• Proceedings of the Korean Society for History of Mathematics Conference
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• 2003.11a
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• pp.10.1-10.1
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• 2003

• Journal for History of Mathematics
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• v.23 no.4
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• pp.1-15
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• 2010

We study the thought of numerical theory of $Sh\grave{a}o$ $K\bar{a}ngji\acute{e}$. He explained the change of universe and everything in his theoretical system in tradition of . It is contained in his . We conjecture that this book influenced . Choi Suk Jung tried to embody the ideas of $Sh\grave{a}o$ $K\bar{a}ngji\acute{e}$ in .

• Journal for History of Mathematics
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• v.24 no.4
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• pp.1-6
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• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• 월간 기계설비
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• no.4 s.189
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• pp.46-52
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• 2006

한국종합건설기계설비협의회(회장 이진호)가 국내 주요 건설사의 시공오류 발생사례와 해결방안에 대한 자료를 광범위하게 수집하여 2년 여에 걸친 작업 끝에 설비시공개선 사례집을 발간했다. 이 책은 설비시공에 있어 공통적으로 발생될 수 있는 중요한 시공오류를 각 공종별로 편집하여 수록함은 물론 필요한 부분은 해설을 추가하므로써 설비인들이 보다 알기쉽고 상세하게 접근하도록 했다. 본지는 앞으로 회원사의 시공에 도움이 될 수 있도록 이 책에 수론된 시공개선사례를 게재하고 있다.

• Korean Journal of Logic
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• v.8 no.2
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• pp.3-32
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• 2005

Hilbert's rational ambition to establish consistency in Number theory and mathematics in general was frustrated by the fact that the statement itself claiming consistency is undecidable within its formal system by $G\ddot{o}del's$ second theorem. Hilbert's optimism that a mathematician should not say "Ignorabimus" ("We don't know") in any mathematical problem also collapses, due to the presence of a undecidable statement that is neither provable nor refutable. The failure of his program receives more shock, because his system excludes any ambiguity and is based on only mechanical operations concerning signs and strings of signs. Above all, $G\ddot{o}del's$ theorem demonstrates the limits of formalization. Now, the notion of provability in the dimension of syntax comes to have priority over that of semantic truth in mathematics. In spite of his failure, the notion of algorithm(mechanical processe) made a direct contribution to the emergence of programming languages. Consequently, we believe that his program is failure, but a great one.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.2
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• pp.49-54
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• 2005

This Paper Presents a non-blocking deadlock detection scheme with immediate cycle detection in multiprocessing systems. We assume an expedient state and a special case where each type of resource has one unit and each request is limited to one resource unit at a time. Unlike the previous deadlock detection schemes, this new method takes O(1) time for detecting a cycle and O(n+m) time for blocking or handling resource release where n and m are the number of processes and that of resources in the system. The deadlock detection latency is thus minimized and is constant regardless of n and m. However, in a multiprocessing system, the operating system can handle the blocking or release on-the-fly running on a separate processor, thus not interfering with user process execution. To some applications where deadlock is concerned, a predictable and zero-latency deadlock detection scheme could be very useful.

• Journal of KIISE:Computing Practices and Letters
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• v.10 no.6
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• pp.507-513
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• 2004

In this paper, we consider the methodology of efficient resource usage, specially web clustering system. We develope an algorithm that distributes the load on the web cluster system to use the system resources, such as system memory equally. The response time is chosen as a performance measure on the various clustering models. And based on the concurrent user to the web cluster system, the response time is also examined as the number of users increases. Simulation experience with this algorithm shows that the response time seems to have a good results compare to those with the other algorithm. And, also the effectiveness of clustered system becomes better as long as the number of concurrent user increases. The usage of developed algorithm is more useful when the system consists of many different sub-systems, a heterogeneous clustering system.

• 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.22 no.3
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• pp.1-30
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• 2009

Frege's logicism has been frequently regarded as a development in number theory which succeeded to the so called arithmetization of analysis in the late 19th century. But it is not easy for us to accept this opinion if we carefully examine his actual works on real analysis. So it has been often argued that his logicism was just a philosophical program which had not contact with any contemporary mathematical practices. In this paper I will show that these two opinions are all ill-founded ones which are due to the misunderstanding of the theoretical place of Frege's logicism in the context of contemporary mathematical practices. Firstly, I will carefully examine Cantorian definition of real numbers and Frege's critiques of it. On the basis of this, I will show that Frege's aim was to produce the purely logical definition of ratios of quantities. Secondly, I will consider the mathematical background of Frege's logicism. On the basis of this, I will show that his standpoint in real analysis was much subtler than what we used to expect. On the one hand, unlike Weierstrass and Cantor, Frege wanted to get such real analysis that could be universally applicable. On the other hand, unlike most mathematicians who insisted on the traditional conceptions, he would not depend upon any geometrical considerations in establishing real analysis. Thirdly, I will argue that Frege regarded these two aspects - the independence from geometry and the universal applicability - as those which characterized logic itself and, by logicism, arithmetic itself. And I will show that his conception of real numbers as ratios of quantities stemmed from his methodological maxim according to which the nature of numbers should be explained by the common roles they played in various contexts to which they applied, and that he thought that the universal applicability of numbers could not be adequately explicated without such an explanation.