A series of fatigue tests has been conducted to clarify the fracture behavior depending on the stacking sequences of quasiisotropic CFRP laminates. Strips of laminate with four different directions were cut out from the same CFRP plate to prepare the specimens with the four stacking sequences. Prior to fatigue tests, the specimens were collided by a lateral load in order to simulate the damage induced by the fallen tools. During the fatigue tests, the damage developed in the specimen was detected by non-destructive techniques such a scanning acoustic microscope (SAM) and a replicating method. Stacking sequences exerted an influence on fracture behavior of laminate specimens, i.e., the stacking position of the zero degree layers, in which fiber direction was parallel to the loading axis, played an important role in the fatigue process. When the zero degree layers were located at the specimen surface, no remarkable damage progress was observed from the surface. On the other hand, when the zero degree layers were located in the middle of laminates, the damage in the surface layer was found in the fatigue process. Not only the degradation of the equivalent elastic modulus was seen in all specimens, but also the degradation curve varied with the stacking sequences.

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Fatigue bending tests on Ni-Ti super elastic wire have been conducted. In order to examine fatigue fracture behavior in the human body condition, three types of conditions were tested; under dripping cold water, warm water and laboratory air. The curvature of specimen was calculated with specified maximum strain and specimen was loaded with cyclic vending deformation using handcrafted fatigue testing machine. As testing results, the number of cycles to failure decreased with increasing maximum strain under every environmental condition. Under the warm dripping water conditions, fatigue limit stress seemed to larger than that of under cold drip and laboratory air conditions. The number of cycles to failure varied slower than with maximum strain under the warm water condition than cold water and laboratory air conditions. In the fractured surface, dimensions of cleavage fractured area  became smaller with increasing maximum strain. The variation range of  in under dripping warm water was smaller than laboratory air and cold water conditions.

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It is well known that the alluvial has its natural period in relation to its depth, and makes the earthquake motion large. On the other hand, the hill also has its natural period in relation to its height. I this paper, the natural period of a hill is calculated in consideration of its sectional shape. As a result, The height and the sectional shape of a hill influences its natural period. But the natural period is proportional to the height of a hill. The mode analysis of the hill at Aobayama Campus of Tohoku University shows that the natural periods (from 1st till 4th) by 3D model are about 1.0 sec. The natural period by 2D model is also 0.92 sec. There are many predominant periods under the 1st natural period of 3D model in the calculated response spectra. And there is no tendency among response spectrum at each point on the 3D model.

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We have made some proposals for the educational method of fundamental mathematics in the college of technology. One aim of the present paper is to state these proposals. In order to give lessons of fundamental mathematics by our own method, it is desirable for the students to be given the textbooks for the method. Moreover, we think that the textbooks on the market are insufficient in some respects to counter the problems in the mathematics education in the college of technology. We want textbooks to contain detailed explanation, a lot of examples, and suitable problems, so that a student can study by himself to some degree. For these reasons, we have been making the teaching handouts for the students in the lower classes of the college of technology. The other aim of the present paper is to report on these teaching handouts.

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The aim of this study was to evaluate the attempt of project-based-learning (PBL) with the industry-academia collaboration (IAC) in physical education-related liberal arts classes. Sixteen technical college students in an advanced course took part in this attempt and answered the questionnaire. As an attempt at initiating IAC, we used a rubber sensor which was developed by Sumitomo Riko Company Limited for measuring body pressure. Company representatives explained to students the development process and the handling method. Students were divided into five groups. Subsequently, each group formed 6 weeks’ exercise training (6ET) plan and an inspection method using the rubber sensor. Based on the data before and after 6ET, each group prepared a presentation file. Finally, each group performed the presentation and exchanged opinions with company representatives about the fine points and the other uses of the sensor. Approximately 80% of the students had a favorable opinion of this attempt. From the present results, it was suggested that this attempt was a worthwhile class for technical students.

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ロープワークで用いられる「トラッカーズヒッチ」という結びについて，その両端をつないで閉じた結 び目を作り，数学の結び目理論において分類されているどの結び目と関係しているのかを探る．トラッカー ズヒッチから結び目図を作成し，そのアレクサンダー多項式を求め，既に知られている結び目のアレクサン ダー多項式と比較することから，数学の世界で分類されている結び目を特定するという方法をとる．

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３辺の長さが整数であって，１つの角度が120◦（あるいは60◦）の三角形は（あるいは半角）アイゼン シュタイン三角形と呼ばれる．アイゼンシュタイン三角形の３辺を求める問題は，楕円上の有理点を求める 問題に翻訳することが出来る．その一方，オイラーの公式を一般化することで楕円上の点を表す新しい関数 が定義できる．この新しい関数は三角関数と類似の加法定理を満たす．この新しい関数を，このノートでは 楕円型２次曲線関数と呼ぶことにする．このノートの後半では，この楕円型２次曲線関数を整数論へ応用す る．アイゼンシュタイン三角形の有理点を与えるパラメータ公式が，この楕円型２次曲線関数の半角の公式 から導けることを示す．

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オイラーの公式は最も美しい公式の１つである．三角関数と指数関数を結びつける関係式である．この オイラーの公式を使うことで，三角関数を定義することも出来る．また，これを利用することで三角関数の 加法定理は指数法則から導くことが出来る．さらに，オイラーの公式の虚数単位i = √−1 を普通の1 に置 き換えることで双曲線関数が定義出来る．オイラーの公式は，三角関数や双曲線関数が指数関数の仲間であ ることを示している． このノートでは，オイラーの公式を拡張することで，２次曲線上の点をパラメトライズする新しい関数 を定義する．この関数は三角関数や双曲線関数を一般化した関数で，三角関数や双曲線関数と同様な加法定 理を持つ．また，２次曲線上の関数なので，このノートでは２次曲線関数と呼ぶことにする．さらに，この ２次曲線関数のパラメータは，２次曲線の「周の長さ」ではなく，「扇形の面積」を表すことを示す．

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双曲線関数のパラメータは双曲線の長さではなく面積に関係している．円から定義される三角関数は，円 弧の長さからも扇形の面積（の２倍）からも定義出来る．しかしながら，双曲線の場合は，扇形の面積（の ２倍）から定義すると双曲線関数が定義できるが，双曲線の長さから定義すると楕円関数になる． このノートでは，この議論を一般化して，周の長さではなく面積（の２倍）を使って，曲線をパラメー タ表示する新しい関数を定義する．最初に，三角関数や双曲線関数を面積の逆関数という観点から復習し， 積分の関係式から加法定理を導く．そして，２次曲線の面積を求める問題から新しい関数を定義する．さら に，この新しい関数は三角関数と双曲線関数を拡張した関数であり，加法定理を持っていることを示す．

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