## 4 Conclusions  
This study aimed to optimize the extraction conditions in the MUAE process to maximize the recovery yields of quercetin and total flavonoids from DOS. The results indicated that the optimum extraction conditions for quercetin were achieved with a microwave time of 60 s, ultrasound time of 15 min, ultrasound temperature of 70 \({}^{\circ}\)C, ethanol concentration of 70% (\(v/v\), water), and a solvent-to-solid ratio of 30 mL/g. Among the factors studied, ultrasound temperature was found to be a highly influential factor in the recovery of both quercetin and total flavonoids, with higher temperatures leading to decreased yields due to potential degradation of bioactive compounds. The maximum recovery yields obtained were 10.32% for quercetin and 12.52% for total flavonoids under the optimized conditions. A comparison of the recovery yields across different extraction methods revealed that MUAE outperformed the other methods, with UMAE yielding 7.66% quercetin and 10.18% total flavonoids, UAE yielding 5.36% quercetin and 8.34% total flavonoids, and MAE yielding 5.03% quercetin and 7.91% total flavonoids. The highly significant results from the RSM analysis confirm the validity of the model for predicting optimal extraction conditions. Based on our knowledge, the recovery yield obtained in this study is the highest compared to previous works, making this method particularly advantageous for practical applications. This method is especially beneficial due to its shorter extraction time, which significantly reduces both operational costs and solvent consumption compared to other methods.  
This study not only provides an efficient method for recovering quercetin but also opens avenues for its use in cancer treatments as its phyto-therapeutic potential has been well documented in recent studies [41]. This work shows strong potential for scale-up in food processing industries, particularly due to its efficiency in reducing extraction time, operational costs, and solvent consumption. These factors make the method highly suitable for large-scale operations aimed at recovering valuable compounds from red onion skin waste. The combination of microwave and ultrasound techniques in the MUAE process allows for more efficient extraction, enabling higher yields in a shorter period while using less solvent. These advantages make the method well-suited for scale-up in food processing industries, offering a sustainable and cost-effective solution for recovering valuable compounds from red onion skin waste.  
Z.J.V.: Investigation; Conceptualization; Visualization; Data Curation; Methodology; Validation; Writing--Original Draft. G.N.D.: Conceptualization; Project Administration; Resources; Writing--Review and Editing. M.M.: Review and Editing. F.P.: Visualization; Review and Editing. A.S.: Writing--Review and Editing; Assistance with Instrumentation. M.J.P.B.: Review and Editing. M.E.: Review and Editing. D.K.M.: Data Curation; Validation; Writing--Review and Editing. All authors have read and agreed to the published version of the manuscript.  
The Biotechnology Research Laboratory, Babol Noshirvani University of Technology, Iran, [Grant Number: BNUT/4150009/1396], supported the present research.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
We gratefully acknowledge Biotechnology Research Laboratory, Babol Noshirvani University of Technology for facilitating the research and providing the necessary support to conduct the present work.  
The authors declare no conflicts of interest.