The present paper establishes a complete result on approximation by rational functions with prescribed numerator degree in
Lpspaces for 1 < p < ∞ and proves that if f(x)∈Lp[-1,1] changes sign exactly l times in (-1,1), then there exists r(x)∈Rnl such that
where Rnl indicates all rational functions whose denominators consist of polynomials of degree n and numerators polynomials of degree l, and Cp, l,b is a positive constant depending only on p, l and b which relates to the distance among the sign change points of f(x) and will be given in 3.
Authors:Q. Xu, H. Fan, Z. Jiang, Z. Zhou, L. Yang, F. Mei and L. Qu
This research was aimed to study the cell wall degradation and the dynamic changes of Ca2+ and related enzymes in developing aerenchyma of wheat root under waterlogging. An examination of morphological development by light and electron microscope revealed that the structure of cell wall in middle cortical cells remained intact after 12 h of waterlogging and turned thinner after waterlogging for 24 h. At 48 h, the aerenchyma has been formed. The cellulase activity gradually increased in middle cortical cells within 24 h of waterlogging, and decreased with the formation of aerenchyma. Fluorescence detection and subcellular localization of Ca2+ showed the dynamic changing of Ca2+ at the cellular and subcellular levels during the development of aerenchyma. The activity of Ca2+-ATPase enhanced markedly in intercellular space, plasma membrane and tonoplast of some middle cortical cells after 8 h of waterlogging and remained high after 24 h, but it decreased after 48 h of waterlogging. All these suggests that cellulase, Ca2+ and Ca2+-ATPase show a dynamic distribution during the aerenchyma development which associated with the cell wall degradation of middle cortical cells. Moreover, there is a feedback regulation between Ca2+ and Ca2+-ATPase.
A simple, accurate and sensitive method of high performance liquid chromatography (HPLC) with diode array detector was established to identify Xinfeng capsules and systematically evaluated its quality, based on chromatographic fingerprint integrated with the similarity analysis, hierarchical cluster analysis and the quantitative analysis of multi-components by single marker (QAMS). In this study, 18 peaks were selected as the common peaks to evaluate the similarities among different batches (S1–S10) of Xinfeng capsules samples, which were manufactured in the First Affiliated Hospital of Anhui University of Chinese Medicine with a three-year span. Compared to control fingerprint, the similarities values for 10 batches of samples were more than 0.90. Moreover, by analyzing the reference of astragalus, the chromatogram of astragalus was developed, and 10 common peaks of astragalus were identified. More importantly, simultaneous quantification of three markers in Xinfeng capsule, including Calycosin-7-glucoside, calycosin and Formononetinaldehyde was performed, the three constituents showed good regression (R > 0.999) within linear ranges, and their recoveries were within the range of 97.6–101.5%. The validation results showed that the developed method was specific, accurate, precise and robust. This study demonstrated that the developed method offers an efficient, reliable and practical approach for systematic quality evaluation of Xinfeng capsule.
Authors:S. Burrascano, R. Copiz, E. Del Vico, S. Fagiani, E. Giarrizzo, M. Mei, A. Mortelliti, F. M. Sabatini and C. Blasi
In recent decades, the European populations of wild boar have grown substantially, as has the impact of this species, owing above all to its rooting activity. Our aim was to investigate the relationships between vascular plant understorey and wild boar rooting intensity. The questions we addressed are: does rooting intensity influence understorey species composition and diversity? Which functional traits are associated with different levels of rooting? We performed a comparative analysis of plant communities in areas with contrasting levels of rooting intensity within a Mediterranean deciduous lowland forest in central Italy. Besides comparing species composition and diversity, we tested the association between species traits and rooting levels through fourth-corner analysis. We found that contrasting levels of rooting were associated to different understorey species composition and evenness, while we observed no significant difference in species richness. In contrast with our expectations, sites with lower rooting returned i) lower evenness values and ii) a higher proportion of species characterized by traits related to resistance or response to herbivory, i.e., spinescence, clonality, endozoochory, underground storage organs, and low height values. Our findings suggest that current vegetation patterns partly depend on the legacy effect of past rooting disturbance, since the areas currently subjected to low rooting intensity were likely to be intensely rooted in the past. These areas may have developed a marked dominance of clonal thorny species that, in turn, inhibited further feeding activities by wild boar.