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The COVID-19 pandemic has significantly affected both the global economy and human health. COVID-19 is a single-stranded RNA virus that spreads through the inhalation of viral droplets. Its genome encodes four structural proteins: the envelop protein, spike protein, membrane protein, and nucleocapsid protein. The virus's capsid is a protein shell that contains a positive RNA strand that allows it to take control of human cell machinery. Currently, the only treatments for COVID-19 are preventative measures and immunization. Some of the anti-COVID and anti-cancer medications used to combat this virus include Camptothecin Polymer, Hyaluronic Acid-curcumin, and Hydroxychloroquine. Graphs are used extensively in chemical investigation to provide a mathematical model of molecules. The selection of graph invariants, formerly known as molecular structure descriptor's, is the mathematical modelling of chemical compounds' physio-chemical, pharmacologic, and toxicological aspects. This paper presents a new technique to compute topological indices for three types of chemical networks for a few anti-COVID and anti-cancer medications. Our findings suggest that these indices show a strong association with the acentric factor and entropy, which make them effective in QSPR and QSAR analysis with high accuracy. [ABSTRACT FROM AUTHOR]

We define the chordal simplicial complex by using the definition of chordal clutter introduced by Woodroofe. We show that the facet ideal of the chordal simplicial complex is Cohen–Macaulay if and only if it is unmixed. Moreover, we prove that the facet ideal of a chordal simplicial complex has infinitely many nontrivial Cohen–Macaulay modifications. [ABSTRACT FROM AUTHOR]

An algorithmic proof of the General Néron Desingularization theorem and its uniform version is given for morphisms with big smooth locus. This generalizes the results for the one-dimensional case (cf. [10], [7]). [ABSTRACT FROM AUTHOR]