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On the Decomposition of Cyclic G-Brauer's Centralizer Algebras
Vidhya, Annamalai,Tamilselvi, Annamalai Department of Mathematics 2022 Kyungpook mathematical journal Vol.62 No.1
In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ<sub>r</sub>.
Growth of rGO nanostructures via facile wick and oil flame synthesis for environmental remediation
Lekshmi G. S.,Tamilselvi R.,Prasad Karthika,Bazaka Olha,Levchenko Igor,Bazaka Kateryna,Mohandas Mandhakini 한국탄소학회 2021 Carbon Letters Vol.31 No.4
Oil spills into ocean or coastal waters can result in signifcant damage to the environment via pollution of aquatic ecosystems. Absorbents based on reduced graphene oxide (rGO) foams have the capacity to remove minor or major oil spills. However, conventional chemical synthesis of rGO often uses petrochemical precursors, potentially harmful chemicals, and requires special processing conditions that are expensive to maintain. In this work, an alternative cost-efective and environmentally friendly approach suitable for large-scale production of high-quality rGO directly from used cooking sunfower oil is discussed. Thus, produced faky graphene structures are efective in absorbing used commercial sunfower oil and engine oil, via monolayer physisorption in the case of used sunfower and engine oils facilitated by van der Waals forces, π–π stacking and hydrophobic interactions, π-cation (H+) stacking and radical scavenging activities. From adsorption kinetic models, frst-order kinetics provides a better ft for used sunfower oil adsorption (R2=0.9919) and second-order kinetics provides a better ft for engine oil adsorption (R2=0.9823). From intra-particle difusion model, R2 for USO is 0.9788 and EO is 0.9851, which indicates that both used sunfower and engine oils adsorption processes follow an intra-particle difusion mechanism. This study confrms that waste-derived rGO could be used for environmental remediation.