First order or pseudo-first order reactions involving reversible linear chain and cyclic reaction networks are considered here for obtaining the respective characteristic polynomials (CPs) in analytical forms as well as the recursion relations among the CP coefficients. The zeros of the CP concerned are the decay constants that are useful in expressing the concentrations of the chemical species involved in the chemical reaction network at any instant of time. Illustrations are given for obtaining the CP coefficients of a few such graphs and some consequences thereof are presented. Facile computer programming can be made with these recursion relations for generating such polynomials.

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Purpose: To investigate the prognostic factors for visual outcome in patients undergoing immediate pars plana vitrectomy (PPV) for posteriorly dislocated lens fragments during phacoemulsification surgery. Methods: This was a single-center, retrospective, cross-sectional study of 37 eyes of 37 patients undergoing immediate PPV for posteriorly dislocated lens fragments from 2015 to 2021. The primary outcome measure was changes in the best-corrected visual acuity (BCVA). Additionally, we analyzed the predictive factors for poor visual outcomes (BCVA <20/40) and perioperative complications. Results: The mean (±standard deviation [SD]) age of the patients was 66.57 (±10.86) years, with an almost identical gender profile (M: F = 18/19 [48.64%:51.36%]). The median (interquartile range [IQR]) log of minimum angle of resolution (logMAR) BCVA improved significantly from the baseline (1 [0.6–1.48], ~20/200) to the final visit (0.3 [0.2–0.6], ~20/40) ( P < 0.0001) after a mean (±SD) follow-up of 6.35 (±6.32) months. The final BCVA was 20/40 or better in 59.5% of the eyes. Poor final BCVA (<20/40) was associated with small preoperative pupillary size ( P = 0.02), presence of preoperative ocular pathology ( P = 0.02) including uveitis, glaucoma, and clinically significant macular edema (CSME), intraoperative displacement of >50% of lens matter into the vitreous ( P < 0.001), use of iris-claw lens ( P < 0.001), and postoperative cystoid macular edema (CME; P = 0.007). The postoperative complications included CME (13.51%), retinal detachment (10.81%), chronic uveitis (8.11%), glaucoma (8.11%), iritis (2.7%), posterior chamber IOL (PCIOL) dislocation (2.7%), and vitreous hemorrhage (2.7%). Conclusion: For retained lens fragments in complicated phacoemulsification surgery, immediate PPV is a viable approach with the potential for a good visual outcome. The important predictors for poor visual outcomes include a small preoperative pupil size, preexisting ocular pathology, displacement of significant volume of lens matter (>50%), use of an iris-claw lens, and CME.