• Title/Summary/Keyword: algebraic structure

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A Study on Algorithms for Calculating the k-Maximum Capacity Paths in a Network (K-최대용량경로(最大容量經路) 계산법(計算法)에 관한 연구(硏究))

  • Kim, Byung-Su;Kim, Chung-Young
    • Journal of Korean Institute of Industrial Engineers
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    • v.19 no.2
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    • pp.105-117
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    • 1993
  • Methods for calculating k shortest paths in a network system, are based on a analogy which exists between the solution of a network problem and traditional techniques for solving linear equations. This paper modifies an algebraic structure of the K shortest path method and develops k maximum flow methods. On the basis of both theoretical and algebraic structure, three iteration methods are developed and the effective procedure of each method are provided. Finally, computational complexity is discussed for those methods.

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A New Aspect of Comrade Matrices by Reachability Matrices

  • Solary, Maryam Shams
    • Kyungpook Mathematical Journal
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    • v.59 no.3
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    • pp.505-513
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    • 2019
  • In this paper, we study orthanogonal polynomials by looking at their comrade matrices and reachability matrices. First, we focus on the algebraic structure that is exhibited by comrade matrices. Then, we explain some properties of this algebraic structure which helps us to find a connection between comrade matrices and reachability matrices. In the last section, we use this connection to determine the determinant, eigenvalues, and eigenvectors of these matrices. Finally, we derive a factorization for det R(A, x), where R(A, x) is the reachability matrix for a comrade matrix A and x is a vector of indeterminates.

AN ALGEBRAIC STRUCTURE INDUCED BY A FUZZY BI-PARTIALLY ORDERED SPACE I

  • JU-MOK OH
    • Journal of Applied and Pure Mathematics
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    • v.5 no.5_6
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    • pp.347-362
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    • 2023
  • We introduce an algebraic structure induced by a fuzzy bipartial order on a complete residuated lattices with the double negative law. We undertake an investigation into the properties of fuzzy bi-partial orders, including their various characteristics and features. We demonstrate that the two families of l-stable and r-stable fuzzy sets can be regarded as complete lattices, and we establish that these two families are anti-isomorphic. Furthermore, we provide two examples related to them.

Mathematical Thinking and Developing Mathematical Structure

  • Cheng, Chun Chor Litwin
    • Research in Mathematical Education
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    • v.14 no.1
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    • pp.33-50
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    • 2010
  • The mathematical thinking which transforms important mathematical content and developed into mathematical structure is a vital process in building up mathematical ability as mathematical knowledge based on structure. Such process based on students' recognition of mathematical concept. Developing mathematical thinking into mathematical structure happens when different cognitive units are connected and compressed to form schema of solution, which could happen through some guided problems. The effort of arithmetic approach in problem solving did not necessarily provide students the structure schema of solution. The using of equation to solve the problem is based on the schema of building equation, and is not necessary recognizing the structure of the solution, as the recognition of structure may be lost in the process of simplification of algebraic expressions, leaving only the final numeric answer of the problem.

Mathematical Structures of Jeong Yag-yong's Gugo Wonlyu (정약용(丁若鏞)의 산서(算書) 구고원류(勾股源流)의 수학적(數學的) 구조(構造))

  • HONG, Sung Sa;HONG, Young Hee;LEE, Seung On
    • Journal for History of Mathematics
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    • v.28 no.6
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    • pp.301-310
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    • 2015
  • Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.

A study on teaching the system of numbers considering mathematical connections (수학적 연결성을 고려한 수 체계의 지도에 관한 연구)

  • Chung, Young-Woo;Kim, Boo-Yoon;Pyo, Sung-Soo
    • Communications of Mathematical Education
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    • v.25 no.2
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    • pp.473-495
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    • 2011
  • Across the secondary school, students deal with the algebraic conditions like as identity, inverse, commutative law, associative law and distributive law. The algebraic structures, group, ring and field, are determined by these algebraic conditions. But the conditioning of these algebraic structures are not mentioned at all, as well as the meaning of the algebraic structures. Thus, students is likely to be considered the algebraic conditions as productions from the number sets. In this study, we systematize didactically the meanings of algebraic conditions and algebraic structures, considering connections between the number systems and the solutions of the equation. Didactically systematizing is to construct the model for student's natural mental activity, that is, to construct the stream of experience through which students are considered mathematical concepts as productions from necessities and high probability. For this purpose, we develop the program for the gifted, which its objective is to teach the meanings of the number system and to grasp the algebraic structure conceptually that is guaranteed to solve equations. And we verify the effectiveness of this developed program using didactical experiment. Moreover, the program can be used in ordinary students by replacement the term 'algebraic structure' with the term such as identity, inverse, commutative law, associative law and distributive law, to teach their meaning.

A Visualization of the Solution of Truncated Series (절적(截積) 해법의 시각화)

  • Lee, Kyung Eon
    • Journal for History of Mathematics
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    • v.28 no.4
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    • pp.167-179
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    • 2015
  • We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

Algebraic Structure for the Recognition of Korean Characters (한글 문자의 인식을 위한 대수적 구조)

  • Lee, Joo-K.;Choo, Hoon
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.12 no.2
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    • pp.11-17
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    • 1975
  • The paper examined the character structure as a basic study for the recognition of Korean characters. In view of concave structure, line structure and node relationship of character graph, the algebraic structure of the basic Korean characters is are analized. Also, the degree of complexities in their character structure is discussed and classififed. Futhermore, by describing the fact that some equivalence relations are existed between the 10 vowels of rotational transformation group by Affine transformation of one element into another, it could be pointed out that the geometrical properting in addition to the topological properties are very important for the recognition of Korean characters.

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On the instruction of concepts of groups in elementary school (초등학교에서의 군 개념 지도에 관한 연구)

  • 김용태;신봉숙
    • Education of Primary School Mathematics
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    • v.7 no.1
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    • pp.43-56
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    • 2003
  • In late 19C, German mathematician Felix Klein declaired "Erlangen program" to reform mathematics education in Germany. The main ideas of "Erlangen program" contain the importance of instructing the concepts of functions and groups in school mathematics. After one century from that time, the importance of concepts of groups revived by Bourbaki in the sense of the algebraic structure which is the most important structure among three structures of mathematics - algebraic structure. ordered structure and topological structure. Since then, many mathematicians and mathematics educators devoted to work with the concepts of group for school mathematics. This movement landed on Korea in 21C, and now, the concepts of groups appeared in element mathematics text as plane rigid motion. In this paper, we state the rigid motions centered the symmetry - an important notion in group theory, then summarize the results obtained from some classroom activities. After that, we discuss the responses of children to concepts of groups.of groups.

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STABLE CLASS OF EQUIVARIANT ALGEBRAIC VECTOR BUNDLES OVER REPRESENTATIONS

  • Masuda, Mikiya
    • Journal of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.331-349
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    • 2002
  • Let G be a reductive algebraic group and let B, F be G-modules. We denote by $VEC_{G}$ (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that $VEC_{G}$ (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor $VEC_{G}$ (B, $F^{\chi}$) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.