A new 4‐point C³ quaternary approximating subdivision scheme with one shape parameter is proposed and analyzed. Its smoothness and approximation order are higher but support is smaller in comparison with the existing binary and ternary 4‐point subdivision schemes.

Malaria has a wide impact on the healthcare system, affecting everyone from hyperendemic areas who dearth access to medical treatment to international tourists returning to nonendemic regions with tertiary referral care. Implementing timely and accurate diagnosis is necessary to stop malaria's growing global effect, which is attributed to the development of antimalarial medication resistance. In this research, potential antimalarial compounds, including quinine, primaquine, artemether, artelinic acid, triazoles‐modified, and so forth are examined with topological indices (TI) and linear regression modeling of said compounds. Some degree based topological indices are assembled for these drugs' chemical graphs. We compute the topological descriptors with the limiting behaviors associated with these pharmaceutical drugs. Moreover, in this study some of the physicochemical features of the drugs are estimated using these TIs in the QSPR models. These indices better reflect chemical properties such as boiling point, complexity, polarity, and so forth and the outcomes of regression technique acquired QSPR studies may aid in the creation of fresh medicines for the treatment of malaria. These indices and antimalarial activity were discovered to be related. Other compound series do very well with this relationship. The TIs could be a key component in creating and synthesizing new antimalarial drugs.

In this paper, the m-point approximating subdivision scheme with one parameter is proposed and analyzed where m> 1. Smoothness of schemes is higher in comparison with the existing binary and ternary...

Subdivision schemes are extensively used in scientific and practical applications to produce continuous geometrical shapes in an iterative manner. We construct a numerical algorithm to estimate subdivision depth between the limit curves/surfaces and their control polygons after k-fold subdivisions. In this paper, the proposed numerical algorithm for subdivision depths of binary subdivision curves and surfaces are obtained after some modification of the results given by Mustafa et al in 2006. This algorithm is very useful for implementation of the parametrization.