In this paper, we present an innovative technique that improves the convergence order of iterative schemes that do not require the evaluation of Jacobian matrices. Using this procedure, we achieve a remarkable increase in the order of convergence, raising it from p to p + 3 units, which results in a remarkable improvement in the overall performance. We have conducted comprehensive numerical tests in various scenarios to validate the theoretical results, showing the efficiency and effectiveness of the new Jacobian-free schemes.

The Opuntia ficus-indica (OFI) prickly pear peel, is a residue product and was used as a substrate in solid-state fermentation (SSF) to obtain bioactive compounds of interest due to its antimicrobial and antioxidant activity. A Box Hunter & Hunter design to evaluate the independent factors was used. These factors were temperature (°C), inoculum (spores/g), humidity (%), pH, NaNO3 (g/L), MgSO4 (g/L), KCl (g/L) and KH2PO4 (g/L). The response factors were hydrolyzable and condensed tannins amount. In addition, the fermentation extracts the antioxidant and antimicrobial activity were evaluated. The results showed that the humidity (%), inoculum (spores/g) and temperature (°C) affect the release of hydrolyzable and condensed tannins. The treatments 13 and 16 were the best to accumulate condensed (43 mg/g) and hydrolyzable tannins (3.8 mg/g) respectively. Besides, the fermented extracts showed a higher antioxidant activity compared than the unfermented peel extracts, as well as a high inhibition versus E. coli, Alternaria sp. and Botrytis spp. The use of the fermentation process is a good alternative for the recovery of waste and the accumulation of bioactive molecules with potential industrial application.

Currently, agro-industrial residues have been used to obtain bioactive compounds. The fermentation process is an alternative for the use of these residues and to be able to accumulate metabolites that may be of interest to different industrial sectors. The aim of this study was to evaluate solid-state fermentation conditions using pineapple waste as substrate with Aspergillus niger spp., to release polyphenolic compounds using a Plackett-Burman exploratory design. Temperature, humidity, inoculum, NaNO3, MgSO4, KCl and KH2PO4 conditions in the fermentation process were evaluated. The results revealed that the Aspergillus niger HT3 strain reached a hydrolyzable tannins accumulation of 10.00 mg/g, while Aspergillus niger Aa20 reached a condensed tannins release of 82.59 mg/g. The KH2PO4 affect the release of condensed tannins with A. niger Aa20 and MgSO4 affect the release of hydrolyzable tannins with A. niger HT3. In addition, a positive antioxidant activity was demonstrated for the DPPH, ABTS and FRAP technique. The HPLC analysis was able to identify compounds in the fermented pineapple peel such as 3-feruloylquinic acid, caffeic acid, lariciresinol and 3-hydroxyphloretin 2'-O-xylosyl-glucoside, among others. The solid-state fermentation process is a biotechnological alternative for the release of bioactive compounds.

Abstract: Pomegranate peels are important source of polyphenols with remarkable interest in food, pharmaceutical and cosmetic industry. An improved extraction of total polyphenolic com-pounds (TPC) from pomegranate peels by Solid-State Fermentation (SSF) was achieved. A Box Hunter & Hunter (BHH) followed by Central Composite Design (CCD) were performed to assess the effect of the process variables on TPC release. The statistic designs indicate that the best TPC extraction (234.85 mg GAE/gdm) by means of SSF occurs, at 42°C, 50 % moisture, pH 5.0, mineral solution (g/L): NaNO3 (3.83), KH2PO4 (1.52), MgSO4 (4.66) and KCl (1.52) at 36 h. At the best fer-mentation conditions, TPC (248.78±1.24 mgGAE/gdm) increased 5.96-fold than values previously reported and antioxidant activity [AA] increased 5.81-fold than the value obtained before the SSF optimization. High-valued citric acid, α and β punicalin, α and β punicalagin, punigluconin, gal-loyl-HHDP hexoside and ellagic acid molecules were identified. The increased extraction of TPC by SSF provides a suitable alternative for pomegranate peels valorization through the re-covery of molecules with high added value with potential use in food, pharmacy and cosmetic industries; a diversification in the use of food agroindustry by-products is obtained as approach to the circular economy model through biotechnological processes.