$\Theta$-Derivations on Prime Rings

Kyoo-Hong Park,Yong-Soo Jung 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.12 No.1-2

In this paper we show the following: Let R be a prime ring (withcharacteristic dierent wo) and a ∈R. Let Θ, :R → R be automorphisms andletd :R → R be a nonzero Θ-derivation. (iif [d(x), a]Θ = 0 (or d([x, a]) = 0 )for all x ∈R, then a + (a) ∈Z, the center ofR, (iiif .d(x), a. = 0 for allx ∈R, then d(a) = 0. (iiiif [ ad(x), x] = 0 for all x ∈R, then eithera = 0 o rR is commutative.AMS Mathematics Subject Classication : 16W25, 16W20, 16U80Key words and phrases : Prime ring, Θ-derivation1. IntroductionThroughout this paper,R will represent an associative ring andZ will be itscenter. Letx,y∈R. The commutatorxy yx will be denoted by [x, y] and theproductxy+ yx by .x, y.. Let:R → R be an automorphism. We write [x, y]forxy (y)x, and will make extensive use of the following basic commutatoridentities: [xy, z] = x[y, z] + [x, z]y, [xy, z] = x[y, z]+ [x, (z)]y =x[y, z]+[x, z]y, [x, yz]=[x, y]z + (y)[x, z].Let Θ :R → R be an automorphism. An additive mapping d :R → R iscalled a Θ-derivation ifd(xy)=d(x)y ( x)d(y) for all x, y∈R.A 1-derivation is called simply a derivation, where 1 :R → R is the identitymap. A derivationd is inner if there exists ana ∈R such thatd(x)=[x, a] forall x ∈R.LetR be a prime ring with characteristic dierent wo andd : R → R anonzero derivation. In [1], I. N. Herstein proved that ifa ∈R and [d(x), a]=0Received July 10, 2002. Revised January 23, 2003This work was done under the support of Seowon University Research Fund 2002.c. 2003 Korean Society for Computational & Applied Mathematics.313314 Kyoo-Hong Park and Yong-Soo Jungfor allx ∈R, thena ∈Z. As a continuation of our earlier works for derivations([2], [3]), we here improve the above result and obtain some analogous results.

중ㆍ고등학생들의 수학교과 호오도(好惡度)의 변화에 대한 분석

박규홍,박기양,김영국,박윤범,박혜숙,임재훈 서원대학교 교육대학원 2000 교육논총 Vol.4 No.-

In this paper we investigate and analyze the variation of secondary school student's like and dislike the school mathematics lesson. First, we investigate the reason that why students dislike mathematics in the class and we search the point of time when the students dislike mathematics in the class. Next, we investigate and analyze the variation of student's inclination to the school mathematics lesson. In this research we try the followings. 1) We analyze the variation of each level school, student's inclination to the school mathematics class, 2) We analyze the variation of student's inclination to the mathematics for each place where the school located. 3) We analyze and compare between the inclination to the mathematics lesson and to each level school. 4) We analyze and compare between the inclination to the mathematics lesson and to each factors of student's inclination From these investigation and analysis, we have the following conclusion . (1) The student's inclination to the mathematics is depend on the teacher's teaching method and on the fact that how can the mathematics lesson be composed easily. (2) The student's response was seen in the same type from the inquiry about the inclination to the mathematics lesson in the school of Seoul and small country town. This is a passing phase caused by the educational environment in Seoul and the small country town's schools is better than that of the big city or medium city. (3) The student group of the human knowledge in the general high school show the negative response for the inclination to the matheirlatics lessen compare to that of the student group of natural science in the general high school. (4) In the middle school, about half of the students dislike mathematics But such dislike rate of mathematics increased in the high school. (5) Teachers must take into consideration to the student in the first grade high school mathematics course To do this, teachers make adapt the curriculum easily for the student and must teach the mathematics to the students who can take interest in the mathematics.

좌심실 수축기 기능장애를 동반한 양수색전증 1예

박대균,홍경순,두영철,한규록,오동진,유규형,임종윤,고영박,이광학,이영,송원근,김현태 대한순환기학회 1999 Korean Circulation Journal Vol.29 No.8

제 7 차 교육과정 고등학교 수학 Ⅰ과정에서의 ICT 활용 학습과정안 개발

박규홍 서원대학교 교육대학원 2003 교육논총 Vol.7 No.-

In this paper we study on the development of teaching-plan by using ICT (information & communication technology) application method in Mathematics 1 course of the 7th national high school curriculum. The teaching method of ICT application is one of priority item in the 7th national educational curriculum. For this study, we survey the recent preceding researches on the practical using of ICT in the school mathmatics. Next, we study on the composite and drawing the teaching plan by using ICT application in Mathematics 1 course which will carry out from 2003 school year. It is concluded that we must consider the following items to composite and drawing the teaching plan by using ICT application in Mathematics 1 course. First, we can find that it is difficult to apply the ICT in Mathematics 1 course of high school for the reason of a special quality of Mathematics 1. But it is one of the good choice to apply the ICT at the 1st lesson time of each chapter respectively. Second, teachers have to consider to the point that many internet sites are easily rise and fall, so teachers must search the adequate sites for the corresponding lessons continuously. Third, teaching plan by using ICT application must be prepared not formally but substantially. Fourth, the references on the 7th educational curriculum are shortage now, teachers must use and update that of the various 6th educational curriculum. Fifth, the ability of computer operating is not difficult, so the senior or the computer illiteracy teachers are able to learn such operating ability easily. The senior or computer illiteracy teachers must learn the opreation ability of computer and internet. It is very important to use the ICT application method for the teachers and students now. Sixth, many of the internet sites are very poor or not freeware, so the concerned authorities must support the teachers and school for the effective education to use the teachins method of ICT application. Seventh, the Mathematic 1 course is very difficult, so the ICT application method is regarded useless method in the lesson. But since we can find the mathematical conceive at the practical life or around us, such method can arouse the students' internet. Eighth, teachers must develope the teaching plan by using ICT application method continuously for the prosperity of the 7th national educational curriculum.

蘇聯의 아시아 集團安保協力體制의 構想과 戰略

朴弘圭 단국대학교 미소연구소 1990 미소연구 Vol.4 No.-

Under Mikhail Gorbachev the Soviet Union has been taking steps to reshape her own economic structure for the better productivity and to improve her bilateral relations with capitalist countries for the better international environment. The tight state control on the Soviet economy and society has been greatly reduced and a number of drastic diplomatic initiatives taken to promote cooperation with former adversaries of the West: Behind all these steps, a set of new concepts such as 'perestroika', 'glasnost' and 'new thinking foreign policy' has been operating. The recent Moscow's proposal made at the international conference held in Vladivostok on September 10, 1990 is one of those steps. In that proposal the foreign minister of the Soviet Union stressed again the significance of those new concepts and put emphasis on humanism and peace in the forthcoming era. In so doing, he expressed his country's willingness to play an active role in Asia and suggested an international forum to be held whereby all Asian countries can participate in a discussion to resolve regional tensions and advance multilateral cooperation in various fields. Needless to say, this proposal is not a new one. It is rather another version of a series of previous proposals whose main objective is to set up an Asian version of CSCE which has been instrumental in reducing tensions in Europe and promoting East-West European cooperation. As European experiences have clearly demonstrated, CSCE proved to be an effective mechanism through which such complicated issues as human rights, confidence building measures and economic cooperation could be dealt with multilaterally and collectively. Since the United States has been taking position that the European experiences can not be duplicated in Asia due to the present security arrangements and the complex nature of the bilateral relations among the nations in the region, the prospect for 'all-Asian forum' is not bright in the near future. However, growing number of Asia-Pacific nations who pay more attention to Moscow's proposal and the Soviet willingness to make more concession in the region imply that some kind of regional mechanism for security and cooperation may not be impossible after all. The Republic of Korea who is now trying to incorporate Korean peace structure within the framework of Northeast Asian peace structure should look into the changing foreign policies of the regional powers in Northeast Asia and also be prepared to play an active role in the regional politics of Asia.

數學科 敎授法에 關한 一硏究 : 高等學校의 統計單元을 中心으로

朴圭弘 서원대학교 교육연구소 1986 敎育發展 Vol.5 No.1

This thesis aims to find out the effective teaching method of statistics unit in high school mathematics curriculum. First we search the object of study by analysing the teaching aims in the curriculum. Second we deal with the methodology of teaching the statistics in high school, the problems from the view point of teaching method, and the case study. This thesis also contains the structural teaching models of statistics unit in high school mathematics. Attaching importance to the logical and systematic properties of mathematics we analyse some theories with which can be dealt carelessly and present the direction of the mathematics teaching which can lead to the interesting and effective method. Lastly the writer come to discusses about the basic attitude of mathematics teachers in high school class room.

오염토양 정화를 위한 계면활성제 선정기법에 관한 연구

박규홍,이재원 中央大學校 建設環境硏究所 1997 環境科學硏究 Vol.8 No.-

The screening test was performed to select the proper surfactant and various operation conditions in applying surfactant flushing to in-situ remediation. Contaminants to be removed were B.T.E.X(Benzene, Toluene, Ethylbenzene. p-Xylene, m-Xylene, o-Xylene) and anionic SDS(Sodium Dodecyl Sulfate), nonionic NEODOLⓡ 25-3, and nonionic SOFTANOLⓡ -90 were used as surfactants. Various experiments including CMC(Critical Micelle Concentration) test MSR(Molar Solubilization Ratio) test, solubility test, sorption test of B.T.E.X, sorption test of surfactant, and permeability test were conducted to optimize treatment condition which are applicable to in-situ remediation salinity control or electrolyte control using ethyl alcohol, hydrotrope, and electrolyte solution was also manipulated. Several properties of aqueous solutions of the surfactants and additives were used in evaluating their suitability. As a result, the main factors for the improvement of the removal efficiency were the retention time and permeability between organic contaminants and flushing solution.

민감도분석을 利用한 흡착전처리 UF공정에서의 입자거동에 관한 硏究

박규홍,김성순,이 웅 中央大學校 建設環境硏究所 1997 環境科學硏究 Vol.8 No.-

To minimize fouling in ultrafilitration process, pretreatment such as coagulation, ozone, or activated-carbon is required. In this study, activated carbon adsorption was applied as pretreatment to UF process. Batch experiments were conducted to test the performance of ultrafiltration following activated carbon adsorption. The model of particle trajectory was used to compare with the experimental results. Sensitivity analysis was also performed to predict the better operation conditions in adsorption and ultrafiltration. Sensitivity analysis showed that the linear velocity was one of the main factors to maintain the high permeate flux in the pretreatment process using activated carbon. Fouling would be efficiently decreased by the active lateral-migration of suspended particles when the linear velocity of higher than 80cm/sec was used.

오존을 이용한 염색폐수처리에 관한 연구

박규홍,이상수,정근진 中央大學校 建設環境硏究所 1999 環境科學硏究 Vol.9 No.2

Ozone has a strong oxidized capacity next to fluorine, so it is used for oxidized dissolution of organism, decoloration, deodorization, fumigation, etc., regarding to water. In this study dye wastewater was treated strongly with ozone at 100g/hr and the flow rate through ozone contact tank was adjusted to 2l/min The experiment was conducted at three different conditions. In the first place, effluent and raw wastewater was ozonized and secondly raw wastewater was treated using AlCl₃ and PAC coagulation. The third condition was post-ozone treatment following PAC coagulation. As a result, pre-ozone treatment process with PAC coagulation and post-ozone treatment showed more efficient effluent quality than the previous conventional process.

數學敎育의 새 方向에 關한 硏究

朴圭弘,金永國 西原大學校 1989 西原大學 論文集 Vol.24 No.-

Many research have been done on New Math. movement and its results. In this paper, we looked into current trends of mathematics education since the late 1960's New Math. movements. And in regard to this, we recommand that the followings should be the core of our future mathematics education. A)In mathematics education emphasis must be put on development of students' ability of mathematical thinking and formation of systematic, logical and rational character. B)Learning mathematics must be 0f help in various ways to students to live a successful life in the future. C)By lessening too severe logical exactness to some extent, in the realm of systematical unity, the secondary school mathematics should be of something that is more easy of access. D)Since the current high school enterance examination system in large city caused many unfavorable impact on secondary school mathematics, more various curriculum should be offered. E)To cope with development of mathematics education, more chances of teacher training and meetings such as seminar, mathematics education study group and mathematic teachers association should be given. F)Computer is an important element which must be took into account in mathematics education.