Characterization of proper curves and proper helix lying on $S_{1}^2(r)$

Abstract

In this paper, we analyse the proper curve γ(s) lying on the pseudo-sphere. We develop an orthogonal frame {V 1 , V 2 , V 3 } along the proper curve, lying on pseudosphere. Next, we find the condition for γ(s) to become V k − slant helix in Minkowski space. Moreover, we find another curve β(s) lying on pseudosphere or hyperbolic plane heaving V 2 = V2 for which { V1 , V2 , V3 }, an orthogonal frame along β(s). Finally, we find the condition for curve γ(s) to lie in a plane.

“Synergistic Innovation: Crafting Indazole Derivatives for Advanced Anticancer, Antioxidant, and Antimicrobial Efficacy through Integrative Design and Holistic Evaluation”

“…MD simulation tests were done using a similar approach as Pal et al ., [55] indicated by the WebGRO web server to investigate the conformational stability of the top‐docked drugs and receptor complex. The first step is to use PyMOL viewer to extract the PDB format of the docked complex (protein‐ligand complex).…”

“…MD simulation studies [55] for the top hit compounds ( 6 b , 6 c , and 6 d ) were carried out to investigate the stability of the docked complexes with the protein. The simulation was conducted for 20 ns, [75] and numerous trajectories were studied, including RMSD, Rg, RMSF, and H‐bonding interactions between ligand and protein (Figure 12).…”

“…These analyses provide a holistic understanding of the compounds’ potential suitability as pharmaceutical agents. Moreover, molecular docking and molecular dynamic simulation studies [55] were executed to forecast the binding conformations of the ligands within the binding site of the target protein and suggested the stability of the most active compounds at the target protein's binding site. This effort to comprehend the binding properties assumes paramount significance in the domain of drug design, furnishing invaluable insights into fundamental biochemical processes [56] .…”