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The aim of this paper is to study stability of the sets of l-minimal approximate solutions and weak l-minimal approximate solutions for set optimization problems with respect to the perturbations of feasible sets and objective mappings. We introduce a new metric between two set-valued mappings by utilizing a Hausdorff-type distance proposed by Han [A Hausdorff-type distance, the Clarke generalized directional derivative and applications in set optimization problems. Appl Anal. 2022;101:1243–1260]. The new metric between two set-valued mappings allows us to discuss set optimization problems with respect to the perturbation of objective mappings. Then, we establish semicontinuity and Lipschitz continuity of l-minimal approximate solution mapping and weak l-minimal approximate solution mapping to parametric set optimization problems by using the scalarization method and a density result. Finally, our main results are applied to stability of the approximate solution sets for vector optimization problems. [ABSTRACT FROM AUTHOR]

This study aimed to optimize the extraction process of total saponins from the fungal matrix resulting from the dual solid-state fermentation of Hericium erinaceus-Astragalus membranaceus residue (HAMTS) and to determine its antioxidant activity. The content of total saponins before and after fermentation was measured using the vanillin method. A response surface method combined with ultrasonication was employed to optimize the extraction of HAMTS, and the reducing power as well as the scavenging ability against DPPH and ABTS+ free radical of HAMTS were analyzed. The results showed that the content of HAMTS after fermentation was 10.34 mg/g, with an increase of 63.35%. Under the optimal extraction conditions: Liquid-to-solid ratio of 19 mL/g, ultrasonication time of 16 min, ethanol volume fraction of 74%, ultrasonic power of 62 W, the extraction amount of HAMTS was 11.48 mg/g. At a concentration of 10 g/L, the reducing power of HAMTS, as well as the DPPH and ABTS+ free radical scavenging rates, were 0.80, 96.48%, and 56.12%, respectively. The study indicates that the regression model established in the experiment can be used to predict the extraction amount of HAMTS, and HAMTS exhibits good antioxidant activity, demonstrating the potential for development as a feed additive. [ABSTRACT FROM AUTHOR]

This paper is devoted to second-order optimality conditions of constrained vector optimization problems with continuously Fréchet differentiable data. Different from conventional approaches, we employ a new one, image space analysis, to establish suitable regularity conditions and then present new second-order necessary optimality conditions that depend on one single KKT multiplier for all critical directions. Moreover, we propose one more regularity condition for the multiobjective case and compare it with the previous one. Besides, we compare the main regularity conditions with the existing ones in the literature for the scalar case. [ABSTRACT FROM AUTHOR]

This paper concentrates on robust duality relations for uncertain cone-constrained vector optimization problems in more general nonconvex settings. First, different from the existing results, a new class of generalized Lagrange functions of the considered problem is introduced by combining the image space analysis method and scalarization technique. Then, the Lagrange robust vector dual problem is formulated. Subsequently, the results of robust weak duality, strong duality and converse duality are given respectively, which characterize vector dual relations between the primal worst and dual best problems. Simultaneously, some examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper concentrates on uncertain multiobjective optimization problems with an arbitrary number of uncertain constraints under nonconvex and nonsmooth assumptions. We analyse the properties of robust infinite constraints and arrive at the Clarke subdifferential of the double supremum function. Subsequently, we employ the obtained subdifferential rules to study KKT robust necessary and sufficient optimality conditions for two types of uncertain multiobjective optimization problems. Simultaneously, some illustrative examples are provided to show the validity of the main results. Our results are new and generalize several corresponding results in the literature. [ABSTRACT FROM AUTHOR]

CCK as brain-gut peptide, binds to its receptor (CCKR) and participates in physiological processes such as feeding and digestion in animals. In order to study the function of CCKs and CCKRs in largemouth bass (Micropterus salmoides) in feeding activities, the coding sequences of CCK1, CCK2, CCK1R and CCK2R were cloned in this study. Their lengths were 414, 387, 1368 and 1359 bp, and their encodes were 137, 128, 455 and 452 amino acids, respectively. Fluorescence quantitative results showed that both CCK1 and CCK2 were highly expressed in brain, followed by intestinal, while CCK1R and CCK2R were highly expressed in gallbladder and brain, respectively. Within 24h after ingestion, the relative expressions of CCK1, CCK2, CCK1R and CCK2R increased first and then decreased. The relative expression of CCK1, CCK1R and CCK2R reached the highest value at 3h after ingestion, while the relative expression of CCK2 was at 12h after ingestion. The relative expression reached the highest value (P<0.05). During fasting, the relative expression of CCK1, CCK1R and CCK2R was significantly increased on the 14th day of fasting (P<0.05). The relative expression trends of CCK1, CCK1R and CCK2R after refeeding were similar to those after meals, showing a trend of first increasing and then decreasing. However, there was no significant change in the relative expression of CCK2 during fasting and refeeding. In conclusion, the results of this study indicated that CCK1 can be combined with CCK1R and CCK2R to act as a satiety signal factor to regulate physiological processes such as feeding and digestion of largemouth bass by suppressing appetite; CCK2 may act as a short-term appetite factor to regulate feeding. Activity. The results of this study can provide a theoretical basis for the regulation of feeding activities of largemouth bass. [ABSTRACT FROM AUTHOR]