• Journal for History of Mathematics
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• v.25 no.4
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• pp.1-10
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• 2012

In Chinese mathematics, there have been two numeral systems, namely one in spoken language for recording and the other by counting rods for computations. They concerned with problems dealing with practical applications, numbers in them are concrete numbers except in the process of basic operations. Thus they could hardly develop a pure theory of numbers. In Song dynasty, 0 and TianYuanShu were introduced, where the coefficients were denoted by counting rods. We show that in this process, counting rods took over the role of the numeral system in spoken language and hence counting rod numeral system plays the role of that for abstract numbers together with the tool for calculations. Decimal fractions were also understood as denominate numbers but using the notions by counting rods, decimals were also admitted as abstract numbers. Noting that abacus replaced counting rods and TianYuanShu were lost in Ming dynasty, abstract numbers disappeared in Chinese mathematics. Investigating JianJie YiMing SuanFa(簡捷易明算法) written by Shen ShiGui(沈士桂) around 1704, we conclude that Shen noticed repeating decimals and their operations, and also used various rounding methods.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.1-16
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• 2005

Chosun dynasty mathematician Park Yul (1621 - ?) wrote San Hak Won Bon(算學原本) which was posthumously published in 1700 by his son Park Du Se (朴斗世). It is the first mathematics book whose publishing date is known, although we have Muk Sa Jib San Bub (默思集算法) by Gyung Sun Jing (慶善徵, 1616-?). San Hak Won Bon is the first Chosun book which deals with tian yuan shu (天元術) and was quoted by many Chosun authors. We do find it in the library in Korea University. In this paper, we investigate its contents together with its historical significance and influences to the development of Chosun dynasty Mathematics and conclude that Park Yul is one of the most prominent Chosun dynasty mathematicians.

• Journal for History of Mathematics
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• v.30 no.3
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• pp.137-162
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• 2017

The Chinese algebraic method, the tian yuan shu, was developed during Song period (960-1279), of which Li Ye's works contain the earliest testimony. Two 18th century editors commentated on his works: the editor of the Siku quanshu and Li Rui, the latter responding to the former. Korean scholar Nam Byeong-gil added another response in 1855. Differences can be found in the way these commentators considered mathematical objects and procedures. The conflicting nature of these commentaries shows that the same object, the quadratic equation, can beget different interpretations, either a procedure or an assertion of equality. Textual elements in this paper help modern readers reconstruct different authors' understandings and reconsider the evolution of the definition of the object we now call 'equation'.

• The Journal of Korean Medical History
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• v.14 no.2
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• pp.109-152
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• 2001

Throughout this paper, I adjusted the study of 'Qian Yi'(錢乙)'s Medical Thought, and the following is the summary. 1. 'Qian Yi' wrote 'Xiao Er Yao Zheng Zhi Jue'("小兒藥證直訣", edited by 誾季忠), and there were 'Shang Han Lun Zhi Wei'("傷寒論指微"), 'Ying Ru Lun', however those are loss of the record. 2. Qian Yi's 'Zhi Jue'("直訣") was influenced by 'Lu Xin Jing', yet if we compare the quality of 'Sheng Li, Byeng Li, Bang Jae'(生理, 病理, 方劑), 'Lu Xin Jing' cannot be the foundation of 'Zhi Jue'. He took over 'Nei Jing, Shang Han Lun, Jin Gui Yao Lue, Shen Long Ben Cao Jing, Tai Ping Sheng Hui Fang'("內經", "傷寒論", "金?要略", "神膿本草經", "太平聖惠方") and put them together to the direct clinical experiences of pediatrics. 3. There is no reference regarding the difficulties of pediatric diagnosis and diseases in 'Huang Di Nei Jing'("黃帝內經") Before 'Bei Song'(北宋), regardless of the lack of data related to pediatric diseases, 'Qian Yi' established the pediatric system in 'Xiao Er Yao Zheng Zhi Jue' for the first time. 4. In his diagnosis of the pediatric diseases, he 'Si Zhen He Can'(四診合參), also considered in the eye exam seriously. In addition, he closely combined 'Wu Zang Bian Zheng'(五臟辨證), and diagnosis the pediatric diseases. 5. 'Wu Zang Bian Zheng', what Qian established method was based on 'Zheng Ti Guan'(整體觀) in 'Huang Di Nei Jing'. It was based on clinical experiences and established the perspectives of 'Tian Ren Xiang Ying'(天人相應). First of all, he pinpointed 'Zhu Zheng'(主證) clearly. Secondly, he pinpointed the relationships to symptoms and then, he distinguished a generic character of 'Xu, Shi, Han, Re'(虛, 實, 寒, 熱). Finally, he made an induction from genealogical pediatric physiology. 6. 'Qian Yi' took a serious view of 'Ban Zhen'(斑疹), the inadequate field in those days. At that time, he criticized on the habituation of the misuse of medication. He treated separately which 'Ji Jing'(急驚) as 'Liang Xie'(凉瀉) and 'Man Jing'(慢驚) as 'Wen Bu'(溫補). He proposed 'Cong Gan Zhu Feng, Xin Zhu Jing'(從肝主風, 心主驚) theory and formulated 'Jing Feng'(驚風) theory as well. 7. As an opponent of a tendency to misusage of medicine, 'Qian Yi' made out a prescription with pliant medicine. He emphasized on the treatment to 'Gong Bu Shang Zheng, Bu Bu Zhi Xie, Xiao Bu Jian Shi'(攻不傷正, 補不滯邪, 消補兼施) because he had so lucid demonstration to 'Xu Shi Han Re'(虛實寒熱) of the five viscera in the field of 'Bang Yak'(方藥). 8. There were no pediatrics schools at that time, however, the pediatrics was being made up gradually by 'Jin Yuan Si Da Jia'(金元四大家) who was influenced by 'Qian Yi'. He raised an objection to medical treatment using pliant medicine. 'Qian Yi' applied 'Qu Xia'(驅下) treatment using 'Han Liang'(寒凉) medicine. 'Han Liang Pai'(寒凉派) is greatly influenced by Qian. 'Chen Wen Zhong'(陳文中) had a great impact on 'Han Liang Pai' who used a 'Zao Shu Wen Bu'(燥熟溫補) medicine for treatment. Since 'Song Jin'(宋金), he had a tremendous influence on pediatrics treating patients in both 'Han Wen'(寒溫) ways. 9. 'Qian Yi' had an influence on his medical thoughts on future generations, especially to 'Wan Quan'(萬全) of 'Ming Dai', 'Wu Tang'(吳塘) of 'Qing Dai'(淸代) and 'Yun Shu Jie'(?樹珏) of 'Min Guo'(民國). 'Wan Quan' is an advocate of 'You Yu, Bu Zu Zhi Shuo'(有餘, 不足之說)of 'Xiao Er Wu Zang'(小兒五臟) that he revealed Qian's 'Wu Zang Bian Zheng'(五臟辨證). 'Wu Tang' disclosed Qian's 'Xiao Er Ti Zhi Shuo'(小兒體質說) and 'Xiao Er Ke'(小兒科)'s 'Yong Yao Lun'(用藥論), therefore, he uncovered pediatric physiological characteristics through the advocate of Qian's 'Zang Fu Rou Ruo, Ji Gu Nen Qie, Yi Xu Yi Shi, Yi Han Yi Re' (臟腑柔弱, 肌骨嫩怯, 易虛易實, 易寒易熱). 'Yun Shu Jie' developed intrinsic relationships among time, symptom and 'Tian Ren Xiang Ying Guan'(天人相應觀), What 'Qian Yi' stated about them. And also, he developed Qian's 'Di Huang Wan'(地黃丸), 'Xie Qing Wan'(瀉靑丸), 'Yi Huang San'(益黃散) clinical usages as well. 10. Regarding Qian's 'Wu Zang Xu Shi'(五臟虛實), it has an influence on 'Zhang Yuan Su'(張元素)'s 'Zang Fu Bing Ji Bian Zheng'(臟腑病機辨證). 'Di Huang Wan', 'Xie Qing Wan', 'Xie Xin Tang'(瀉心湯), 'Yi Huang San', 'Xie Huang San'(瀉黃散) are the standard prescription of 'Wu Zang Bu Xie'(五臟補瀉). It is under the influence of Qian's treatment. Besides, 'Qian Yi' took a serious view of 'Xiao Er'(小兒)'s 'Pi Wei'(脾胃). 'Qian Yi' had an impact on 'Li Dong Yuan'(李東垣) one of the member of 'Bu Tu Pai'(補土派). 'Di Huang Wan', which placed great importance on 'Bu Yi Shen Yin'(補益腎陰), had a great impact on 'Da Bu Yin Wan'(大補陰丸) and 'Jin Yuan Si Da Jia' as well. 11. In a theory of Qian's 'Wu Zang Bian Zheng', though it had been stated clearly in 'Wu Zang Bian Zheng', but he neglected in 'Liu Fu Bian Zheng'(六腑辨證). In prescription field, The problem with the medicine is that it is either toxic or mineral, therefore, we are not able to use those medicine in a clinical testing at the present time.

• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.123-130
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• 2013

It is well known that SuanXue QiMeng has given the greatest contribution to the development of Chosun mathematics and that the topics and their presentation including TianYuanShu in the book have been one of the most important backbones in the developement. The purpose of this paper is to reveal that Zhu ShiJie emphasized decidedly mathematical structures in his SuanXue QiMeng, which in turn had a great influence to Chosun mathematicians' structural approaches to mathematics. Investigating structural approaches in Chinese mathematics books before SuanXue QiMeng, we conclude that Zhu's attitude to mathematical structures is much more developed than his precedent ones and that his mathematical structures are very close to the present ones.

• 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.14 no.4
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• pp.2577-2582
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• 2013

Objectives: Interleukin (IL) -10 is a potent cytokine with a dual ability to immunosuppress or immunostimulate. We aimed to explore the association of IL10 promoter polymorphisms with risk of gastric cancer (GC) in a Han population in Southwestern China. Methods: We enrolled 308 pairs of GC and control subjects from four hospitals and a community between October 2010 and August 2011 in a 1:1 matched case-control design. Demographic information was collected using a designed questionnaire. IL10-592 A>C and IL10-1082 A>G polymorphisms were determined by Sequenom MassARRAY analysis. Results: Patients with GC reported statistically higher proportions of family history of cancer (29.9% versus 10.7%, P<0.01) and alcohol drinking (54.6% versus 43.2%, P<0.01) than did controls. Similar results were observed in comparison between non-cardia GC patients and controls (P<0.01 and P=0.03). Variant genotypes of IL10-592 A>C and IL10-1082 A>G were not associated with overall GC risk (adjusted OR, 0.94, 95% CI, 0.66-1.33; adjusted OR, 1.00, 95% CI, 0.62-1.60). Sub-analysis showed that the IL10-592 AC/CC variant genotype was associated with decreased non-cardia GC risk (adjusted OR, 0.58; 95% CI, 0.36-0.95). No association was found between any of the IL10 haplotypes established from two polymorphisms and risk of non-cardia GC. Conclusions: In conclusion, our data do not link the two SNPs of IL10-592 and IL10-1082 with overall GC risk. We demonstrate that IL10-592 polymorphism is associated with protective effect against non-cardia GC. Our findings may offer insight into risk associated with the development of GC in this region.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.11
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• pp.5637-5642
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• 2012

Objective: Gastric cancer (GC) is one of the most common malignancies and its mortality ranks third among all cancers in China. We previously noted that XRCC1 Arg194Trp was associated with GC risk in Western China in a study on XRCC1 Arg194Trp and ADPRT Val762Ala. We aimed to further explore the association of these polymorphisms with risk of the noncardia subtype. Methods: We enrolled 176 noncardia GC patients and 308 controls from four hospitals and a community between October 2010 and August 2011. Genotyping was performed in a 384-well plate format on the Sequenom MassARRAY platform. A self-designed questionnaire was utilized to collect epidemiological data from the subjects regarding demographic factors and potential risk factors. Results: Subjects were aged $56.8{\pm}11.8$ (mean ${\pm}$ standard deviation) and $57.6{\pm}11.1$ years in the case and control groups, respectively. Individuals carrying the XRCC1 Trp/Trp or Arg/Trp variant genotype were at significantly increased risk of noncardia GC (adjusted OR, 1.48; 95% CI, 1.00-2.17), after adjustment for family history of cancer, drinking, and smoking. The increased risk of XRCC1 Arg194Trp variant genotype was more pronounced among subjects below 60 years old (adjusted OR, 1.78; 95% CI, 1.07-2.96), compared to older individuals. ADPRT Val762Ala variants (Ala/Ala or Val/Ala) were not associated with noncardia GC (adjusted OR, 1.03; 95% CI, 0.69-1.54). Conclusions: Our study suggests that XRCC1 Arg194Trp is a genetic susceptibility factor for developing noncardia GC in Han Chinese in Western China. In particular, individuals with the XRCC1 Arg194Trp variant genotype are at increased risk for GC below 60 years old.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.2139-2144
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• 2012

Objective: Gastric cancer remains a major health problem in China. We hypothesized that XRCC1 Arg194Trp and ADPRT Val762Ala may be associated with risk. Methods: We designed a multicenter 1:1 matched case-control study of 307 pairs of gastric cancers and controls between October 2010 and August 2011. XRCC1 Arg194Trp and ADPRT Val762Ala were sequenced, and demographic data as well as lifestyle factors were collected using a self-designed questionnaire. Results: Individuals carrying XRCC1 Trp/Trp or Arg/Trp variant genotype had a significantly increased risk of gastric cancer (OR, 1.718; 95% CI, 1.190-2.479), while the OR for ADPRT Val762Ala variant genotype (Ala/Ala or Val/Ala) was 1.175 (95% CI, 0.796-1.737). No gene-gene or gene-environment interactions were found. In addition, family history of cancer and drinkers proportion were higher among cases than among controls (P<0.05). Conclusions: XRCC1 194 Arg/Trp or Trp/Trp genotype, family history of cancer, and drinking are suspected risk factors of gastric cancer from our study. Our findings may offer insight into further similar large gene-environment and gene-gene studies in this region.

• Journal of Korean Medical classics
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• v.19 no.1 s.32
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• pp.26-40
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• 2006

It is generally understood that San Bu Jiu Hou is the pulse form at CunGuanChi(寸關尺) as in ${\ulcorner}$NanJing(難經)${\lrcorner}$. However, it is totally different in ${\ulcorner}$HuangDiNeiJing${\lrcorner}$. This only appears in tew chapters of ${\ulcorner}$SuWen(素問)${\lrcorner}$ and does not appear in ${\ulcorner}$LingShu(靈樞)${\lrcorner}$. SanBu in ${\ulcorner}$SuWen SanBuJiuHouLun${\lrcorner}$ refers to top, middle, bottom and each part is divided into 3 parts, Tian(天), Di(地), Ren(人) to form JiuHou, and through Jiu Hou, not only does it diagnose ShenZang(神臟) and XingZang(形臟), but also goes on to form a diagnostic system by fusing diagnostic skill and treatment into one. ${\ulcorner}$JiuZhenShiErYuan(九針十二原)${\lrcorner}$ discusses detailed shapes and functions of nine types of acupuncture, and the ${\ulcorner}$GuanZhen(官針)${\lrcorner}$ explains how to manipulate Jiu Zhen adequately, but there is more to it than just shape and function in techniques of acupuncture. It is because it fuses (or merges) pathology, diagnostics, treatment etc to form a single diagnosis system. ${\ulcorner}$JinFu(禁服)${\lrcorner}$ discusses about nine types of acupuncture of pulse form and effect, which are treatment means based on RenYingCunKouMaiFa(人迎寸口脈法). Various pulse daignosises exist in ${\ulcorner}$HuangDiNeiJing${\lrcorner}$, but those influence of future generations can be divided into SanBuJiuHouMaiFa(三部九候脈法) and RenYingCunKouMaiFa(人迎寸口脈法), and which medical ideologies this kind of pulse daignosis originates from should be discusssed. We will finally expolre and report the process its development into 寸尺脈(Cun Chi Mai).