We study the computation of canonical bases of sets of univariatein Hermite form. We exploit the triangular shape of M to generalize a divide-and-conquer approach which originates from fast minimal approximant basis algorithms. Besides recent techniques for this approach, we rely on high-order li ing to perform fast modular products of polynomial matrices of the form PF mod M.Our algorithm usesindicates that logarithmic factors are omi ed, and ω is the exponent of matrix multiplication. is had previously only been achieved for a diagonal matrix M. Furthermore, our algorithm can be used to compute the shi ed Popov form of a nonsingular matrix within the same cost bound, up to logarithmic factors, as the previously fastest known algorithm, which is randomized.

Ten triterpenoid glycosides including two new (1 and 2) were isolated from the methanol extract of Allium ascalonicum rhizomes. These compounds were structurally elucidated to be 3β(2), lactifoloside C (3), lactifoloside H (4), randiasaponin IV (5), kudinoside G (6), ilexkudinoside W (7), lactifoloside G (8), kudinoside D (9), and ilexkudinoside T (10) by analyzing their HR-ESI-MS, NMR spectral data and by comparison with those reported in the literature. Compounds 1-10 were evaluated for anoctamin-1 (ANO1) inhibitory activity using yellow fluorescent protein reduction assays. At the concentration of 30 µM, compounds 2 and 9 displayed significant ANO1 inhibitory percentages of 28.9 and 26.2%, respectively.

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Phytochemical study on the roots of Achyranthes bidentata Blume led to the isolation of sixteen compounds including three new ones (1-3). Their chemical structures were determined as oleanolic acid 28-O-β-D-glucopyranoside-3-O-[β-D-glucopyranosyl-(1→3)-β-Dgalactopyranoside) (1), methyl (8Z,11Z)-5,6,7-trihydroxytetradeca-8,11-dienoate (2), methyl (6E,11Z)-5,8,9-trihydroxytetradeca-6,11-dienoate (3), fulgidic acid (4), (9E,11E)-13oxooctadeca-9,11-dienoic acid (5), (9Z,11E,15Z)-13-hydroxyoctadeca-9,11,15-trienoic acid (6), oleanolic acid 28-O-β-D-glucopyranoside-3-O-α-L-rhamnopyranosyl-(1→4)-β-Dglucuronopyranoside (7), oleanolic acid 28-O-β-D-glucopyranoside-3-O-β-D-glucopyranosyl-(1→2)-[α-L-rhamnopyranosyl-(1→3)]-β-D-glucuronopyranoside (8), oleanolic acid 3-O-β-Dglucopyranosyl-(1→2)-[α-L-rhamnopyranosyl-(1→3)]-β-D-glucuronopyranoside (9), oleanolic acid 3-O-α-L-rhamnopyranosyl-(1→3)-β-D-glucuronopyranoside (10), blumenol C glucoside (11), citroside A (12), 6S,9S-roseoside (13), ginsenoside Rg1 (14), 20-hydroxyecdysone (15), and benzyl α-L-rhamnopyranosyl-(1→6)]-β-D-glucopyranoside (16) by spectroscopic analysis. Compounds 1, 7 and 11-16 inhibited NO production in LPS-activated RAW264.7 cells with IC 50 values in the range from 28.03 to 54.23 µM (positive control, L-NMMA: IC 50 = 35.52 µM). Compounds 14 and 15 showed anti α-glucosidase activity with IC 50 values of 176.24 and 156.92 µM, respectively, compared with the positive control, acarbose, IC 50 = 160.99 μM.