In this paper, by introducing some parameters and by employing a sharpening of Hölder's inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder's theorem is given.
Drought stress has a significant effect on the growth, physiology and biochemistry of medicinal plants. SDIR1 (Salt- and Drought-Induced Ring Finger1), a C3H2C3-type RING-finger E3 ubiquitin ligase gene plays an important role in the stress response of various plants. However, the role of this gene is not clear in Coptis chinensis. In this study, the CcSDIR1 gene was cloned from C. chinensis using RACE and RT-PCR. Sequence analysis revealed that CcSDIR1 had an open reading frame of 840 bp that encodes 279 amino acids with a theoretical molecular weight about 31 kDa and pI value of 5.65 and shared conserved domains with other plants. On comparison with the wild-type plants, overexpression of CcSDIR1 in transgenic tobaccos increased drought tolerance and showed better growth performance. However, lower malondialdehyde contents and high antioxidant enzyme activities were observed in transgenic tobacco plants compared to wild-type plants. In addition, Evans blue staining showed high cell viability of transgenic lines under drought stress. These results suggest that CcSDIR1 regulates various responses to drought stress by increasing antioxidant enzyme activities and reducing oxidative damage. From the study results, the CcSDIR1 gene will be very useful for drought stress research in plants.
A protocol is described for plant regeneration from protoplasts of Gentiana straminea Maxim. via somatic embryogenesis. Protoplasts were isolated from embryogenic calli in an enzyme solution composed of 2% Cellulase Onozuka R-10, 0.5% Macerozyme R-10, 0.5% Hemicellulase, and 0.5 M sorbitol with a yield of 3.0 × 106 protoplasts per gram of fresh weight. Liquid, solid-liquid double layer (sLD) and agar-pool (aPL) culture systems were used for protoplast culture. The aPL culture was the only method that produced embryogenic, regenerative calli. With aPL culture, the highest frequencies of protoplast cell division and colony formation were 39.6% and 16.9%, respectively, on MS medium supplemented with 2 mg/L 2,4-dichlorophenoxyacetic acid (2,4-D) and 0.5 mg/L N6-benzylaminopurine (BA). Microcalli were transferred to solid MS medium containing a reduced concentration of 2,4-D (0.5 mg/L) to promote the formation of embryogenic calli. Somatic embryos developed into plantlets on MS medium supplemented with 2 mg/L BA at a rate of 43.7%.
In this paper, by making use of the generating function methods and Padé approximation techniques, we establish some new recurrence formulas for the Hermite polynomials and their squares. These results presented here are the corresponding extensions of some known formulas.
In view that the traditional dynamic recrystallization (DRX) model cannot effectively predict the DRX process in the hot deformation process of sheet metal, DRX behavior modeling and simulation of q890 steel plate based on the plane strain compression test are designed. The plane strain thermal simulation tests were performed at 1,223–1,373 K and the strain rates of 1–50−1 on Gleeble-3500 thermal–mechanical simulator. The flow stress curves were well smoothed. The stress–strain data were investigated for the analysis of the dynamic recrystallization in the process of thermal deformation. The activation energy of DRX was calculated as Q = 394.53 kJ/mol by the simulation data. The equation of peak strain was developed with the flow stress data by the Zener–Hollomon parameter. The DRX transformation fraction of Q890 steel was studied, and the DRX kinetics equation was developed by the Avrami equation. The experimental data are in good agreement with the calculated values, which proves the reliability of the DRX model and can be widely used in real life.