This short communication makes use of the principle of singular perturbation to approximate the ordinary differential equation (ODE) of prompt neutron (in the point kinetics model) as an algebraic equation. This approximation is shown to yield a large gain in computational efficiency without compromising any significant accuracy in the numerical simulation of primary coolant system dynamics in a PWR nuclear power plant. The approximate (i.e., singularly perturbed) model has been validated with a numerical solution of the original set of neutron point-kinetic and thermal–hydraulic equations. Both models use variable-step Runge–Kutta numerical integration.

Our previous study found that intravesical perfusion metformin has excellent inhibitory effects against bladder cancer (BC). However, this administration route allows the drug to be diluted and excreted in urine. Therefore, increasing the adhesion of metformin to the bladder mucosal layer may prolong the retention time and increase the pharmacological activity. It is well known that chitosan (Cs) has a strong adhesion to the bladder mucosal layer. Thus, this study established a novel for-mulation of metformin to enhance its antitumor activity by extending its retention time. In this research, we prepared Cs freeze-dried powder and investigated the effect of metformin-loaded chitosan hydrogels (MLCH) in vitro and in vivo. The results showed that MLCH had a strong in-hibitory effect against proliferation and colony formation in vitro. The reduction in BC weight and expression of tumour biomarkers in orthotopic mice showed the robust antitumor activity of MLCH via intravesical administration in vivo. The non-toxic profile of MLCH was observed as well, using histological examinations. Mechanistically, MLCH showed stronger functional activation of the AMPK/mTOR signalling pathway compared with metformin alone. These findings highlighted the potential of this novel formulation as an efficient candidate for managing BC via intravesical ad-ministration.