The purpose of this research is to clarify the way of the treatment of Sakumon in "life-centered arithmetic" in the early part of the Showa era. We pay attention to the arithmetic education on which Iwashita, Fujiwara and Inatsugu insist. They play a central role in the practice of "life-centered arithmetic". Through consideration, we find the following facts. (1) The chief aim of arithmetic education by Iwashita is to develop the qualitative thinking. To realize this aim, he introduces the practice to develop the qualitative thinking in daily life. For instance, gathering the qualitative facts, measurement are examples of this activity. Children pose the problem by the use of these facts or the result of measurement. Sakumon is a part of the practice to develop childeren's qualitative attitude in daily life. (2) Fujiwara restricts the position of Sakumon in his arithmetic education with the reflections that arithmetic education based on Sakumon is not able to preparete the curriculum. He changes Sakumon's position into one of methods of teaching arithmetic, namely the representation of the qualitative life. (3) Inatsugu attemptes to accord logicism with psychologism in arithmetic education. Generalization and specialization of mathematical thinking are the scaffold to accord them. Sakumon becomes the teaching and learning method to cultivate specialization. Simizu's study of curriculum development based on Sakumon has an attraction for him.

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In this paper, we discussed the formation process and the characteristics of the arithmetic workbook edited by Zingo Shimizu in 1933 and 1934. He was a leading arithmetic teacher of Sakumon-centered Arithmetic Education which had been put into practice under the leadership of the director Takezi Kinoshita at the elementary school attached to Nara Women's University since the middle of the Taisho period. The arithmetic workbook was made to answer questions and requirements form elementary school teachers who worried about how to implement Sakumon-centered Arithmetic Education into their classes. The major problems were as follows: (1) Children had a tendency to make the same arithmetic problem; (2) The problems posed by children were on the whole easy in the higher classes of elementary school; (3) It was very difficult to treat the national textbook with reference to the problems posed by children; and (4) Teachers were worried that they failed to make children obtain satisfactory results on the performance of computation. In response to these requests, Shimizu developed a new curriculum which was intended to coordinate children's mathematical activities in daily life and the contents of the national textbook. But, this curriculum required a great deal of teacher's efforts in implementing into classes. Then, he set himself to make the arithmetic workbook which was in conformity to ideas of Sakumon-centered Arithmetic Education and could be used together with the national textbook in class by teachers. Through discussing the characteristics of the arithmetic workbook, we pointed out that firstly it was the utilizable learning resources for teachers to encourage children's qualitative thinking, secondly it covered the demand of the national textbook, thirdly it was affected by the spirit of that time, totalitarianism. The Shimizu's attempt should be evaluated on the point that he developed it as a mediator between the two national textbooks, Black Cover and Green Cover.

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The purpose of this paper is to study the transfiguration of the education of function in text books compiled by the Ministry of Education, founding on higher elementary schools from 1904 to 1935. We can classify the teaching content into four periods, as follows. In the first period, from 1904 to 1909, textbooks did not teach functions. In the second period, from 1910 to 1918, there are only three questions about functions but there is a conscious awareness of the existence of functions. In the third period, from 1919 to 1925, compared to the progress in the education of function from the first to the second period, rapid progress is made. The teaching contents in this period are substantially similar to the fourth period teaching contents. The 1919 revision was aware of the improvement movement of mathematics education in secondary school and anticipated the changes needed for the 1926 revision. In the fourth period, from 1926 to 1935, functions are formally dealt with. The teaching contents from the third period are reconstructed and quantity of functions taught is increased. Characteristically, falling movement is dealt with using geometry. The transfiguration in this period reflects the mathematics education improvement movement which had been rapidly improving. The transfiguration in this period reflects indirectly the demands of those who were concerned about education. The demands tried to approximate the higher elementary school to the preceding term of the secondary education. The 1926 revision also included the innovation of the subject/teacher system and the introduction of compulsory industrial subjects. We can find the following as a whole. The graph is a useful way to represent the relationship and variety of the quantity. The transfiguration of education in the higher elementary and secondary schools occurred at about the same time frame, but characteristically, the change in the higher elementary schools went a step ahead of the change in the secondary school.

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The purpose of this paper is to study how Motoji Kunieda (1873-1954) understood the concept of function and how he thought about the education of function. He considered that the goal of mathematical education was to cultivate mathematical common sense, which gives the person knowledge and the power of judgment in mathematics and arithmetic, and the concept of function was one aspect of mathematical common sense. He thought that the basic functional relations could be learned at elementary school, but that the real leaning of function should be cultivated in junior high school. This is because the comprehending of function was depended on the understanding of variables, and variables are represented by algebraic symbols. We can classify the teaching contents in his textbooks into four periods, as the followings. In the first period, from 1912 to 1921, the education of function began to be taught to students. But, some of the contents were omissible in teaching. In the second period, from 1922 to February 1926, the teaching contents have been developed. Especially in algebra, the teaching contents which had been omissible in the first period were formally treated. In the third period, from March 1926 to 1932, the teaching contents were enriched, quantitatively and qualitatively. In the forth period, from 1933 to 1937, the teaching contents have been edited a little and ordered.

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本稿の目的は,生活運動が緑表紙教科書に与えた実践的影響の実際を知るために,生活運動の指導的実践家の一人である香取良範の生活理論と実践を明らかにすることである。香取は,生活全盛期に生活を重視するあまり数理を軽視する傾向がみられた実践を憂い,教育学者篠原助市の『理論的教育学』理論を基盤に,篠原教育学の基本概念である「自然の理性化」を枠組みとして「生活」と系統的な「数理」とを分離した上で,両者を統合し一元化した組織的な教育実践の構築に取り組んだ。生活から数量を取り出し数理を導く「生活の数理化」と,発見した数理で生活を見る「数理の生活化」の連続した学習過程が「自然の理性化」の過程であり,篠原教育学を香取が教育に具体化した姿である。香取の学習過程と,作業を重視した実際的な学習法,学習者の課題探求心を喚起し続ける教師の働きかけは香取の教育カリキュラムの根幹である。

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画像信号への符号の適用は2値画像に始まり，現在では多値画像，動画像へと適用範囲が拡大されている．これらの多値情報源に符号化を適用する上では多値情報源を2値情報源に分解し2値符号化を適用する手法が一般的である．筆者は既に多値情報源をそのまま多値符号化する場合について，必要なレジスタ長，各シンボルの領域割り当て方法についての基本的な検討を行ってきた．今回は乗算フリー多値符号についてその基本的な検証を行う．

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生活は大正末期から昭和初期にかけて展開された教育運動であり,わが国の教育が現代性を獲得する過程で注目すべき実践の総体である。しかし,生活の全体像は今日においてなお明確にされているわけではない。本稿は生活の全体をとらえるための基礎的研究として,生活実践家の一人である藤原安治郎の実践に焦点をあて,その実践の具体的様相を理解しようとするものである。本稿では大正末期から昭和初期の藤原の教育実践について,「生活」,「数理」,及び両者の関係を中心に時系列的に検討した。その結果,藤原の教育実践は「生活」から「数理」を切り離してそれぞれを独立してとらえる過程で,両者を結びつける統一原理として「函数観念」が意識され,「生活」と「数理」は循環作用をもつものとなった。更に「数理」を中心概念として「生活」をとらえ,「数理」の会得が生活力の基礎であると主張するに至っている。このような変容の過程は4つの時期に区分できた。

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演算を必要とするため，そのままでは符号化及び復号に多大な時間を要する．このためLangdonらのシフト型符号やPennebakerらのQコーダ，上野らのSTTコーダなどでは，領域計算における乗算のシフト演算や加減算への置き換え，領域の下位アドレスの条件設定などにより，符号の高速化を図っている．その結果，領域の近似が生じ，乗算型符号よりも符号化効率が低下する．しかし，近年のハードウェアの技術進歩により，乗算の高速化や記憶装置の大容量化が進んでいることから，乗算型符号での最大符号化効率を維持したうえで，高速化を実現する検討も必要と考えられる．そこで本論文では，乗算型符号における最大符号化効率を維持したうえで高速化を実現するために，無記憶情報源に対して情報源の拡大処理を導入し, 通報の確率と下位アドレスを計算するために必要となる確率値を保持するテーブルサイズを変化させ，それに伴う演算回数の削減度を調べて高速化の可能性を検討した．実験の結果，提案方式は符号化時間及び復号時間を，それぞれ，従来の2値乗算型符号の約13/100及び約56/100まで削減できることがわかった．

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This paper is a part of "Research on Cultural Value in Mathematics Education". The author has aimed to clarify the problem that the present school mathematics education has by catching the mathematics development as the organic whole, clarifying the culture seen there, and applying this aspect to historical development of the mathematics education of our country. In the process, the following problems have come to the surface. Does the handling of the algebra expression that does the base of high school mathematics really make the best use of cultural value of the algebra expression now? In the preceding paper, it approached a part of details how the algebra expression that does the base of high school mathematics was formed, how it developed, and how our country accepted the European calculation when our country took the European mathematics. In this paper, the focus was applied to the receipt of the European mathematics in the age when the mathematics education of Japan did shape. Especially, the focus was applied to the receipt of the elementary algebra that was the content that which was related to the algebraic representation previously described and related to the secondary education. And it searched for the modality of mathematics and the mathematics education at that time. As a result, the following has been understood. The elementary algebra was digested to Japan through the movement of the mathematics technical term unification, the enhancement of the translation book, and the maintenance of the textbook, etc. in about the middle of the Meiji era. It arrived at "Receipt" of the elementary algebra by completing Japanese original "Textbook" in around 1897. And, it is deeply taken part by there was a tradition of Japanese mathematics "Wasan" in Japan in the process of the "Receipt". In addition, when the process from relations with Japanese mathematics "Wasan" to "Receipt" of arithmetic and the elementary algebra is caught, the process is roughly divided into the next three stages. The first stage: Stage of "Conversion" from expression of Japanese mathematics "Wasan" to expression of West mathematics. The second stage: Stage of "Translation" from original of West mathematics to Japanese. The third stage: Stage of Japanese "Textbook" compilation of original Japanese it. It is future tasks to consider details afterwards of received arithmetic and elementary algebra, and to consider the receipt of other fields of European mathematics to which light has not been applied yet.

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本稿では最近注目を浴びている符号の画像符号化への適用について考察している．まず，マルコフ情報源の符号化に関し，開始状態に応じてその遷移を求めることで，複数のブロック符号を設計し，これを切り替えて使用する状態混在型の拡大情報源符号化処理の問題点を明らかにし，符号化処理の持つ利点を再確認した．続いて符号とブロック符号を対比させ，いくつかの事項に関してその対応関係を明らかにした．また，これに関連して符号における復号終了条件と復号シンボルの有効性の判定法について明示した．最後に，2元符号を多値の情報源に適用する上で重要となる2元情報源への変換をはじめ，画像信号の符号化におけるいくつかの設計要素について考察した．

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This paper is a part of "Research on Cultural Value in Mathematics Education". The author has aimed to clarify the problem that the present school mathematics education has by catching the mathematics development as the organic whole, clarifying the culture seen there, and applying this aspect to historical development of the mathematics education of our country. This paper considered what the concept of quantity on "Decimal" cultivated by Japanese mathematics "Wasan" culture was. And, this paper considered how to have transformed the concept of quantity in Japan by receiving European mathematics based on "Fraction" at how to catch the quantity. The transition of the handling of "Decimal" and "Fraction" in the arithmetic textbooks at the last years of the Tokugawa shogunate and the Meiji era period was examined. First of all, the receipt of "Fraction" of European mathematics in study was examined. The modality of two receipts of "Fraction" of European mathematics was confirmed. One is the receipt of "Fraction" being based on the idea of the fraction caused from the result of the multiplication and division calculation, and with "Concrete number" including "Decimal". Another is the receipt of "Fraction" being based on the idea of the fraction caused by the equal dividing operation, and without putting "Decimal". Next, the modality of the receipt of "Fraction" of European mathematics in educational was examined. When the education of the arithmetic at the Meiji era period was developed, development being based on the receipt that was based on "Decimal" deeply related to Japanese mathematics "Wasan" culture and "Concrete number" did the main current such as becoming the model of the authorized textbook. On the other hand, development based on the receipt being based on the idea of the fraction caused by the equal dividing operation saw faddish. However, it can be thought that it was excluded from the authorized textbook, and removed from the main current of the development of the arithmetic education gradually. As a result, it is possible to conclude it as follows. By receiving European mathematics, the concept of quantity of taking root in Japanese mathematics "Wasan" culture managed by "Concrete number" including "Decimal" was transformed to the concept of quantity of developing in the direction where it comprehends past "Decimal" and "Fraction" connected with algebra, through to place based on the treatment by "Concrete number" including "Decimal", to catch "Fraction" of European mathematics based on the fraction caused by the division operation, and to catch "Algebra fraction" caused as a result of the multiplication and division calculation.

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　　 The aim of this paper is to clarify what the experienced teachers in Japan have regarded important in constructing mathematics lessons.  Therefore, we interviewed two experienced mathematics teachers by using mathematics lesson documents from the historical resources, which may permit them to reveal the underlying principles of their teaching more easily.  At the result of these interviews, we found some principles that worked when the experienced teachers construct their classroom lessons.  Firstly, the lessons can be identified in terms of “the narrative coherence of a mathematics lesson”.  Secondly, the teachers shape their lessons by dividing them into two parts: before and after setting the problems.  Thirdly, there are four viewpoints in talking about the document; teacher’s own teaching style, children’s learning, contents of teaching and a general teaching style.  We found that experienced mathematics teachers have their own principles of the lesson construction and were able to talk about them through the interviews.

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SN比は簡単で便利な画質評価基準として一般に多くの場で用いられている．しかし，カラー画像のSN比をどう求めるかについては必ずしも充分な検討や理解がされていない．よく見かける方法に，色成分ごとのSN比（dB値）を求め，その平均をカラー画像のSN比とするものがある．しかし，SN比として誤差電力の対数を用いる場合，一旦，各成分のSN比を求めてからその平均をとるのと，各成分画像の誤差電力の平均を求めてからその対数をとるのとでは値が大きく異なることがある．本稿では，複数の色成分を持つ信号において，各成分のSN比の平均をもってそのSN比としてしまうことの問題点を指摘し，カラー画像の場合を例にとって，各成分画像の誤差電力の平均からSN比を計算する場合と，各成分画像のSN比の平均からSN比を導く場合とを比較し，両者の数量的相違について考察する．

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At first, it was considered the method how to extend a line of sight to invisible distant points, because there were described directions toward mountains quite far more than 500 kilometers in the Chinese book of recollected notes from “Chou-Shu”（逸周書）. Land surveying traditionally used geometric methods based on similar triangles to measure distances. By measuring the length of one side of the larger triangle, surveyors could use trigonometry to calculate the length of the other two sides. As nautical distance was impossible to measure directly, its calculated value was obtained by combining two similar triangles using a method called the ‘double difference method’ （重差術）. In astronomical surveying, ‘gnomon shadow length method’ was used for far locations without a line of sight. North-South distance was calculated from difference of shadow length between two points. `Effectiveness of this method’ （一寸千里法） is limited to when the sun is high because this method depends on first-order Tylor approximation of the trigonometric function. The distance values in the historical books are equivalent to differences in shadow length, so the solar altitude can be calculated and then the latitude can be obtained from this.

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粗い空間刻み幅を用いて浸透数値計算を行う際に，グリッド境界透水係数の算出法の相違がどのような影響をもたらすか比較検討した．また，新たに粗い空間刻み幅においても定常状態の圧力水頭分布を近似計算できる，変動重み付け法（η法）を提示した．計算手法として，圧力水頭平均法，体積含水率平均法，透水係数平均法，透水係数相乗平均法，透水係数調和平均法，上流法，η法を比較した．定常状態の数値実験より，上流法，η法を除いて，粗い空間刻み幅の時に圧力水頭分布に空間的な振動が発生することが分かった．ここで，透水係数平均法での振動幅がもっとも大きかった．乾燥土壌への浸透数値実験より，透水係数平均法，上流法，η法で安定して計算可能であることがわかった．一方，圧力水頭平均法，体積含水率平均法，透水係数相乗平均法，透水係数調和平均法において，空間刻み幅を粗くした場合に計算不能になる場合があることが分かった．排水過程での非定常数値計算より，圧力水頭平均法とη法が粗い空間刻み幅においても精度の良い近似結果を示すことが分かった．総合的に見て，粗い空間刻み幅を用いる場合はη法が有効であるが，事前にη値を算出するという前処理が必要になる．

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整数の集合Zに対して,加算を持つ整数の理論(Z,+,-,=,<,0,1)をプレスブルガー(Presburger)

と呼び,古くからその判定問題が決定可能であることが知られている.本稿では,プレスブルガーとその判定問題の解法の概略,並びに判定に要する計算量などについて説明する.また,プログラムやシステム開発におけるプレスブルガーの利用,特に,プログラムの正しさの証明にプレスブルガーがどのように利用可能か,について具体例を交えて説明する.

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