Quintic trigonometric Bézier curve with two shape parameters

The fifth degree of trigonometric Bézier curve called quintic with two shapes parameter is presented in this paper. Shape parameters provide more control on the shape of the curve compared to the ordinary Bézier curve. This technique is one of the crucial parts in constructing curves and surfaces because the presence of shape parameters will allow the curve to be more flexible without changing its control points. Furthermore, by changing the value of shape parameters, the curve still preserves its geometrical features thus makes it more convenient rather than altering the control points. But, to interpolate curves from one point to another or surface patches, we need to satisfy certain continuity constraints to ensure the smoothness not just parametrically but also geometrically

α‑Iminyl Cation-Involved Indole Construction via Brønsted Acid-Promoted Reaction of Isoxazol-5-ones

Herein, we report a strategically novel method for the efficient construction of indole skeletons using 2-phenylisoxazol-5-ones as the starting material. This reaction proceeds via Brønsted acid-promoted α-iminyl cation generation by N–O bond cleavage and a subsequent intramolecular cyclization to afford 1H-indole-3-carboxylic acid, which further undergoes decarboxylation to yield the final product. Control experiments show that N–O bond cleavage and intramolecular cyclization proceed so fast that the 1H-indole-3-carboxylic acid could be isolated in high yields even after 5–10 min. The substrate scope of this transformation is broad, and the desired products are obtained in moderate to good yields. The transition-metal-free reaction condition, CO2 as the sole byproduct, and good practicability add to the synthetic potential of this transformation in the pharmaceutical and flavor industries

Comparison of DEGs in different tissues.

The x-axis represents different tissues, and the y-axis represents the number of differentially expressed genes. Black indicates down-regulated expressed genes, white indicates up-regulated expressed genes. LMP Bud: bud mixed pool with extremely low SD; HMP Bud: bud mixed pool with extremely high SD, P1:No.935, P2: No.3641. (DOC)</p

Venn diagram of DEGs.

Red indicates differentially expressed genes in buds, blue indicates differentially expressed genes in leaves, green indicates differentially expressed genes in siliques. Commonly overlapping parts indicate differentially expressed genes in the three tissues. (DOC)</p

Variance analysis of seed density per silique in DH population.

Variance analysis of seed density per silique in DH population.</p

Distribution of SNP index association values on chromosomes.

The abscissas indicate the chromosome names, the colored dots represent the calculated SNP index (or Δ [SNP index]) values, and the black lines represents the fitted SNP index (or Δ [SNP index]) values. The top figure shows the distribution of SNP index values of recessive pools; the middle figure shows the distribution of SNP index values of dominant pools; and the bottom figure shows the distribution of Δ (SNP index) values, where the red lines represent the confidence intervals. The threshold lines are equal to 0.99, the blue lines represent the threshold lines with a confidence level of 0.95, and the green lines represent the threshold lines with a confidence level of 0.90. (DOC)</p

Map of flanking markers of major loci.

(A) Mapping of SD QTLs in B. napus. (B)Mapping of physical bins within the candidate intervals. (C) Genetic position mapping after candidate interval markers. (D) Mapping of the physical location of candidate interval markers. Note: The black solid lines represent the SD QTL mapping intervals; the yellow lines represent the confidence intervals of the QTLs in 2019HZ; the green line represents the confidence interval of the QTL in 2019XN; the red line represents the confidence interval of the QTL in 2020HZ; the purple line represents the confidence interval of the QTL in 2020XN; and the blue line represents the QTL confidence interval according to the results of a meta-analysis.</p

Summary table of SNP annotation results in the candidate interval chrA09: 6.04–11.21Mb.

Summary table of SNP annotation results in the candidate interval chrA09: 6.04–11.21Mb.</p

Parental phenotypes.

SD was measured as the ratio of the number of seeds per silique to the silique length. (Pedicels and silique beaks are not included in the silique length).</p

Analysis of the differential expression of candidate genes.

A represents the relative differential expression of the candidate gene BnaA09g14070D in different tissues, B represents the relative differential expression of the candidate gene Bna09g14800D in different tissues, C represents the relative differential expression of the candidate gene BnaA09g18250D in different tissues. LMPBud: bud mixed pool with extremely low SD; HMPBud: bud mixed pool with extremely high SD, P1: No.935, P2: No. 3641.</p