• Title/Summary/Keyword: algebraic structure

Search Result 48, Processing Time 0.128 seconds

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
    • /
    • v.19 no.2
    • /
    • pp.105-117
    • /
    • 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.

  • PDF

A New Aspect of Comrade Matrices by Reachability Matrices

  • Solary, Maryam Shams
    • Kyungpook Mathematical Journal
    • /
    • v.59 no.3
    • /
    • pp.505-513
    • /
    • 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.

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

  • 김용태;신봉숙
    • Education of Primary School Mathematics
    • /
    • v.7 no.1
    • /
    • pp.43-56
    • /
    • 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.

  • PDF

A Two-Step Soft Output Viterbi Algorithm with Algebraic Structure (대수적 구조를 가진 2단 연판정 출력 비터비 알고리듬)

  • 김우태;배상재;주언경
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.26 no.12A
    • /
    • pp.1983-1989
    • /
    • 2001
  • A new two-step soft output Viterbi algorithm (SOVA) for turbo decoder is proposed and analyzed in 7his paper. Due to the algebraic structure of the proposed algorithm, slate and branch metrics can be obtained wish parallel processing using matrix arithmetic. As a result, the number of multiplications to calculate state metrics of each stage and total memory size can be decreased tremendously. Therefore, it can be expected that the proposed algebraic two-step SOVA is suitable for applications in which low computational complexity and memory size are essential.

  • PDF

Synthesizing a Boolean Function of an S-box with Integer Linear Programming (수리계획법을 이용한 S-box의 부울함수 합성)

  • 송정환;구본욱
    • Journal of the Korea Institute of Information Security & Cryptology
    • /
    • v.14 no.4
    • /
    • pp.49-59
    • /
    • 2004
  • Boolean function synthesize problem is to find a boolean expression with in/outputs of original function. This problem can be modeled into a 0-1 integer programming. In this paper, we find a boolean expressions of S-boxes of DES for an example, whose algebraic structure has been unknown for many years. The results of this paper can be used for efficient hardware implementation of a function and cryptanalysis using algebraic structure of a block cipher.

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
    • /
    • v.12 no.2
    • /
    • pp.11-17
    • /
    • 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.

  • PDF

A study on the teaching of algebraic structures in school algebra (학교수학에서의 대수적 구조 지도에 대한 소고)

  • Kim, Sung-Joon
    • Journal of the Korean School Mathematics Society
    • /
    • v.8 no.3
    • /
    • pp.367-382
    • /
    • 2005
  • In this paper, we deal with various contents relating to the group concept in school mathematics and teaching of algebraic structures indirectly by combining these contents. First, we consider structure of knowledge based on Bruner, and apply these discussions to the teaching of algebraic structure in school algebra. As a result of these analysis, we can verify that the essence of algebraic structure is group concept. So we investigate the previous researches about group concept: Piaget, Freudenthal, Dubinsky. In our school, the contents relating to the group concept have been taught from elementary level indirectly. Tn elementary school, the commutative law and associative law is implicitly taught in the number contexts. And in middle school, various linear equations are taught by the properties of equality which include group concept. But these algebraic contents is not related to the high school. Though we deal with identity and inverse in the binary operations in high school mathematics, we don't relate this algebraic topics with the previous learned contents. In this paper, we discussed algebraic structure focusing to the group concept to obtain a connectivity among school algebra. In conclusion, the group concept can take role in relating these algebraic contents and teaching the algebraic structures in school algebra.

  • PDF

SOME PROPERTIES OF MV-ALGEBRAS

  • Ko, Jung Mi;Kim, Yong Chan
    • Korean Journal of Mathematics
    • /
    • v.10 no.1
    • /
    • pp.37-44
    • /
    • 2002
  • In this paper, we obtain an algebraic structure which is equivalent to an MV-algebra. Moreover, we show that $t$-norm and $t$-conorm can be obtained from MV-algebras.

  • PDF

ON THE SIZES OF DUAL GROUPS

  • Song, Joungmin
    • Bulletin of the Korean Mathematical Society
    • /
    • v.59 no.3
    • /
    • pp.609-615
    • /
    • 2022
  • We give a formula for the sizes of the dual groups. It is obtained by generalizing a size estimation of certain algebraic structure that lies in the heart of the proof of the celebrated primality test by Agrawal, Kayal and Saxena. In turn, by using our formula, we are able to give a streamlined survey of the AKS test.