피보나치 수열에 관한 고찰

양영오 한국수학사학회 2000 Journal for history of mathematics Vol.13 No.1

In this paper we survey the main properties of a Fibonacci sequence, and find out examples of Fibonacci sequence in our nature and daily life.

제주첨단과학기술단지의 개발전략

양영오 제주대학교 기초과학연구소 2002 基礎科學硏究 Vol.15 No.1

Jeju meets several problems in the preponderance on the primary and tertiary industry, the undevelopment of the second industry such as a high-technology industry, the regional brain drain, the failure in employment supply, and the relatively poor surroundings in science researches. Thus we are now confronting a serious crisis making weak our regional competitiveness. In order to strengthen the competitiveness of Jeju tourism and industry on international markets and in the knowledge-based society, the Jeju Free International City special law has been established last December and carry into effect on and after April 1. According to its basic planning, the development of Jeju High-Tech Science and Technology Park is one of the seven leading projects. The purpose of developing this park is to support technical innovation for regional medium and small enterprises, to support founding of a business, to advance the regional industrial structure, to invite domestic and foreign high-technology companies, and to enlarge employment. In this paper we investigate the present conditions, the main objects and several problems of domestic and foreign technoparks, and suggest the development strategies, facility block planning, the driving systems, the financial support and tax revision to develop Jeju High-Tech Science and Technology Park successfully.

피보나치 수열의 일반화에 관한 고찰

양영오,김태호,Yang, Young-Oh,Kim, Tae-Ho 한국수학사학회 2008 Journal for history of mathematics Vol.21 No.4

본 연구에서는 유명한 피보나치 수열을 일반화하는 g-피보나치 수열 $\{g_n\}$={a, b, a+b, a+2b, 2a+3b, 3a+5b,...}의 여러 가지 성질과 특성을 조사한다. 특히, g-피보나치 수열의 합에 관한 항등식과 제 n항 $g_n$(비네의 공식의 일반화)을 구체적으로 구한다. 또한 피보나치 수열에 관한 카타란의 항등식의 일반화된 항등식과 A. Tagiuri의 항등식을 구하고 $g_n$과 파스칼 삼각형과의 관계식과 g-피보나치 수 $g_n$이 얼마나 빨리 커지는가를 조사한다. 아울러 g-피보나치 수열의 초항과 둘째 항이 서로 소일 때 연속하는 두 항은 서로 소이며, 연속하는 두 항의 비율 $\{\frac{g_{n+1}}{g_n}\}$은 황금비 $\frac{1+\sqrt5}2$ 수렴함을 밝히고자한다. In this paper we investigate several properties and characteristics of the generalized Fibonacci sequence $\{g_n\}$={a, b, a+b, a+2b, 2a+3b, 3a+5b,...}. This concept is a generalization of the famous Fibonacci sequence. In particular we find the identities of sums and the nth term $g_n$ in detail. Also we find the generalizations of the Catalan's identity and A. Tagiuri's identity about the Fibonacci sequence, and investigate the relation between $g_n$ and Pascal's triangle, and how fast $g_n$ increases. Furthermore, we show that $g_n$ and $g_{n+1}$ are relatively prime if a b are relatively prime, and that the sequence $\{\frac{g_{n+1}}{g_n}\}$ of the ratios of consecutive terms converges to the golden ratio $\frac{1+\sqrt5}2$.

師範大學 數學敎育科 敎旭課程의 改善에 관한 硏究

梁永五 제주대학교 1988 논문집 Vol.26 No.-

This is to examine and improve the curriculm of mathematics educatin in teachers' college. Today the teacher education in Korea seems to confront some critical problems. In an effort to solve one of the most importent problems, that of quality, in mathematics teacher edcation. I have analyzed the curriculum of secondary schools and of mathematics inour 11 national teachers' colleges, and the teacher education system of Japan and America respectively. Then I have systematically and logically a new curriculum of mathematics teacher education on the basis of 150 credits. This study could be a suggestion of the model for the mathematics teacher education.

ON SPECTRA OF 2-ISOMETRIC OPERATORS

양영오,김철준 한국수학교육학회 2009 純粹 및 應用數學 Vol.16 No.3

A Hilbert space operator T is a 2-isometry if T*²T²-2T*T +I = 0. We shall study some properties of 2-isometries, in particular spectra of a non-unitary 2-isometry and give an example. Also we prove with alternate argument that the Weyl's theorem holds for 2-isometries.

수학교육에 관한 연구 : 중학교 수학과 교육과정 중심으로

양영오 濟州大學校 師範大學 科學敎育硏究所 1988 科學敎育 Vol.5 No.-

This is to examine the characteristic and trends of lower secondary school mathematics curricula in major five countries-Korea, Japan, China, Soviet Union, and U. S.A. Focusing the curriculum documents and reports in each country, characteristic. system, guidance (framework), objectives and areas of mathematics curriculum, major characteristic of instructional contents, development and evaluation of curriculum. and trends of recent reforms in mathematical cuniculum are discussed. Finally, significant suggestions which are necessary in revising the secondary school mathematics in Korea are given.

삼성신화에 나타난 수 3과 삼분구조에 관한 고찰

양영오,Yang Young-Oh 한국수학사학회 2006 Journal for history of mathematics Vol.19 No.3

본 논문에서는 종교, 세계관, 자연세계 등에서 수 3의 의미와 상징성, 삼분구조, 그리고 양 고 부 삼성(三姓)이 건국하였다는 탐라개국신화인 삼성신화(三姓神話)에서 나타난 수 3의 의미와 삼분구조를 살펴보고자 한다. In this paper, we study the meaning and symbols of the number three and the structure of dividing into three parts in the religions, views of the world and the nature. Also we investigate the meaning of the number three, and the structure of dividing into three in the Samsung myth. According to legend, the 'Three Names' (Samsung-Yang, Ko and Pu) which are three demi-gods emerged from Samsung-hyeol(called Moheung-hyeol), and became the progenitors of the Jeju people who founded the Kingdom of Tamna.

지식기반사회에서 기초과학 진흥과 대학의 역할

양영오 濟州大學校 基礎科學硏究所 2001 基礎科學硏究 Vol.14 No.2

According to the crossing application for admission to a university, applicants for the government-sponsored scholastic aptitude test to college of natural science have been seriously decreased up to 26.9 percent in the 2002 entrance year. Because of the enforcement of the faculty system, we meet several problems in avoidance of natural science courses and decrease in applicants for the faculty of science and engineering. Also the Government's educational reform policy increased the serious decrease in applicants for the college of science and engineering and the relatively poor surroundings in education and researches. Thus we are now confronting a basic science and national crisis making weak our national competitiveness. In this paper we point out the present conditions and several problems of our university concerning the basic sciences policy and educational reform, the national academic aptitude test and crossing application, the enforcement of the faculty system, a curriculum, etc., and suggest the promotion of basic sciences and the role of university in the knowledge-based society.

Spectral,Theory for Nonimear Maps

Yang,Young-oh 제주대학교 1992 논문집 Vol.34 No.-

Banach 空間에서 結合的 *-準有界(*-quasibounded) 函數空間 및 결합적 *-數値的 有界(*-numerically bounded)인 連續函數族의 함수공간의 特性을 밝히고, 이 결합적*-수치적 유계인 함수족의 結合數域(numerical range)을 정의하여 이의 여러가지 性質을 조사한다. 특히, 이 數域은 ?? 의compact 連合 部分集合이고, 이 함수족이 線形 作用素族일 때는 이 空間的 수역의 閉包와 일치한다. 또한 결합적 *-준유계인 함수족의 結合的 點近似 스펙트럼을 정의하여 이 스펙트럼이 수역의 compact 부분집합임을 보이고,一樣볼록 공간에서 이 스펙트럼과 수역과의 관계를 밝힌다. 그리고 Banach 공간의 雙對空間에서 연속함수족의 아래 *-수역을 정의하여 이 수역이 結合數域과 일치하기 위한 條件을 구한다 ,

SPECTRAL MAPPING THEOREM FOR THE WEYL SPECTRUM

YANG,YOUNGOH,LEE,JIN A 濟州大學校 基礎科學硏究所 1995 基礎科學硏究 Vol.8 No.1

In this paper we show that the Weyl spectrum of a M-hyponormal operator satisfies the spectral mapping theorem for analytic functions and then answer an old question of Oberai. Also we show that the set of operators T satisfying w(T)=σe(T) is closed in B(H), and invariant under compact perturbation. In particular we show that the Weyl spectrum of a operator T satisfying w(T)=σe(T) satisfies the spectral mapping theorem for analytic functions.