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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 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]

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]

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]

Millions of adenosine (A) to inosine (I) RNA editing events are reported and well‐studied in eukaryotes; however, many features and functions remain unclear in prokaryotes. By combining PacBio Sequel, Illumina whole‐genome sequencing, and RNA Sequencing data of two Klebsiella pneumoniae strains with different virulence, a total of 13 RNA editing events are identified. The RNA editing event of badR is focused, which shows a significant difference in editing levels in the two K. pneumoniae strains and is predicted to be a transcription factor. A hard‐coded Cys is mutated on DNA to simulate the effect of complete editing of badR. Transcriptome analysis identifies the cellular quorum sensing (QS) pathway as the most dramatic change, demonstrating the dynamic regulation of RNA editing on badR related to coordinated collective behavior. Indeed, a significant difference in autoinducer 2 activity and cell growth is detected when the cells reach the stationary phase. Additionally, the mutant strain shows significantly lower virulence than the WT strain in the Galleria mellonella infection model. Furthermore, RNA editing regulation of badR is highly conserved across K. pneumoniae strains. Overall, this work provides new insights into posttranscriptional regulation in bacteria. [ABSTRACT FROM AUTHOR]

A microcavity laser with linear polarization finds practical applications in metrology and biomedical imaging. Through a pulsed light excitation, the polarization characteristics of amplified spontaneous emissions (ASEs) from ten-period ZnO/Zn 0.8 Mg 0.2 O multiple quantum wells (MQWs) on a C-Plane sapphire substrate were investigated at room temperature. Unlike unpolarized spontaneous emissions, with 35 meV of energy differences between the C and AB bands, the ASE of MQWs revealed transverse-electric (TE) polarization under the edge emission configuration. The excited ASE from the surface normal of the polar ZnO/Zn 0.8 Mg 0.2 O MQWs with hexagonal symmetry revealed linear polarization under the pump of the stripe line through the focusing by using a cylindrical lens. The polarization direction of ASE is independent of the pump polarization but always perpendicular to the pump stripe, even if the cylindrical lens is rotated 90 degrees because of the gain-guiding effect. [ABSTRACT FROM AUTHOR]

In this paper, we investigate robust necessary optimality for scalar uncertain optimization problems under the strictly robust counterpart, where the uncertainties are included in the objective and the constraints. Based on generalized differentiable assumptions, some robust necessary conditions via a separation scheme are derived. Besides, by means of strong separation functions, several characterizations of robust necessary optimality can be established. Finally, an example is given to show the effectiveness of the results derived in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the general dual problems in robust optimization without any convexity or concavity assumptions are investigated by using the image space analysis. A generalized Lagrange function is proposed by the class of regular weak separation functions. Then, two types of generalized robust dual problems are established. Under the appropriate assumption, the equivalent assertions of the zero duality gap property are characterized between the robust counterpart of an uncertain constrained optimization problem and the optimistic counterpart of its uncertain generalized Lagrange dual. Similarly, these theories and results can be extended to the deterministic dual pair of the robust counterpart and its Lagrange dual. [ABSTRACT FROM AUTHOR]

In this paper, we characterize robust solutions for uncertain multiobjective optimization problems on the basis of vectorization models by virtue of image space analysis. By introducing corrected image of original uncertain problem or the selected and corrected images of its robust counterpart, an equivalent relation between multiobjective robustness and the separation of two sets in the image space is well established. Moreover, by means of linear (vector/scalar) separation functions, some Lagrangian-type sufficient robust optimality conditions are presented. Especially, under suitable restriction assumptions, we derive Lagrangian-type necessary robust optimality conditions in terms of nonlinear separation functions. These results obtained in this paper extend and improve some existing ones recently. Finally, several examples are given to show the effectiveness of the conclusions. [ABSTRACT FROM AUTHOR]