Browsing by Author "Kumar, Virendra"

Now showing 1 - 4 of 4
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    A coumarin based fluorescent probe enabling nanomolar detection of Zn2+ and Cu2+
    (Elsevier B.V., 2022) Kumar, Virendra; Diwan, Uzra; Tyagi, Nidhi; Mishra, Rakesh K.; Singh, Manish Kumar; Upadhyay, K.K.
    A rationally designed fluorescent probe constructed on a coumarin platform (R-1) distinguished sequentially & distinctly two vital ions viz. Zn2+ and Cu2+ through different mechanistic approaches at their nanomolar concentrations. The native dark state (off-state) of R-1 was illuminated (on-state) upon its interaction with Zn2+ and further reverted back to its natural dark state in the presence of Cu2+ in aqueous medium. The structural details of R-1 and its ensemble with Zn2+ were unambiguously elucidated through their single-crystal XRD studies. The single crystals of R-1-Zn2+ with chloride and acetate counter anions displayed a fascinating 1-D co-ordination polymeric supramolecular structures. The strategic incorporation of pyridine �N in R-1 introduced a yet another binding site and consequently modulated its optical characteristics, while the analogous derivative R-3, inspite of having electron withdrawing �NO2 group, (instead of pyridine �N as in R-1 and R-2) was unable to produce any significant sensing response under similar conditions. The corresponding optical responses with Zn2+/Cu2+ were equated with INHIBIT logic- gate function. Moreover, the R-1 was deployed for imaging the above ionic analytes in rat glioblastoma cell lines (c6) through confocal laser scanning microscopy. � 2021 Elsevier B.V.
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    Investigation of Closed Derivation Formulas for GQ and QG Indices of a Graph via M-polynomial
    (University of Kashan, 2022) Das, Shibsankar; Kumar, Virendra
    A topological index is a numerical data which significantly correlates with the fundamental topology of a given chemical structure. The M-polynomial is a key mathematical tool to determine the degree-dependent topological indices. Very recently, the geometric-quadratic (GQ) and quadratic-geometric (QG) indices of a graph are introduced and computed their values by their respective mathematical formulas on some standard graphs and jagged-rectangle benzenoid system. In this research work, we propose M-polynomial based closed derivation formulas for determining the above two indices. In addition, we derive the GQ and QG indices for each of the abovementioned graphs by applying the derivation formulas, and also produce some fundamental relationships between the indices. � 2022. University of Kashan Press. All rights reserved
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    ON M-POLYNOMIAL OF THE TWO-DIMENSIONAL SILICON-CARBONS
    (Palestine Polytechnic University, 2022) Das, Shibsankar; Kumar, Virendra
    Topological indices of a molecular structure are numerical variables that significantly correlate various biological activity, physico-chemical properties and chemical reactivity. Representing molecular structure with M-Polynomial and computing the degree-based topological indices via M-polynomial of a graph network is a recent trade. In this article, we determine a closed-form of M-Polynomial for 2-dimensional Silicon-Carbons namely Si2C3-I[p, q], Si2C3-II[p, q] and Si2C3-III[p, q], and hence compute various degree-based topological indices. Additionally, we visualize the graphical representation of M-Polynomials and all the related degree-based topological indices of the above-mentioned Silicon-Carbons. � Palestine Polytechnic University-PPU 2022.
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    On Nirmala Indices�based Entropy Measures of Silicon Carbide Network
    (University of Kashan, 2023) Kumar, Virendra; Das, Shibsankar
    Topological indices are numerical parameters for understanding the fundamental topology of chemical structures that correlate with the quantitative structure-property relationship (QSPR) / quantitative structure-activity relationship (QSAR) of chemical compounds. The M-polynomial is a modern mathematical approach to finding the degree-based topological indices of molecular graphs. Several graph assets have been employed to discriminate the construction of entropy measures from the molecular graph of a chemical compound. Graph entropies have evolved as information-theoretic tools to investigate the structural information of a molecular graph. The possible applications of graph entropy measures in chemistry, biology and discrete mathematics have drawn the attention of researchers. In this research work, we compute the Nirmala index, first and second inverse Nirmala index for silicon carbide network Si2C3-I[p, q] with the help of its M-polynomial. Further, we introduce the concept of Nirmala indices-based entropy measure and enumerate them for the above-said network. Additionally, the comparison and correlation between the Nirmala indices and their associated entropy measures are presented through numerical computation and graphical approaches. Following that, curve fitting and correlation analysis are performed to investigate the relationship between the Nirmala indices and corresponding entropy measures. � 2023 University of Kashan Press. All rights reserved.