This study reconsiders the problem of reachable set bounding for a class of linear systems in the presence of both discrete and distributed delays. Some new criteria are established where the useful term is retained when we estimate the upper bound of the derivative of the Lyapunov-Krasovskii functional. The free-weighting matrix technique is utilised to realise such a purpose. Moreover, the special structure constraint on the final expression of the derivative of the Lyapunov functional in the previous result of authors is removed. Consequently, a tighter bound of the reachable set is obtained. Numerical examples are given to illustrate the merit of the proposed method comparing with the existing ones.
Hydrogen sulfide (H2S) has been postulated to be the third gasotransmitter in both animals and plants after nitric oxide (NO) and carbon monoxide (CO). In this review, the physiological roles of H2S in plant growth, development and responses to biotic, and abiotic stresses are summarized. The enzymes which generate H2S are subjected to tight regulation to produce H2S when needed, contributing to delicate responses of H2S to environmental stimuli. H2S occupies a central position in plant sulfur metabolism as it is the link of inorganic sulfur to the first organic sulfur-containing compound cysteine which is the starting point for the synthesis of methionine, coenzyme A, vitamins, etc. In sulfur assimilation, adenosine 5′-phosphosulfate reductase (APR) is the rate-limiting enzyme with the greatest control over the pathway and probably the generation of H2S which is an essential component in this process. APR is an evolutionarily conserved protein among plants, and two conserved domains PAPS_reductase and Thioredoxin are found in APR. Sulfate reduction including the APR-catalyzing step is carried out in chloroplasts. APR, the key enzyme in sulfur assimilation, is mainly regulated at transcription level by transcription factors in response to sulfur availability and environmental stimuli. The cis-acting elements in the promoter region of all the three APR genes in Solanum lycopersicum suggest that multiple factors such as sulfur starvation, cytokinins, CO2, and pathogens may regulate the expression of SlAPRs. In conclusion, as a critical enzyme in regulating sulfur assimilation, APR is probably critical for H2S generation during plants’ response to diverse environmental factors.
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