$\Theta$-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.

한국 성인을 대상으로 한 전산화 Standard Progressive Matrices의 표준화 예비연구

홍경수,이민수,오병훈,하규섭,유한익,이창욱,연병길,김성윤,신민섭,김재진,권준수 大韓神經精神醫學會 1999 신경정신의학 Vol.38 No.5

연구목적 : 전산화 Standard Progressive Matrices(SPM) 검사의 한국인 성인 표준자료를 확립함으로써, 간이로 지능을 평가하는 경우에도 보다 정확하게 지능지수를 추정하기 위해서 본 연구를 수행하였다. 방 법 : 18세 이상의 남녀 정상인 자원자 353명을 대상으로 전산화 SPM 검사를 시행하고, 백분율 및 표준점수(T-점수)를 기준으로 하여 표준화 자료를 작성하였다. 전체 대상군을 성별, 연령별로 구분한 후 평균과·분포가 유사한 집단은 군을 합치는 방법을 사용하였다. 한국인 표준자료에 근거하여 추정한 SPM 지능지수와 외국인 표준자료에 근거하여 추정한 SPM 지능지수를 각각 KWAIS 지능지수와 비교함으로써 타당도를 검증하였다. 결 과 : 18∼30세, 31∼40세, 41∼50세, 51세 이상의 연령군으로 구분된 한국 정상 성인의 SPM 표준화 자료를 산출하였다. 본 연구 결과에 의한 표준화 자료를 적용하여 지능지수를 추정하는 것이 현재 사용하고 있는 외국인의 표준화 자료를 이용하는 것보다 KWAIS 지능지수에 더욱 근접한 결과를 보였다. 결 론 : 18세에서 50세까지의 한국인 남녀에게는 간이지능평가도구로서 전산화 SPM 검사의 한국인 표준화 자료를 유용하고 타당하게 적용할 수 있음을 확인하였다. Objectives : We conducted this study to provide standardized data of the computerized Standard Progressive Matrices(SPM) test in Korean adults. Methods : The computerized SPM test was administered to 353 healthy volunteers aged 18 years over. We provided the standardized data(percentile and standardized T-scores) for the groups with similar mean and distribution of SPM scores, which was originally divided by age and sex. The validity of the new standardized data was tested by comparing IQs estimated by SPM and K-WAIS. Results : The standardized SPM data were provided for four age groups : 18 to 30 years, 31 to 40 years, 41 to 50 years, 51 years and over. IQ estimated by this standardized data tends to be closer to IQ by K-WAIS than the IQ estimated by foreign normative data. Conclusion : The standardized data of the computerized SPM were proven to be a useful and valid tool for measuring IQ briefly, compared with the conventional way of measuring IQ.

力動的 總評이 數學態度 및 數學成就에 미치는 效果分析

卞烘圭,閔丙德 全北大學校 敎育大學院 1997 敎育論叢 Vol.17 No.-

This study is aimed at examining the effects of the dynamic assessment on the mathematics attitude and achievement. Forty senior high school students were assigned to the two conditions of experiment: dynamic assessment (N=20) and traditional evaluation (N=20). The experiment was conducted by dynamic assessment such as writing essays, conducting experiments, providing written answers to problems or preparing portfolios. The results obtained from this experiment were as follows: First, the dynamic assessment showed a higher positive attitude on mathematics learning than the traditional evaluation. Second, the dynamic assessment showed a critically higher achievement on mathematics learning. A conclusion derived here is that the dynamic assessment is definitely a strong factor to bring higher cognitive skills, and thus an integrated instruction and assessment in mathematics must be encouraged.

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.

디밍 안정기를 이용한 형광등의 퍼지 제어기 설계

崔洪圭,全光鎬,姜太垠,崔琁雄 홍익대학교 산업기술연구소 1997 産業技術 Vol.7 No.-

This paper proposes Dimming Ballast illumination control method using fuzzy reasoning the proposed method has the following effects. First the power saving above 50% is accompanied by the automatic control of the illumination and the choice of a turn-on or -off of a fluorescent lamps that is accompanied by the number of person and working time and weather Second the maintainment of the best illumination in spite of time and weather variation. Third More simple establishment and low than BAS(Building Automation System) because need not main control unit or communication cable

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.

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.

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.

大學綜合試驗 出題에 關한 硏究

卞烘圭,吳鎭坤,申鎔鎭,金泳喆,鄭求福,柳哲鍾,洪允杓 全北大學校 1977 論文集 Vol.19 No.-

The Comprehensive Examination for the undergraduate students is planned to adopt the Jeonbug National University for the purpose of enhancing the quality of its educational outputs. In order to effectively measure and evaluate the level of student progress toward the minimun standard as the students who have finished their general education and basic education for their major field study, the university has decided to make an item pool related to the subjects for the examination. This study is an attempt to make good items of five required courses among general education subjects which are Korean Language, English, Korean History, National Ethics. and Natural Science and are expected to be the subjects of the examination. Instead of making those items separately from the regular examination during the academic semesters, the university plans to collect and use good items from the usual mid-term and final examinations of those subjects. A key concern, in this study, therefore, is to analyze all the items used for the mid-term and final examinations of those subjects during the regular academic semesters. From the data of an about 100 sample in each subject at each time of total three tests, the difficulty index, discrimination index, the response rate of students on each item, and other general descriptive statistics are calculated and then good items are pooled for the future use for the Comprehensive Examination. Anhother important concern in this study is this study is given to the collection and analysis of controversial issues and problems on the process of operating the examination at other universities where the Comprehensive Examination is already adopted. The data from four institutions and from opinions of six participants of this study are used. The following main findidings are summarized : 1. The items have generally shown to be easy while the degree of discrimination is low. 2. Among the five subjects, Korean Language shows the highest rate of right answer (difficulty index) while English the strongest one in the discrimination index. 3. When comparing two types of test between the multiple choice and the short-answer, the latter seems to be powerful in both difficulty and discriminative. 4. The only one question of essay type test reveals clear limitations in scoring and evaluating students progress. 5. All items are constructed under the consideration of content-referenced base, not of the basis on behavioral aspect. 6. The analysis of issues and problems related to the Comprehensive Examination suggests that it is acceptable to test in terms of required subjects of general education and a few most basic subjects of major areas of study. 7. The examination can be functionally operated when it is held at the end of the first year of and before the beginning of the second year of the college years. The length of the examination is usally held from three to five hours. 8. Since the examination should be existed on the idea of criterion-referenced base rather than of norm-referenced one because of its testing the qualification of the entering behavior of students for the further study in their major field, the standard of the pass-and-failure should be set on at least 60 percent of correct answers in each subject. But there must be provided at least two additional opportunities for the make-up examination for those who failed in the first one. 9. A special committee must be established in order to deal with all the details related to the Comprehensive Examination.

質的 評價에 관한 最新 硏究動向과 그 敎育的 意義

卞烘圭,閔丙德 全北大學校 1997 論文集 Vol.43 No.-

This syudy is aimed at analyzing current trends in research on qualitative evaluation and deriving possible educational implications through the review of background literature. In the current development of cognitive psychology, a most important trend in research is focused on the qulitative evluation. Qualitative evaluation can be named as the "performance based" dynamic assessment. That is, it requires to complete tasks such as writing essays, conducting experiments, providing written answers to problems or preparing portfolios. A critical point of this qualitative evaluation is that it is likely to measure higher level cognitive skills, and thus it is recommended to integrate the instruction into the assessment.