Department of Physical Science

Revan topological indices of supramolecular Fushine acid useful in medical applications

2025-01-01T00:00:00Z

Revan topological indices of supramolecular Fushine acid useful in medical applications Gunawardhana, D.C.; Sino, A. M. F. S.; Moulis, K.; Perera, K. K. K. R.; Lanel, G. J. Chemical graph theory plays a pivotal role in mathematical chemistry by representing chemical structures as graphs, with vertices denoting atoms and edges denoting chemical bonds. Topological indices, numerical invariants derived from such graphs, have been widely employed in quantitative structure property relationship (𝑄𝑆𝑃𝑅) and quantitative structure activity relationship (𝑄𝑆𝐴𝑅) studies. These indices correlate molecular structure with physicochemical and biological properties and have become crucial tools in drug design. Supramolecular chemistry, which studies entities formed bymolecular self-assembly through non-covalent interactions, offers an exciting avenue for designing complex molecular architectures. In this work, we investigate the supramolecular structure of Fuchsine (C₂₀H₁₉N₃HCl), a magenta dye of significant microbiological and histological importance. We construct a supramolecular sheet, denoted [𝑚, 𝑛], comprising 𝑚 × 𝑛 units of Fuchsine molecules. The corresponding chemical graph is simple, connected, and finite, consisting of 38𝑚𝑛 + 𝑚 + 𝑛 vertices and 42𝑚𝑛 edges, which are further classified by the Revan degrees of their end vertices. We derive closed-form expressions for several Revan degree-based topological indices of the supramolecular Fuchsine sheet, including the first and second Revan indices(𝑅1 and 𝑅2), Atomic Bond Connectivity Revan index(ABCR), Geometric-Arithmetic Revan index(𝐺𝐴𝑅), the first and second hyper Revan indices(𝐻𝑅1 and 𝐻𝑅2), the first and second modified Revan indices(𝑚𝑅1 and 𝑚𝑅2) , forgotten Revan index(𝐹𝑅). A detailed numerical and graphical analysis demonstrates that all these indices increase monotonically with the parameters m and n, reflecting the scaling behaviour of the supramolecular structure. Among the indices studied, the first hyper Reven index exhibits the highest values, whereas the first modified Revan index yields the lowest. Our findings provide a comprehensive mathematical characterization of the supramolecular Fuchsine graph, offering valuable insights for modelling and predicting the properties of complex chemical systems using topological descriptors.

Rehan-lanel indices of anti-tuberculosis drugs

2025-01-01T00:00:00Z

Rehan-lanel indices of anti-tuberculosis drugs Gunawardhana, D. C.; Sino, A. M. F. S.; Moulis, K.; Perera, K. K. K. R.; Lanel, G. J. Tuberculosis (TB), caused by Mycobacterium tuberculosis, remains a major global health threat and continues to demand new, effective therapeutic agents. Chemical graph theory offers a powerful approach to studying molecular structures and predicting their physicochemical properties without the need for extensive laboratory experiments. In chemical graph theory, molecules are represented as graphs where atoms are vertices and covalent bonds are edges, allowing computation of numerical descriptors called topological indices that capture the structural and connectivity features of molecules. The objective of this study is to identify the selected Rehan–Lanel(RL) indices that are highly correlated with the physicochemical properties of anti-tuberculosis drugs and to use these indices to build regression models capable of predicting properties such as boiling point, flash point, molar refractivity, molar volume, and polarizability for anti-tuberculosis drugs, namely, amikacin, bedaquiline, clofazimine, delamanid, ethambutol, ethionamide, imipenem-cilastatin, isoniazid, levofloxacin, linezolid, moxifloxacin, and 𝑝-aminosalicylic acid. Chemical graphs of these anti-tuberculosis drugs were constructed, representing each atom as a vertex and each bond as an edge. The first, second, third, and fourth RL indices and corresponding Revan versions of these RL indices were calculated for each drug. Six physicochemical properties were compiled for the same set of compounds. Statistical analyses were performed to investigate the relationships between each topological index and each physicochemical property. The results revealed that different indices exhibited strong and highly significant correlations with specific properties. Certain Rehan–Lanel indices showed the highest correlations with molar refraction, molar volume, and polarizability, while specific Rehan– Lanel Revan indices correlated best with boiling point and flash point. This study demonstrates that chemical graph theory and topological indices provide an efficient, low- cost approach to predict physicochemical properties of anti-tuberculosis drugs, supporting early-stage drug screening and design. Future research may focus on integrating these indices or developing hybrid descriptors to simultaneously predict multiple properties, further enhancing their application in quantitative structure–property relationship studies and drug discovery.

Exact relativistic charged stellar models with problems in linear programming

2024-01-01T00:00:00Z

Exact relativistic charged stellar models with problems in linear programming Moulis, K.; Komathiraj, K. In this work, we introduce a formal framework to derive interior solutions for the Einstein Maxwell system, describing the configuration of a relativistic charged fluid sphere within the context of spherically symmetric gravitational fields, which are matched to the exterior Reissner-Nordstrom space–time. Building upon previous methodologies, particularly the innovative approach by Komathiraj and Sharma (2018), we refine the process by reducing the system to a recurrence relation with variable rational coefficients. This enables us to obtain a solution in terms of an infinite series. We demonstrate that it is possible to closed form solutions within a specific range of model parameters. By imposing constraints on these parameters, we simplify the solutions to express them in terms of elementary functions, enhancing their accessibility and interpretability. The streamlined approach involves deriving solutions through series analysis and solving resulting difference equations, ultimately yielding expressions in the form of polynomials and products involving algebraic functions. Our study thus presents a comprehensive set of general solutions, offering insights into the behavior of charged fluid spheres in relativistic gravitational environments.

Inference-Driven Logistic Regression Approach for Identifying Risk Factors of Myopia

2026-01-01T00:00:00Z

Inference-Driven Logistic Regression Approach for Identifying Risk Factors of Myopia Kayathiri, T.; Kayanan, M.; Wijekoon, P. Myopia is a prevalent refractive error among children and adolescents and represents an increasing global public health issue. The present study aims to identify key risk and protective factors associated with myopia onset through statistical inference. A real-world myopia dataset from the R statistical package, which has been referenced in prior research for theoretical validation and factor identification, was analyzed. This investigation extends previous work by utilizing statistical inference to distinguish between variables that elevate myopia risk and those that confer protection. The dataset comprises 618 individuals who were non-myopic at baseline and were observed over a period of at least five years. During this period, 17 clinical and behavioral variables were recorded. Predictor variables include age, spherical equivalent refraction (SPHEQ), axial length (AL), anterior chamber depth (ACD), lens thickness (LT), vitreous chamber depth (VCD), and time spent on activities such as sports (SPORTHR), reading (READHR), computer use (COMPHR), studying (STUDYHR), and watching television (TVHR). The binary response variable was coded as 1 for myopic and 0 otherwise. Logistic regression coefficients were estimated using maximum likelihood estimation (MLE). Findings indicated that age, SPHEQ, AL, SPORTHR, STUDYHR, and TVHR exhibited negative coefficients, suggesting that increases in these variables are associated with a reduced risk of developing myopia. Conversely, positive coefficients for ACD, LT, VCD, READHR, and COMPHR point to elevated myopia risk. At the 5% significance level, SPHEQ and SPORTHR emerged as statistically significant predictors, while READHR and STUDYHR achieved significance at the 10% level. At the 90% confidence interval for odds ratios, SPHEQ, SPORTHR, and STUDYHR show protective effects (odds ratios < 1), whereas READHR is linked to greater risk; these protective effects remain significant at the 95% level. In summary, reduced reading time, increased participation in sports and studying, along with specific ocular measurements, may mitigate the risk of myopia development.