Fusarium wilt is a soil-borne disease that leads to wilting, yellowing, and sometimes death of various plant species. This article examines the correlations between physicochemical properties and molecular invariants of the chemical structures of molecular biocontrol agents used to mitigate Fusarium wilt, a plant disease. The study considers effective agents like fungicides (thiophanate-methyl, azoxystrobin, trifloxystrobin, fludioxonil, and metalaxyl), soil fumigants (chloropicrin, metam sodium, and 1,3-dichloropropene), and molecular biocontrol agents (methionine and adenosine). This is the first review of QSPR studies on plant diseases in the literature. For the chemical structures of these molecular biocontrol agents, we have calculated M-polynomials of various molecular invariants, including the Zagreb-type indices, atom-bond connectivity index, harmonic index, Sombor index, forgotten index, and symmetric division degree index. The relationships identified through regression analysis provide insights into their effectiveness and optimization. Our findings highlight the best regression coefficients, which have the lowest RMSE and the maximum F-statistics values for significant correlations. Using these regression coefficients, we can predict the behavior of bioagents.

Hantavirus Pulmonary Syndrome (HPS) is a severe rodent-borne viral disease that can rapidly progress from influenza-like symptoms to life-threatening cardiopulmonary failure, while therapeutic options remain limited. This study develops a quantitative structure–property relationship (QSPR) framework for a curated set of fourteen HPS-related drug candidates using key physicochemical endpoints. Molecular structures are modeled as graphs, and degree-based topological descriptors are systematically derived via the M-polynomial techniques. Linear, quadratic, power, and logistic regression models are fitted to quantify structure–property relations, and model quality is assessed using R, \(R^{2}\), RMSE, SE, and F-statistics, with internal predictivity evaluated through leave-one-out cross-validation (LOOCV) using \(Q^{2}\). Results indicate that selected degree-based descriptors capture meaningful variation in the considered physicochemical properties and support reproducible, computation-driven screening of candidate compounds. In future directions, integrating pharmacokinetic and toxicity-oriented computational assessment is expected to further enhance the practical relevance of the proposed framework. Graphical Abstract

Objective of this paper is to study natural convection MHD flow past over a moving porous plate with heat source in the porous medium. The motion of the plate is translating as well as oscillating and embedded in the porous medium. The exact solution of the governing equations, of the flow and heat transfer for this model is obtained. To study heat flux for our model we use Nusselt number. Comparisons of effects of magnetic parameter $M$, translation $a$ and heat source parameter $S$ on velocity and temperature profile is given. The effects of some other physical parameters like Prandtl number $P_r$, Grashof number for heat transfer $G_r$, Permeability parameter $K_p$, is presented graphically on the distributions of velocity and temperature. It is concluded that the fluid motion in the boundary layer increases with increase of $a$, $S$, $G_r$ and $K_P$. Whereas opposite behavior is observed for $M$ and $P_r$. The heat source parameter increases the temperature of fluid and on the other hand cooling effects occur due to $P_r$ and $v_0$.

In this work, we define a controlled rectangular partial metric space, which is a generalization of a controlled rectangular metric space and a controlled metric space. Furthermore, we derive some fixed point results with suitable conditions in this setting. As an application, we give a fixed point theorem for graphic contractions on a controlled rectangular partial metric space via a graph structure.