arXiv subjects

G. H. J. Lanel

Publications and source records attributed to G. H. J. Lanel.

3 recordsLinked to original sources

arXiv2024

On Novel Approach for Computing Distance based Indices of Anti-tuberculosis Drugs

This work aims to assess the molecular architectures of anti-tuberculosis drugs using both degree-based topological indices and novel distance based indices. We can represent the chemical arrangement as a graph, with atoms serving as the vertices and connections as the edges. Here, the multi bonds were considered as multi edges and included all the hydrogen atoms. Also, we consider three dimensional molecular graph. As a result, the actual bond lengths have been used for computation of new distance based indices. Compared to numerous studies, this is a significant improvement. Furthermore, the investigation of these indices includes a study on the quantitative structure-property relationship (QSPR). The research demonstrates a notable correlation between these indicators and the physical attributes of anti-tuberculosis drugs. Here, Since we reduced the some of existing critical assumptions in the literature, chemists and pharmaceutical professionals might potentially eliminate the need for clinical trials by employing this theoretical model. These models would enable them to predict the characteristics of anti-tuberculosis medications.

q-bio.BM↗

arXiv2024

Rehan-Lanel Indices of Graphs

A graph $G$ consists of vertices $V(G)$ and edges $E(G)$. In this paper, we propose four new indices defined and named as first Rehan-Lanel index of $G$ $(RL_1)$, second Rehan-Lanel index of $G$ $(RL_2)$, second Rehan-Lanel index of $G$, third Rehan-Lanel index of $G$, $(RL_3)$ and fourth Rehan-Lanel index of $G$ $(RL_4)$. The degrees of the vertices $u, v \in V(G)$ are denoted by $d_G(u)$ and $d_G(v)$. Based on these new indices and the definitions of Revan degree, Domination degree, Banhatti degree, Temperature of a vertex, KV indices, we subsequently introduced an additional 448 indices/exponentials and computed results for the first four new indices of each subsequent definition, for the standard graphs such as $r-$ regular graph, complete graph, cycle, path and compete bipartite graph. In addition, we performed calculations for the Wheel graph, Sunflower graph, and French Windmill graph. Furthermore, using the exponential of a degree of a vertex, the centrality concept, we introduced another 8 indices. Furthermore, we defined a new degree called Chandana-Lanel degree of a vertex of a graph(CL degree). Using this degree, new 6 indices were defined. Also, we defined the index called the Heronian Rehan-Lanel index using the Heronian mean of two numbers. These novel 462 indices would be advantageous in QSPR/QSAR studies.

math.CO↗

arXiv2022

On the Primal Feasibility in Dual Decomposition Methods Under Additive and Bounded Errors

With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems. Nonetheless, inevitable system-specific challenges such as limited computational power, limited communication, latency requirements, measurement errors, and noises in wireless channels impose restrictions on the exactness of the underlying algorithms. Such restrictions have appealed to the exploration of algorithms' convergence behaviors under inexact settings. Despite the extensive research conducted in the area, it seems that the analysis of convergences of dual decomposition methods concerning primal optimality violations, together with dual optimality violations is less investigated. Here, we provide a systematic exposition of the convergence of feasible points in dual decomposition methods under inexact settings, for an important class of global consensus optimization problems. Convergences and the rate of convergences of the algorithms are mathematically substantiated, not only from a dual-domain standpoint but also from a primal-domain standpoint. Analytical results show that the algorithms converge to a neighborhood of optimality, the size of which depends on the level of underlying distortions. Further elaboration of a generalized problem formulation is also furnished, together with the convergence properties of the underlying algorithms. Finally, theoretical derivations are verified by numerical experiments.

math.OC↗