Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

In the chloroplast, Calvin-Benson-Bassham enzymes are active in the reducing environment imposed in the light via the electrons from the photosystems. In the dark these enzymes are inhibited, and this regulation is mainly mediated via oxidation of key regulatory cysteine residues. CP12 is a small protein that plays a role in this regulation with four cysteine residues that undergo a redox transition. Using amide-proton exchange with solvent measured by nuclear magnetic resonance (NMR) and mass-spectrometry, we confirmed that reduced CP12 is intrinsically disordered. Using real-time NMR, we showed that the oxidation of the two disulfide bridges are simultaneous. In oxidized CP12, the C23-C31 pair is in a region that undergoes a conformational exchange in the NMR-intermediate timescale. The C66-C75 pair is in the C-terminus that folds into a stable helical turn. We confirmed that these structural states exist in a physiologically relevant environment that is, in cell extract from Chlamydomonas reinhardtii. Consistent with these structural equilibria, the reduction is slower for the C66-C75 pair compared to the C23-C31 pair. Finally, the redox mid-potentials for the two cysteine pairs differ and are similar to those found for phosphoribulokinase and glyceraldehyde 3-phosphate dehydrogenase, that we relate to the regulatory role of CP12.

Plant N concentration (PNC) has been commonly used to guide farmers in assessing maize (Zea mays L.) N status and making in-season N fertilization decisions. However, PNC varies based on the development stage and therefore a relationship between biomass and N concentration is needed (i.e., critical N dilution curves; CNDC) to better understand when plants are N deficient. A few CNDC have been developed and used for plant N status diagnoses, but have not been tested in the US Midwest. The objective of this study was to evaluate under highly diverse soil and weather conditions in the US Midwest the performance of CNDCs developed in France and China for assessing maize N status. Maize N rate response trials were conducted across eight US Midwest states over three years. This analysis utilized plant and soil measurements at V9 and VT development stages and final grain yield. Results showed that the French CNDC (y=34.0x-0.37, where y is critical PNC, x is aboveground biomass) was better with a 91% N status classification accuracy compared to only 62% with the Chinese CNDC (y=36.5x-0.48). The N nutrition index (NNI), which is the quotient of the measured PNC and the calculated critical N concentration (Nc), based on the French CNDC was significantly related to soil nitrate-N content (R2=0.38-0.56). Relative grain yield on average reached a plateau at NNI values of 1.36 at V9 and 1.21 at VT, but for individual sites ranged from 0.80 to 1.41 at V9 and from 0.62 to 1.75 at VT. The NNI threshold values or ranges optimal for crop biomass production may not be optimal for grain yield production. It is concluded that the CNDC developed in France is suitable as a general diagnostic tool for assessing maize N status in US Midwest. However, the threshold values of NNI for diagnosing maize N status and guiding N applications vary significantly across the region, making it challenging for guiding specific on-farm N management. More studies are needed to determine how to effectively use CNDC to make in-season N recommendations in the US Midwest.