Fractional Hermite interpolation for non-smooth functions. ETNA - Electronic Transactions on Numerical Analysis

The interpolation of functions plays a fundamental role in numerical analysis. The highly accurate approximation of non-smooth functions is a challenge in science and engineering as traditional polynomial interpolation cannot characterize the singular features of these functions. This paper aims at designing a fractional Hermite interpolation for non-smooth functions based on the local fractional Taylor expansion and at deriving the corresponding explicit formula and its error remainder. We also present a piecewise hybrid Hermite interpolation scheme, a combination of fractional Hermite interpolation and traditional Hermite interpolation. Some numerical examples are presented to show the high accuracy of the fractional Hermite interpolation method

Analysis of Molecular Mechanism of YiqiChutan Formula Regulating DLL4-Notch Signaling to Inhibit Angiogenesis in Lung Cancer

In order to explore the specific mechanism of YiqiChutan formula (YQCTF) in inhibiting the angiogenesis of lung cancer and its relationship with delta-like ligand 4- (DLL4-) Notch signaling, 30 healthy BALB/c-nu/nu rats were selected and divided into three groups: A549 group (implanted with lung adenocarcinoma cell line A549), NCI-H460 group (implanted with human lung large-cell carcinoma cell line NCI-H460), and NCI-H446 group (implanted with human lung small cell carcinoma cell line NCI-H446) for constructing lung cancer transplanted tumor models. After modeling, the group treated with normal saline was taken as control group, 200 mg/kg of YQCTF was adopted for intervention, and the tumor volume and growth inhibition rate were compared with the vascular targeted inhibitor Sorafenib. HE staining, CD31 fluorescent antibody staining, and microelectron microscopy were adopted to observe the neovascular endothelial cells of the transplanted tumor. The expression of VEGF, HIF-1α, DLL4, and Notch-1 in the transplanted tumors in each group was detected by Western blot and RT-PCR at the protein level or mRNA level. Compared with the control group, the YQCTF-treated group had obvious inhibitory effect on lung cancer transplanted tumor and lung cancer angiogenesis. In the YQCTF-treated group, the density of angiogenesis decreased significantly and the vascular lumen structure also decreased, and the expression levels of VEGF, HIF-1α, DLL4, and Notch-1 in the YQCTF-treated group were all lower than those in the control group. YQCTF could inhibit the growth of lung cancer transplanted tumor through antiangiogenesis, and it could also reduce the amount of angiogenesis in lung cancer transplanted tumor. In addition, the generation of lumen structure was also hindered, which was realized through the VEGF signaling pathway and DLL4-Notch signaling pathway

The distribution of flowering time (R1) of an F₂ population derived from Kariyutaka × Suzumaru at Harbin in 2013 (A) and in 2014 (B). The flowering time (R1) for parents are indicated by arrows; DAE, days after emergence.

<p>The distribution of flowering time (R1) of an F₂ population derived from Kariyutaka × Suzumaru at Harbin in 2013 (A) and in 2014 (B). The flowering time (R1) for parents are indicated by arrows; DAE, days after emergence.</p

Alignment of <i>e1-ba3</i> with other known <i>E1</i> mutations.

<p>The SNP mutation site for <i>e1-as</i>, <i>e1-fs</i> are marked by black boxes; and the 5 bp mutation is marked with a red box. The bipartite nuclear localization sites are marked by black dashed line. The B3-like domain is also indicated with a dashed red line.</p

The distribution of flowering time (R1) of F₂ populations derived from Kariyutaka × Moshidougong 503 at Harbin in 2013 (A), in 2014 (B and C), and at Hailun in 2014 (D).

<p>The flowering time (R1) for parents are indicated by arrows; DAE, days after emergence.</p

Diurnal Expression Pattern, Allelic Variation, and Association Analysis Reveal Functional Features of the <i>E1</i> Gene in Control of Photoperiodic Flowering in Soybean

<div><p>Although four maturity genes, <i>E1</i> to <i>E4</i>, in soybean have been successfully cloned, their functional mechanisms and the regulatory network of photoperiodic flowering remain to be elucidated. In this study, we investigated how the diurnal expression pattern of the <i>E1</i> gene is related to photoperiodic length; and to what extent allelic variation in the B3-like domain of the <i>E1</i> gene is associated with flowering time phenotype. The bimodal expression of the <i>E1</i> gene peaked first at around 2 hours after dawn in long-day condition. The basal expression level of <i>E1</i> was enhanced by the long light phase, and decreased by duration of dark. We identified a 5bp (3 SNP and 2-bp deletion) mutation, referred to an <i>e1-b3a</i>, which occurs in the middle of B3 domain of the <i>E1</i> gene in the early flowering cultivar Yanhuang 3. Subcellular localization analysis showed that the putative truncated e1-b3a protein was predominately distributed in nuclei, indicating the distribution pattern of e1-b3a was similar to that of E1, but not to that of e1-as. Furthermore, genetic analysis demonstrated allelic variations at the <i>E1</i> locus significantly underlay flowering time in three F₂ populations. Taken together, we can conclude the legume specific <i>E1</i> gene confers some special features in photoperiodic control of flowering in soybean. Further characterization of the <i>E1</i> gene will extend our understanding of the soybean flowering pathway in soybean.</p></div