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Abstract In the current solution for multiwavelength achromatic flat lenses, a one-to-one correspondence exists between the number of writing phase distributions and the number of achromatic wavelengths. Breaking this correspondence requires a complex phase design and parameter optimization. Here, we show that a dual-layer cascade liquid crystal Pancharatnam-Berry lens (CLCPBL) with two writing phase distributions and a specific coupled phase distribution between the layers can achieve three wavelength achromaticity without any parameter optimization process. Similarly, in a three-layer cascade, the number of achromatic wavelengths increases to seven through the permutations of the layers, with adjustable amplitude factors. We fabricate a three-layer CLCPBL with the design wavelengths of 396.8 nm, 1064 nm, and 1550 nm, which theoretically allows the light at 632.8, 532.8, 3383 and 450 nm to form a common focus, and test such structure. Our CLCPBL enables a wider range of applications than conventional achromatic flat lenses.

With the increasing demands of consumers for product grade, the C2B model of high-grade e-commerce emerges as required. In order to solve the problem of coordination and cooperation between e-commerce platforms and manufacturers, and to further develop the C2B model of high-grade e-commerce, this paper studies the coordination of supply chain interests by establishing a differential game model considering product grade factors. By comparing the equilibrium solutions of differential games under different decision-making situations, a cooperative coordination mechanism is proposed. Next, the equilibrium solution is further analyzed by means of numerical simulation. Finally, the influence of several important parameters on the equilibrium solution is discussed through sensitivity analysis. It is found that (1) the supply chain parties have optimal quality behavior in the centralized decision-making situation, and the overall benefit is the greatest. (2) Compared with the Nash non-cooperative game, the optimal quality behavior of the dominant party remains unchanged, and the optimal quality behavior of the following party is enhanced after both parties move from the Stackelberg master-slave game, and the optimal profits of both parties, as well as the overall increase. (3) The cooperative coordination model can coordinate the quality behavior of both sides of the supply chain when the benefit distribution coefficient is within a specific range.

Monosaccharides and oligosaccharides produced by agarose degradation exhibit potential in the fields of bioenergy, medicine, and cosmetics. Mangrove sediments (MGSs) provide a special environment to enrich enzymes for agarose degradation. However, representative investigations of the agarlytic genes in MGSs have been rarely reported. In this study, agarlytic genes in MGSs were researched in detail from the aspects of diversity, abundance, activity, and location through deep metagenomics sequencing. Functional genes in MGSs were usually incomplete but were shown as results, which could cause virtually high number of results in previous studies because multiple fragmented sequences could originate from the same genes. In our work, only complete and nonredundant (CNR) genes were analyzed to avoid virtually high amount of the results. The number of CNR agarlytic genes in our datasets was significantly higher than that in the datasets of previous studies. Twenty-one recombinant agarases with agarose-degrading activity were detected using heterologous expression based on numerous complete open-reading frames, which are rarely obtained in metagenomics sequencing of samples with complex microbial communities, such as MGSs. Aga2, which had the highest crude enzyme activity among the 21 recombinant agarases, was further purified and subjected to enzymatic characterization. With its high agarose-degrading activity, resistance to temperature changes and chemical agents, Aga2 could be a suitable option for industrial production. The agarase ratio with signal peptides to that without signal peptides in our MGS datasets was lower than that of other reported agarases. Six draft genomes, namely, Clusters 1–6, were recovered from the datasets. The taxonomic annotation of these genomes revealed that Clusters 1, 3, 5, and 6 were annotated as Desulfuromonas sp., Treponema sp., Ignavibacteriales spp., and Polyangiaceae spp., respectively. Meanwhile, Clusters 2 and 4 were potential new species. All these genomes were first reported and found to have abilities of degrading various important polysaccharides. The metabolic pathway of agarose in Cluster 4 was also speculated. Our results showed the capacity and activity of agarases in the MGS microbiome, and MGSs exert potential as a repertory for mining not only agarlytic genes but also almost all genes of the carbohydrate-active enzyme family.