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Green synthesis is the most effective and environmentally friendly way to produce nanoparticles. The present research aimed at the biosynthesizing of silver nanoparticles (AgNPs) using Tribulus terrestris seed extract as the reducing and stabilizing agent and investigating their anti-diabetic properties. Fourier transformation infrared (FTIR), X-ray diffraction (XRD), scanning electron microscopy (SEM), and UV-Vis spectroscopy were used to analyze the synthesized silver nanoparticles from Tribulus terrestris (TT-AgNPs). The spectroscopic characterization revealed a surface Plasmon resonance band at 380 nm, which verified the development of TT-AgNPs. The transmittance peaks were observed at 596, 1450, 1631, 2856, 2921, and 3422 cm−1 through the FTIR spectrophotometer. The XRD spectrum showed four distinct diffraction peaks in the 2θ range at 20° to 60°. Intense peaks were at 26.32°, 30.70°, 44.70°, 56.07°, 53.75°, 66.28°, and 75.32°. The SEM analysis revealed that the prepared TT-AgNPs were clustered loosely with a smooth and spherical structure and were of relatively uniform size. The in vitro antidiabetic potential of TT-AgNPs was assessed by using glucose yeast uptake, glucose adsorption, and alpha-amylase assays. TT-AgNPs showed the highest activity (78.45 ± 0.84%) of glucose uptake by yeast at 80 µg/mL. In the glucose adsorption assay, the highest activity of TT-AgNPs was 10.40 ± 0.52% at 30 mM, while in the alpha-amylase assay, TT-AgNPs exhibited the maximum activity of 75.68 ± 0.11% at 100 µg/mL. The results indicate a substantial anti-diabetic effect of the TT-AgNPs. Furthermore, the in vivo antidiabetic study was performed on TT-AgNPs in streptozotocin-induced diabetic mice. After receiving TT-AgNPs treatment for 30 days, the mice were sacrificed for biochemical and histological analyses of pancreatic and liver samples, which demonstrated a good improvement when compared to the control group. Mice treated with TT-AgNPs showed a significant drop in blood sugar levels, showing that the biosynthesized TT-AgNPs have effective anti-diabetic properties.

In matrix analysis, the scaling technique reduces the chances of an ill-conditioning of the matrix. This article proposes a one-parameter scaling memoryless Davidon–Fletcher–Powell (DFP) algorithm for solving a system of monotone nonlinear equations with convex constraints. The measure function that involves all the eigenvalues of the memoryless DFP matrix is minimized to obtain the scaling parameter’s optimal value. The resulting algorithm is matrix and derivative-free with low memory requirements and is globally convergent under some mild conditions. A numerical comparison showed that the algorithm is efficient in terms of the number of iterations, function evaluations, and CPU time. The performance of the algorithm is further illustrated by solving problems arising from image restoration.