost and large-scale production, and sustainability features could be exploited in the generation of nanostructured heterogeneous catalysts. This review article outlines the organic transformations catalyzed by diverse carbohydrate-based nanostructured catalysts in greener and environmentally friendly processes. Selected examples are highlighted for a variety of organic reactions exploiting the proposed catalysts’ reactivity and reusability, and interactions with the intrinsic nature of the applied carbohydrate supports; advantages and speculated challenges of the introduced catalysts are deliberated as well.     

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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PANI-Fe3O4@ZnO nanocomposite as magnetically recoverable organometallic nanocatalyst promoted synthesis of new Azo chromene dyes and evaluation of their antioxidant and antimicrobial activities

Molecular Diversity - A new series of azo chromene dyes were synthesized via a facile cyclocondensation reaction of (E)-1,2-diphenyl-1-diazene and 4-aminocoumarin with 1:2 molar ratio catalyzed by...     

Numerical analysis of the effects of roughness on the electro-osmotic laminar flow between two parallel plates

Meccanica - In the present study, the effects of wall roughness on the dynamic of laminar electro-osmotic flow (EOF) between two parallel plates have been investigated numerically. The governing...     

Synthesis of fish scale derived hydroxyapatite silica propyl bis aminoethoxy ethane cuprous complex (HASPBAEECC) as a novel hybrid nano-catalyst for highly efficient synthesis of new benzimidazole-1,2,3-triazole hybrid analogues as antifungal agents

Molecular Diversity - The preparation, characterization and application of hydroxyapatite silica propyl bis aminoethoxy ethane cuprous complex (HASPBAEECC) as a novel hybrid nano-catalyst for...     

Solar dryers as a promising drying technology: a comprehensive review

Journal of Thermal Analysis and Calorimetry - Dryers are utilized in food industry and agriculture in order to extend the useful lifespan of corps. Thermal energy is required for water removal in...