In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the ...In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.展开更多
We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,thi...We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner's method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.展开更多
A novel series of resveratrol derivatives were synthesized according to Wittig-Horner reaction with 3,5-dihydroxybenzyl alcohol or 3,5-dimethoxybenzyl alcohol or 4-hydroxybenzyl alcohol as raw material and the inhibit...A novel series of resveratrol derivatives were synthesized according to Wittig-Horner reaction with 3,5-dihydroxybenzyl alcohol or 3,5-dimethoxybenzyl alcohol or 4-hydroxybenzyl alcohol as raw material and the inhibitory activities on breast carcinoma (MDA-MB-231) and gastric carcinoma cell lines (SGC-7901) in vitro were evaluated by the standard methyl thiazole tetrazolium (MTT) method. The result of biological test shows that some of resveratrol derivatives possess stronger anti-cancer activities than 5-FU. Compound 5c shows the strongest activity against breast carcinoma (MDA-MB-231) and gastric carcinoma cell lines (SGC-7901) with IC50 value of 50.19 ± 1.02 μM, 122.68.27 ± 2.04 μM, compared to that IC50 value of 5-FU is 98.59±3.61 μM,156.74±6.16 μM, respectively.展开更多
文摘In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.
基金Supported by the Graduate Starting Seed Fund of Northwestern Polytechnical University(Z2012030)
文摘We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner's method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.
文摘A novel series of resveratrol derivatives were synthesized according to Wittig-Horner reaction with 3,5-dihydroxybenzyl alcohol or 3,5-dimethoxybenzyl alcohol or 4-hydroxybenzyl alcohol as raw material and the inhibitory activities on breast carcinoma (MDA-MB-231) and gastric carcinoma cell lines (SGC-7901) in vitro were evaluated by the standard methyl thiazole tetrazolium (MTT) method. The result of biological test shows that some of resveratrol derivatives possess stronger anti-cancer activities than 5-FU. Compound 5c shows the strongest activity against breast carcinoma (MDA-MB-231) and gastric carcinoma cell lines (SGC-7901) with IC50 value of 50.19 ± 1.02 μM, 122.68.27 ± 2.04 μM, compared to that IC50 value of 5-FU is 98.59±3.61 μM,156.74±6.16 μM, respectively.
