A functional equation related to hyperplanes

박원길,Jae-Hyeong Bae 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1

In this paper, we obtain the general solution and the stabilityof the multi-dimensional Jensen’s functional equation2f.x1 + y12,· ,xn + yn2.= f(x1,· ,xn )+ f(y1,· ,yn ).The function f given by f(x1,· ,xn ) = a1x1 + · + an xn + b is a solutionof the above functional equation.AMS Mathematics Subject Classication : 39B52, 39B72.Key words and phrases : Solution, stability, multi-dimensional Jensen’sfunctional equation.1. IntroductionIn the general case, a hyperplane is an ane subspace of codimension 1. Inother words, a hyperplane is a higher-dimensional analog of a (two-dimensional)plane in three-dimensional space. An ane hyperplane inn-dimensional spacecan be described by a non-degenerate linear equation of the following form:a1x1 + a2x2 + · + an xn + b =0where a1,· ,an,b∈R. Here, non-degenerate means that not all theai arezero. Ifb= 0, one obtains a linear hyperplane, which goes through the origin ofthe space.In this paper, letX and Y be real vector spaces. For a mappingf :Xn → Y,consider the multi-dimensional Jensen’s functional equation:2f.x1 + y12,· ,xn + yn2.= f(x1,· ,xn )+f(y1,· ,yn) (1When X = Y = R, the functionf :Rn → R given byf(x1,· ,xn)=a1x1 + · + anxn + bis a solution of (1Received October 20, 2006.Corresponding author.c. 2007 Korean Society for Computational & Applied Mathematics and Korean SIGCAM .513514 Won-Gil Park and Jae-Hyeong BaeFor a mapping g :X → Y, consider the Jensen’s functional equation:2g.x + y2.= g(x)+g(y). Recently, the authors investigeted various functional equations ([2], [3], [4]). Inthis paper, we investigate the relation between (1and (2And we nd out thegeneral solution and prove the generalized Hyers-Ulam stability of (1

연암 그룹과 담원 곽집환의 문예교류

유재형 ( Yu Jae-hyeong ) 한국한문학회 2017 韓國漢文學硏究 Vol.0 No.66

조선의 문인들이 중국 문인 곽집환의 문집을 두루 보고 이에 관련된 글을 쓰게 된 경위와 그 이유를 파악하였다. 1765년 홍대용은 숙부 홍억의 자제군관이 되어 연행을 떠났다. 다음 해 3월 2일 귀로에서 중국의 문인 등사민을 만나 의기투합했다. 홍대용이 귀국한 뒤에도 이들의 교류는 서신을 통해 유지되었다. 그러다 1773년 등사민이 보낸 편지 한 통이 조선에 닿았다. 여기에서 등사민은 자신의 동향 사람인 곽집환을 홍대용에게 소개한다. 편지의 요지는 이렇다. 등사민과 홍대용의 교류를 부러워하던 곽집환이 자신의 문집인 『회성원집』을 조선에 부쳐서 명사들의 서문과 발문 등을 구하려고 했다는 것이다. 홍대용은 이 소식을 자신의 벗들인 연암 그룹에게 알렸고 박지원과 이덕무, 유득공, 박제가 등은 서로 앞다투어 차운시와 서·발문을 써 주었다. 연암 그룹의 글은 곽집환에게 부쳐졌고 곽집환 또한 이에 열렬한 반응을 보였다. 이들의 교류는 곽집환이 죽기 전까지 이어졌다. 이들이 주고받은 편지와 시문 또한 『燕杭詩牘』과 『中士寄洪大容手札帖』, 그리고 『湛軒書』와『搢紳赤牘』 등 관련 자료에 그대로 남아 있다. 주목할 점으로는 연암 그룹과 곽집환은 면식이 전혀 없는 상태였다는 것이다. 곽집환은 유명한 문인도 아니었다. 곽집환을 위해 연암 그룹이 보인 정성은 쉽게 납득되지 않는다. 이들의 교유를 추동했던 요인을 살필 필요가 있다. 일전 홍대용은 연경에서 항주의 세 거자를 만나고 『會友錄』을 썼다. 연암 그룹은 『회우록』을 돌려보며 공간의 제약을 뛰어넘는 참된 우정을 갖기를 소망했다. 홍대용은 『회우록』으로 인해 김종후와 논쟁을 벌이기도 하였는데, 논쟁 이후 청국 인물과의 사귐이 더 이상 금기가 아님을 확인했다. 그러다 곽집환의 『회성원집』이 조선에 닿았다. `벗의 친구를 벗하라`라는 『교우론』의 명제 속에서 연암그룹은 등사민의 벗 곽집환을 친구로 인정하였다. 동시에 당대의 인물을 벗삼으려는 병세의식 또한 사행을 통한 경험 속에서 확산되었다. 연암 그룹과 담원 곽집환의 교류는 이러한 맥락 속에서 이루어질 수 있었다. The aim of this article is to promote an understanding regarding 『Hoiseongwonjip(繪聲園集)』 was read by various writers of the Joseon Dynasty; the author was the Chinese poet Kwak Jip-hwan. In 1765, Hong Dae-yong as a military officer under his uncle. In the following year, on his way back, Hong Dae-yong met with the Chinese poet Deung Sa-Min. Even after Hong Dae-yong returned home, their exchanges were maintained through correspondence. Then, in 1773, a letter from Deung Sa-Min reached the Chosun, and Deung Sa-Min introduced a young poet Kwak Jip-hwan to Hong Dae-yong. The point of the letter was this: Kwak Jip-hwan, who was envious of exchanges between Deung Sa-Min and Hong Dae-yong, tried to obtain the preface and footnotes by sending his 『Hoiseongwonjip(繪聲園集)』 to the Joseon Dynasty. Hong Dae-yong informed his friends in the Yeonam group ―Park Ji-won, Lee Deok-moo, Yu Deuk-Gong, and Park Je-ga. The writings of the Yeonam group were sent to Kwak Jip-hwan, who was enthusiastic about them. These exchanges continued until Kwak Jae-hwan died. Along with the letters and poems sent and received, other materials were included. Noteworthy is that the Yeonam group and Kwak Jong-hwan were completely hollow. The latter was not a famous writer. It is necessary to examine the factors that motivated these parties. Earlier, Hong Dae-yong met with three elders of Hangzhou in Yanqing and wrote 『Hoiwoorok (會友錄)』. The Yeonam group hoped to have a true friendship that transcended the boundaries of space by turning the 『Hoiwoorok(會友錄)』. Hong Dae-yong argued with Kim Jong-hoo because of 『Hoiwoorok(會友錄)』; after their debate, they confirmed that the relationship with was no longer taboo. Eventually, Kwak Jip-hwan`s 『Hoiseongwonjip(繪聲園集)』 reached Korea. At that time, the Yeonam group recognized Kwak Jip-hwan as a friend because of the “Dating theory.” With contemporary consciousness, the exchanges of the Yeonam group with Kwak Jip-hwan were possible.

마리화나 흡연 후 발생한 뇌경색

이일형,김성민,배재천,권기한,이병철 대한신경과학회 1999 대한신경과학회지 Vol.17 No.2

평가 문항을 통한 중학교 과학영재 학생들의 빛 개념 지식상태 분석

이형재,하지선,박상태 韓國英才學會 2011 영재교육연구 Vol.21 No.4

이 연구에서는 K대학교 영재교육원의 중학교 과학영재 학생들 30명을 대상으로 빛에 관한진단평가 15문항을 개발하여 적용하였다. 그리고 빛에 대한 학생들의 지식상태에 관하여 지식공간론을 활용하여 분석하고 이것으로부터 얻은 위계를 도식화함으로써 중학교 과학영재학생들의 지식상태를 파악함은 물론 교수 학습 방법을 개선하기 위한 기초자료로 활용하고자하였다. 이러한 연구 목적을 달성하기 위하여 중학교 과학영재 학생들의 빛에 대한 지식상태평가결과를 분석하였고, 문항 간 위계구조 및 개별 학생들의 지식상태를 분석하였다. 그 결과학습 집단 내에서 개인별로 서로 다른 지식구조를 갖고 있었고, 이에 따른 학습 진단도 서로다르게 평가해야 함을 알 수 있었으며, 평가 문항과 문항 간의 관계(위계 구조)와 개별 학습자의 지식상태를 알 수 있게 한다는 시사점을 얻을 수 있었다. In this study, we developed and applied 15 evaluation questions about light to 30middle school students in K University Science Education Institute for the Gifted .Then we used the theory of knowledge space and analyzed the middle school ScienceGifted Students' knowledge state about light. By schematizing the hierarchy from it, weintended to not only measure students' knowledge state about light, but use it as thebasic materials to improve teaching methods. To achieve the purpose of this study, weanalyzed the evaluation results and individual knowledge state and hierarchy ofquestions. As a result, there were different knowledge structures in the individual, andwe found that we should diagnose them differently. In addition, we have hadimplications that it has the connection with each questions and the individualknowledge state.

RFID를 활용한 3차원 물류 창고 관리 시스템의 설계 및 구현

형대진,김승구,이재윤,박경환 東亞大學校附設 淸報技術硏究所 2006 情報技術硏究所論文誌 Vol.13 No.2

At present, a business management is managing to minimize a investment or a stock cost for a warehouse. So the essential point of warehouse's function is exchanged to attach greate important to information technology and client services. But the existing warehouse management systems have many weak points in part of information technology and client services. In this paper, we suggest the plan of introducing the RFID system into warehouse management system for an efficient management. We also develop warehouse management system to show in realtime 3D a location information of goods in the warehouse.

RFID를 적용한 항공물류 SCM 시스템의 설계 및 구현

형대진,김승구,이재윤,조현준,박경환 東亞大學校附設 情報技術硏究所 2005 情報技術硏究所論文誌 Vol.13 No.1

The present the information sharing among the subjects was not enough in Airway Logisctics Industry, because each subject use the independent system. The Airway Logistics Network is suggestion, but the Airway Logistics Network dose not operate with efficient connection, because each subject attached to the connection among the internal system. If the RFID system which one of Auto-ID systems is introduce into Airway Logistics, an efficient management of Airway Logistics will be possible. In this Paper, we introduce the RFID system into Airway Logistics SCM system for an efficient management and an efficient information sharing. We also develop Airway Logistics SCM system with priority given to Forwarder which is occupy an important position in Airway Logistics industry.

國際機構의 法秩序와 國際人權基準

柳在馨 청주대학교 학술연구소 2007 淸大學術論集 Vol.10 No.-

Of the numerous references to human rights in the UN Charter, at least one is clearly of normative character. By Art. 56, "All Members pledge themselves to take joint and separate action in co-operation with the⌈United Nations⌉Organization for the achievement of the purposes set forth in Articles 55" ; one of those purposes is the promotion of "universal respect for, and observance of, human rights and fundamental freedoms for all without distinction as to race, sex, language, or religion". The precise content and import of that undertaking are subject to controversy and have not been authoritatively determined, but at least deliberate, gross violations of human rights by a UN member would appear to be a violation by that State of its pledge to take action to promote respect for and observance of human rights. Thus, for example, the → International Court of Justice(ICJ) has declared → apartheid to be "a flagrant violation of the purposes and principles of the Charter". This dissertation is research about ‘the law order of international organization and international standard of human right. Namely, it aims to search method to clearly define 「binding force」 of international standard of human right in UN. Thus, preceding researches made from the viewpoint of organization of international society was examined in Clause 1. For this purpose, I checked the external effect of internal law of international organization and exterior activity law. Based on this, I examined the 「binding force」 of international standard of human right and structure of coercion in Clause 2 and investigated how it can be explained from the viewpoint that the 「binding force」 of standard is accommodated is the international organization. Namely, this dissertation aims to examine the issue of 「binding force」of international standard of human right from theoretic aspect and to define the issue of 「binding force」 of international standard of human right in UN. Then, the role of international standard of human right has legal function and energy which is not in human right treaty as international law and domestic law. As a matter of fact, there are some problems, i.e., whether the contents of international standard of human right really have universality or surveillance activity is optional. However, the role that the activity plays to guarantee human right is clear. Compared to domestic law, it is required to reconfirm that guarantee of human right by UN, namely, non-judicial guarantee of human right is actually maintained by the legal device of UN. Since international standard of human right is established nowadays, the guarantee of human right by UN prepares list of right to restrict the arbitrary infringement by state notwithstanding the in existence of sufficient standard for judgment in the international and domestic law. Furthermore, it can be said that international standard of human right is enforced by constant monitor by the own law order of UN. key word : 人權의 國際的 基準(international standard of human rights), 國際機構(international organization), 拘束力(binding forces), 內部法(internal law), 人權保障(guarantee of human rights).

내측회장동맥에 의해 형성된 척수경막동정맥루로 인한 척수병증 1예

이일형,배재천,이상무,김진혁,권기한,이병철 대한신경과학회 1999 대한신경과학회지 Vol.17 No.3

서울의 Penicillinase Producing Neisseria Gonorrhoeae 발생빈도(1996)

김재홍,황동규,전재홍,김윤석,김중환,김용준,이창균,임동진,김현수,조창근,김경문,박상훈,전우형,김희성,이호정,차명수,김갑형,김형석,김석우,황지환,박병순,권오상,이민수,송기훈,성소영,이인섭,부태성 대한화학요법학회 1999 대한화학요법학회지 Vol.17 No.2

Background : In recent years, gonorrhea has been panedemic and remains one of the most commom STDs in the world, especially in developing countries. Objective & Methods: For the detection of a more effective therapeutic regimen and assessing the prevalence of PPNG, we have been trying to study the patients who have visited the VD Clinic of Choong-Ku Public Health Center in Seoul since 1980 by means of the chromogenic cephalosporin method. Results: In 1996, 139 strains of N. gonorrhoeae were isolated, among which 53(39.0%) were PPNG. Conclusion: Our results suggests that after a peak of 74.3% in 1993, the prevalence of PPNG in Seoul is gradually declining.

釜山大學校 학생 써클활동 實態와 그 運營改善方案에 관한 調査硏究

李衡基,李成海,李大雨,鄭榮洪,林再澤 부산대학교 학생생활연구소 1983 硏究報 Vol.19 No.1

The present study deals with student circle activities at Pusan National University in an effort to improve student circle guidance. University circles are regarded as influencing an individual's self-growth. Two sources of data were used for this research. A total of 764 students at Pusan National University who were randomly sampled out of the registered students in 1982 Spring semester were the main subjects. Another source for the study were from 70 student circle leaders whose responses to another questionaire in a special leader training session held on October of 1982. Student respondents for this study were analyzed in three groups;(1) students who participate in circle activities at the time of the research, (2) students who participated in a circle in the past but not active at the time of the questionaire interview, (2) students who have never been members of a circle. The student respondents who were or have been members of the circles in which they participate:social service circles;academic circles; circles for special hobbies; religious circles; athletic circles for special hobbies; anti-communism circles. Some of the important findings from this research are summarized in the following. (1) Pusan National University students enjoy more student circle activities as demonstrated in the sheer number of student circle activities registered in the Student Affairs Section of the University. Circles with friendship purpose seem to decline, while circles for special hobbies and academic purposes tend to increase. (2) Many students were found to drop out of the circle activity mainly due to the lack of the circle activity information before their participation in those circle. More coeds than male students show this tendency. (3) Student circle members with specific purpose and goal in mind before participating in those circle regard aircle activity as contributing to the self-growth. (4) Many respondents think that circle activities are vital and necessary in the campus life. However, they do not find proper circle to paticipate. (5) The role of the student circle guidance professors was found to be important. (6) Problems for funding the student circles and finding meeting places for the circle activity remain to be solved. In short, the present study underlines the importance of the activization student activities which can be achieved through intensive circle guidance by circle advice professor and proper funding.