• Honam Mathematical Journal
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• v.30 no.4
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• pp.733-741
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• 2008

Let T be Gauss transformation on the unit interval defined by T (x) = ${\frac{1}{x}}$ where {x} is the fractional part of x. Gauss transformation is closely related to the continued fraction expansions of real numbers. We show that almost every x is mod M normal number of Gauss transformation with respect to intervals whose endpoints are rational or quadratic irrational. Its connection to Central Limit Theorem is also shown.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.23-32
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• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.

• Proceedings of the Korea Information Processing Society Conference
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• 2012.11a
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• pp.990-993
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• 2012

SCADA(Supervisory Control and Data Acquisition) 시스템은 국가중요기반망인 전력, 가스 등을 제어하기 위해 사용되어 왔다. 최근에는 기존의 폐쇄적인 통신 환경과 달리 외부망과 연결된 개방 통신 환경을 사용함에 따라 안전한 통신을 위한 암호화 기술이 연구되고 있다. 기존 시스템에 적용되고 있는 프로토콜들은 공유키를 갱신하기 위해 수동적으로 설정해야했다. 본 논문에서는 SCADA 시스템을 구성하는 Server와 RTU가 상호 인증하여 무리수 기반의 스트림 암호화 통신과 타임스탬프를 이용한 키 갱신 프로토콜을 제시하여 재사용공격과 가장공격이 불가능한 실시간 암호화통신 프로토콜을 연구하였다.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.985-1000
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• 2019

Let k be an integer with $k{\geq}3$. Define $h(k)=[{\frac{k+1}{2}}]$, ${\sigma}(k)={\min}\(2^{h(k)-1},\;{\frac{1}{2}}h(k)(h(k)+1)\)$. Suppose that ${\lambda}_1,{\ldots},{\lambda}_5$ are non-zero real numbers, not all of the same sign, satisfying that ${\frac{{\lambda}_1}{{\lambda}_2}}$ is irrational. Then for any given real number ${\eta}$ and ${\varepsilon}>0$, the inequality $${\mid}{\lambda}_1p^2_1+{\lambda}_2p^2_2+{\lambda}_3p^2_3+{\lambda}_4p^2_4+{\lambda}_5p^k_5+{\eta}{\mid}<({\max_{1{\leq}j{\leq}5}}p_j)^{-{\frac{3}{20{\sigma}(k)}}+{\varepsilon}}$$ has infinitely many solutions in prime variables $p_1,{\ldots},p_5$. This gives an improvement of the recent results.

• Journal for History of Mathematics
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• v.25 no.3
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• pp.1-14
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• 2012

Since JiuZhang SuanShu(九章算術), the basic field of the traditional mathemtics in Eastern Asia is the field of rational numbers and hence irrational solutions of equations should be replaced by rational approximations. Thus approximate solutions of equations became a very important subject in theory of equations. We first investigate the history of approximate solutions in Chinese sources and then compare them with those in Chosun mathematics. The theory of approximate solutions in Chosun has been established in SanHakWonBon(算學原本) written by Park Yul(1621 - 1668) and JuSeoGwanGyun(籌書管見, 1718) by Cho Tae Gu(趙泰耉, 1660-1723). We show that unlike the Chinese counterpart, Park and Cho were concerned with errors of approximate solutions and tried to find better approximate solutions.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.5
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• pp.61-69
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• 2017

The study on interference channel is very important information theoretically and many studies have been done on it. However, even in the simplest case, even in the case of two user interfering channels, the channel capacity is not yet known except in special cases. Recently, research on the multiplexing gain that shows the tendency of the transmission rate in the high signal to noise ratio (SNR) band has been actively carried out, instead of accurately grasping the channel capacity. Obtaining optimal multiplexing gain can reveal trends in channel capacity at high signal-to-noise ratio bands. In an interfering channel with two users, the best multiplexing gain can be obtained by eliminating the interference. However, recent research shows that when the number of users is more than three, the optimal multiplexing gain can not be obtained only by zero forcing and a new technique called interference sorting is needed. There are two types of interference sorting techniques. Beamforming A method of effectively separating signals and interference by properly selecting matrices and constructing structured codes using rational numbers and irrational numbers. The interference alignment technique can achieve optimal multiplexing gain in various environments such as interference channel, X channel, compound broadcast channel, and multi hop network for multi source multi destination. In recent years, it has also been applied to distributed storage. Lee et al., "Lattice Code Interference Alignment in Cooperative Multipoint Transmission (COMP) for Interference Channels of Three Users", Journal of the Institute of Electronics Engineers, vol.49-TC,no.6,2012. In this paper, the DoF of delayed channel information is obtained.

• Proceedings of the Korean Society of Crop Science Conference
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• 2017.06a
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• pp.7-7
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• 2017

Unfavorable weather and soil conditions reduce rice yield and land and water productivity, aggravating existing encounters of poverty and food insecurity. These conditions are foreseen to worsen with climate change and with the unceasing irrational human practices that progressively debilitate productivity despite global appeals for more food. Our understanding of plant responses to abiotic stresses is advancing and is complex, involving numerous critical processes - each controlled by several genetic factors. Knowledge of the physiological and molecular mechanisms involved in signaling, response and adaptation, and in some cases the genes involved, is advancing. Moreover, the genetic diversity being unveiled within cultivated rice and its wild relatives is providing ample resources for trait and gene discovery, and this is being scouted for rice improvement using modern genomics and molecular tools. Development of stress tolerant varieties is now being fast-tracked through the use of DNA markers and advanced breeding strategies. Large numbers of drought, submergence and salt tolerant varieties were commercialized over recent years in South and Southeast Asia and more recently in Africa. These varieties are making significant changes in less favorable areas, transforming lives of smallholder farmers - progress considered incredulous in the past. The stress tolerant varieties are providing assurance to farmers to invest in better management of their crops and the ability to adjust their cropping systems for even higher productivity and more income, sparking changes analogous to that of the first green revolution, which previously benefited only favorable irrigated and rainfed areas. New breeding tools using markers for multiple stresses made it possible to develop more resilient, higher yielding varieties to replace the aging and obsolete varieties still dominating these areas. Varieties with multiple stress tolerances are now becoming available, providing even better security for farmers and lessening their production risks even in areas affected by complex and overlapping stresses. The progress made in these less favorable areas triggered numerous favorable changes at the national and regional levels in several countries in Asia, including adjusting breeding and dissemination strategies to accelerate outreach and enabling changes at higher policy levels, creating a positive environment for faster progress. Exploiting the potential of these less productive areas for food production is inevitable, to meet the escalating global needs for more food and sustained production systems, at times when national resources are shrinking while demand for food is mounting. However, the success in these areas requires concerted efforts to make use of existing genetic resources for crop improvement and establishing effective evaluation networks, seed production systems, and seed delivery systems to ensure faster outreach and transformation.

• Journal of the Korean Society for Library and Information Science
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• v.24
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• pp.9-51
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• 1993

The purpose of this study is twofold: to investigate into general characteristics of the abstracting services in Korea and to discuss general directions of development of the abstracting services in the country. This study is designed to achieve the purpose by gathering and analysing data related to the abstracting journals published in the past ten years and by comparing the results with similar data gathered by the investigator in 1984. The major conclusions made in this study is summarised as follows. (1) Researchers and professionals working in limited numbers of subject fields are benefited by abstracting services of recent achievements in research and development in Korea. Those in most of the fields have essentially no abstracting services of such achievements. Even many researchers and professionals in the limited numbers of the fields that have some elementary abstracting services are not informed of research results in their fields because the abstracting journals are scattered in many narrow subjects and in many cases, the abstracting journals only cover publications in some specific forms and kinds. (2) Abstracting journals of general subjects, which are supposed to be of more or less help to the researchers in the subject fields that have no abstracting journals of their own, have rapidly increased in number in the past ten years. Most of such abstracting journals carry thesis and dissertation abstracts, and the rest those of research papers published in specific places, in specific forms, by specific institutes, and of reports of research projects sponsored by specific foundations. These abstracting journals are not of the kind that comprehensively provide general readers with current awareness of publications of research results in Korea. (3) Most of the abstracting journals existing in Korea are published by institutions of higher education and research institutes, and the rest by commercial publishers, industrial firms, libraries, information centers, government agencies, research foundations, learned societies, etc. Those which publish many titles are small in number and those publish one or two titles are large in number. The former is largely made up of institutions of higher education and research institutes. (4) Ten years ago, there was not a single publishing house that produced abstracting journals. Three commercial publishing houses now produce abstracting journals. As this change occurs, centers of excellence are founded and competitive elements are introduced in abstracting services. This change, in turn, is expected to improve quality of the other abstracting journals in Korea. (5) The abstracting journals published in Korea are classified by type into those of dissertations, research papers, journal articles, patent specifications in that descending order. The fact that Master's and doctoral dissertation abstracts are dominating in Korea is due to the irrational practice of publishing those abstracts at many institutions. (6) Most of the abstracting journals existing in Korea are published by national or government-supported research institutes in order to publicise their own research outputs. Their coverage of literature is normally narrow, and naturally their value to users is limited. (7) The abstracting journals published in Korea increased in number at the rate of $77.8-100\%$ every five years in the past twenty-five years. Most of the abstracting journals that ceased to be published during the period survived for two years. (8) Korean is the desirable language for the abstracting journals designed to be distributed within Korea. About half of the abstracting journals published in Korea is printed in Korean and the other half in foreign languages, and in Korean with foreign languages. All the abstracting journals in foreign languages are printed in English xcept one, which is printed in Japanese. (9) Some twenty percent of the abstracting journals in Korea is published monthly, bimonthly, and quarterly. Others are published annually, biannually, and irregularly. The latter may not function properly as a current-awareness tool due to long intervals between their issues. It is particularly undesirable that about half of the abstracting journals in Korea is published irregularly. Most of the abstracting journals published in Korea are distributed freely to individuals and institutions selected by the publishers. (10) The abstracting journals published by the use of computers increased drastically in the past ten years. The abstracting journals produced by the conventional type-setting method will probably disappear In Korea in another ten years to come. Automation of the production of abstracting journals does not simply mean technical, economic improvement of publishing processes but availability of machine-readable databases that can be used for other purposes, including the generation of other publications and the provision of machine literature searching capabilities. Necessary steps should be taken for this important development that is occurring in the abstracting services in Korea.