Let (X, x) be a purely elliptic singularity, I.e., the plurigenera δ_m(X, x) of the singularity (X, x) is equalto 1 for every m [0x81b8(Shift-JIS)] N. In the two dimensional case, simple elliptic singularities and cusp singularities are purely elliptic singularities.On the other hand, Knoller defined other plurigenera {γ_m(X, x)}_<mN> for a normal isolated singularity (X,x), Between δ_m(X,x) and γ_m(X,x) there is an inequality 0 【less than or equal】 δ_m(X,x) 【less than or equal】 γ_m(X,x).Then the plurigenera γ_m(X, x) make it possible for us to classify purely elliptic singularities.We describe some properties of Knoller's plurigenera defined for normal isolated singularities, especially in case singularities are so-called hypersurfce purely elliptic singularities.Consequently we have made examples of families for hypersurfce purely elliptic sungularities with constant γ_m

Through education that aims at development of indivisible talent, facilitating pupils' abilities for positive living is going to be placed in the center of education naow and future. It is requested for emphasizing "the will and power of thinking and learning for oneself. SBased on this spirit, basic policy of the improvement of school mathematics was shown emphasizing pupils' activities and pleasure in the comment given in the Final Report of the Curriculum Council. How should we appreciate this meaning? Furthermore, how should we just improve school mathematics?We discussed four items as follows. 1. The way that should be of school mathematics which aims at cultivating zest for living / 2. The tend of school mathematics reform of foreign countries / 3. The comparative study of the curriculum among Korea, the U.S.A., Australia and Japan / 4. The way that should be of the lesson which aims at cultivating zest for livingAs a result, we achieved the following points. 1. Suitable aims and evaluation aspects for cultivating zest for living / 2. The trend of school mathematics reform of several countries / 3. The comparative study of school mathematics curriculum standard

Recently increasing use of some computers and internets in Japan, many schools has been also influenced in the information society. We need to think creatively in the information society with multimedia. We should change some traditional forms that forty students passively study in the classroom all day.In particular, some members in the commission of curriculum assert that teaching hours and contents in mathematics and arithmetic should be decreased. Because many students don't understand many contents in mathematics and arithmetic well. Because of these contents are constructed based on the culture and history in our country, we have to teach to these contents in school.Many students need to do the following ways of living with humanity ; they are moved their heart for seeing to beautiful subjects, they corroborate others with harmony and cooperation. These mind is called "ability for living". We would like to develop these abilities in the classroom of mathematics and arithmetic. We can't teach "ability for living" only through paper pencil approach. We must use the computer for engaging the mathematics teaching to be more effective, and make to environments where involved moder

The educational eviropment of today around the hgigh technological society has changed. For instance, many knowledgeable people point out that students'saidestepping mathematics and science may risk our fortune on the fundation of Japan as a sientific nation. For these tasks, Japan Society of Mathematical Education, Japan Society for Science Education, and Japan Society of Educational Technology and so on, we have held some symposiums and seminars, and appealed to many researchers, teachers and parents in collaboration with knowledgeable people.On the other hand, the scholastic ability admitted in the current school is out of date and emphasized to master higher tactics and precised skills based on the systematics structure of completed mathematics, unfortunately. People have maintained it and the method for assessing it. As a results, the ability taught in school mathematics has been separating from the mathematical ability necessary for our society. In the recent mathematics education reforms of the foreign countries, it is emphasizied mathematical abilities which correspond to the social needs for rebuilding economics and culture, for example : "Mathematical Proficiency", and na

本科研費の援助の下で,3月下旬開催の国際研究集会「幾何学的複素解析」の準備会として,九州大学及び富山大学に於いて研究集会を行い,その他にも小グループ間の研究連絡や情報交換会等を行って,以下の通りの研究成果を得た.研究代表者藤本は,極小曲面の値分布論的性質を研究し,複素平面に定義域を持つ極小曲面に対するBeckenbachの与えた値分布論を,放物型Riemann面を定義域とする極小曲面の場合に拡張した.関連して,梶原壌二は,極小曲面に近い曲面のガウス写像の擬等角性を調べた.野口潤次郎は,複素射影空間内の高次数双曲的超曲面の存在を示すと共に,値分布論の第2主定理を関数体上の場合に確立し,方程式の有理数解の有限性の問題に応用した.神保敏弥及び坂井章は,C^<12>の全実集合を一成分とする直積集合上の関数の整関数による近似問題を研究した.浜田英隆は,或2次元のラインハルト領域の固有正則写像及び球の間の固有正則写像で平行な超平面上線形であるものを全て決定した

Through collaborative research the results of "how to use software in school geometry in both countries? and what kinds of effects are found in using software?" were reported at the International conference of Mathematics, Education held in Spain and Psychology of Mathematics Education held in Finland. Then the difference between France and Japan on the cognitive aspects when students solved the proof problems was found. The following results of research was found in Japan. On the process of problem solving in geometry, students find the characteristics of figures and theory of geometry by themselves after exploring activities with computer software "Cabri-Geometry". And then they tried to find the reason why these characteristics and theorems come from. This approach for proof is very interested by students.As the results of these research a Japanese text book for using Cabri-Geometry in Junior high school edited by Professor Nohda and Nakayama was published in 1996. And samples of materials of geometry course to use this software in class were produced in floppy disk by Shimizu and Kakihara and distributed to school teachers. This book and these materials are very helpful for sch

変形という観点で特異点を捉えると最も基本的であるといわれる有理二重点の境界に位置する特異点として単純楕円型特異点とカスプ特異点がある。これらの特異点は渡邊の多重種数により純楕円型特異点として捉え直すことができた。純楕円型特異点にquasi-Gorensteinという条件を課し、まず病的な純楕円型特異点を排除し、次にCohen-Macaulayか否かで2つのタイプに分け、さらに真性例外集合のMixed Hodge構造により、次元個のタイプにわけることが可能となった。おかげで、2n個のタイプに応じた研究が可能となり、具体的に定義式を計算することが容易になった。このようにして、単純楕円型特異点とカスプ特異点の概念は高次元へと拡張され、(0,i)-type純楕円型特異点として生まれ変わった。特に3次元においてはQ-factorial terminal modificationにおけるterminal singularityの分布を超曲面のときに記述することができたので、ある意味において特異点が超曲面であるための必要条件を得ることができた。

In order to clarify the conformity degree of education target, education policy, and admission policy in each university to the variety of secondary education, we, in this research, conducted the investigation about admission policy and the questionnaire about the enforcement situation of Admissions office examination, the present conditions and problems of the information for a high school student in an open campus, the present conditions of admission of the students from a specialty senior high school and a comprehensive high school, and the motivation of a new student. We held several meetings far the study and talked with the articulation of high school and university concerning with the topics of specialty senior high schools, comprehensive high schools, super science high schools, and diversification of learning in senior high schools. From the rapid increase of admissions office examination and diversification of admission policy, we thought that a static model with fuzziness is not effective, and we analyzed the present conditions. It is necessary to think about the dynamic model that can express environment adaptation ability to treat the newly started admission system tha

本研究の目的は、国際数学オリンピック(IMO)総合順位上位国と、我が国の秀でた生徒の教育方法を、出場者個別育成ストラテジの次元で比較調査することを通して数学における秀でた生徒を育てる教育のノウハウの相違を明らかにし、その結果から教育研究への範例、実践開発への教材を得て、国内、途上国における人材育成方略への提言をすることである。具体的には、1).入試選抜による特別学校を基盤とする中国の英才教育と、自主セミナーという機会均等・公正理念のもと、誰もが参加しえるブルガリア方式など、秀でた生徒を育てる教育に対する考え方の相違を明らかにする。2).本調査では、IMO出場者輩出校での教育方法・内容調査を行う。具体的にはカリキュラム(教科書、教材)、指導法、指導者、生徒、入学、進路、動機の項目毎に、英才教育のプロセスを質的に調査し、関連資料を収集する。3).収集資料を基に、カリキュラム・教材資料集を作成する。4).適宜、それぞれの立