• Journal for History of Mathematics
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• v.24 no.1
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• pp.1-13
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• 2011

In Tian mu bi lei cheng chu jie fa(田畝比類乘除捷法) of Yang Hui suan fa(楊輝算法)), Yang Hui annotated detailed comments on the method to find roots of quadratic equations given by Liu Yi in his Yi gu gen yuan(議古根源) which gave a great influence on Chosun Mathematics. In this paper, we show that 'Zeng cheng kai fang fa'(增乘開方法) evolved from a process of binomial expansions of $(y+{\alpha})^n$ which is independent from the synthetic divisions. We also show that extending the results given by Liu Yi-Yang Hui and those in Suan xue qi meng(算學啓蒙), Chosun mathematican Hong Jung Ha(洪正夏) elucidated perfectly the 'Zeng cheng kai fang fa' as the present synthetic divisions in his Gu il jib(九一集).

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.8
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• pp.3675-3680
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• 2012

Objective: To investigate the expression of endogenous hypoxia-related markers identified as being involved in vulvar squamous cell carcinoma (VSCC). Methods: We performed immunohistochemical staining of hypoxia-inducible factor-$1{\alpha}$ (HIF-$1{\alpha}$), glucose transporter-1 (GLUT-1), carbonic anhydrase 9 (CA-9) and vascular endothelial growth factor (VEGF), on tissue sections of 25 VSCC patients, 10 vulvar intraepithelial neoplasia (VIN) patients and 12 healthy controls. Results: HIF-$1{\alpha}$ expression was found in all sections, with no significant difference between controls, VIN and VSCC sections (all P<0.05). Glut-1 expression was found in 25% of control, 90% of VIN and 100% of VSCC sections. A significant difference between control and VIN or VSCC was observed (all P<0.05), while no difference was found between VIN and VSCC sections (P>0.05). CA-9 expression was negative in control sections, but it was found in 30% of VIN sections and 52% of VSCC sections with strong staining. Similarly, CA-9 expression also showed obvious differences between controls and VIN or VSCC sections (all P<0.05). However, there was no significant difference between VIN and VSCC (P>0.05). There were only 25% of control sections with weak VEGF expression, while strong staining was found in about 60% of VIN sections and 25% of VSCC sections (all P<0.05). In addition, a difference was also found between VIN and VSCC sections (P<0.05). Conclusion: Expression of endogenous hypoxia markers (HIF-$1{\alpha}$, GLUT-1, CA-9 and VEGF) might be involved in the malignant progression of VSCC.