• Title/Summary/Keyword: remainder

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The division algorithm for the finite decimals (유한소수에서의 나눗셈 알고리즘(Division algorithm))

  • Kim, Chang-Su;Jun, Young-Bae;Roh, Eun-Hwan
    • The Mathematical Education
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    • v.50 no.3
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    • pp.309-327
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    • 2011
  • In this paper, we extended the division algorithm for the integers to the finite decimals. Though the remainder for the finite decimals is able to be defined as various ways, the remainder could be defined as 'the remained amount' which is the result of the division and as "the remainder" only if 'the remained amount' is decided uniquely by certain conditions. From the definition of "the remainder" for the finite decimal, it could be inferred that 'the division by equal part' and 'the division into equal parts' are proper for the division of the finite decimal concerned with the definition of "the remainder". The finite decimal, based on the unit of measure, seemed to make it possible for us to think "the remainder" both ways: 1" in the division by equal part when the quotient is the discrete amount, and 2" in the division into equal parts when the quotient is not only the discrete amount but also the continuous amount. In this division context, it could be said that the remainder for finite decimal must have the meaning of the justice and the completeness as well. The theorem of the division algorithm for the finite decimal could be accomplished, based on both the unit of measure of "the remainder", and those of the divisor and the dividend. In this paper, the meaning of the division algorithm for the finite decimal was investigated, it is concluded that this theory make it easy to find the remainder in the usual unit as well as in the unusual unit of measure.

GROUP S3 CORDIAL REMAINDER LABELING OF SUBDIVISION OF GRAPHS

  • LOURDUSAMY, A.;WENCY, S. JENIFER;PATRICK, F.
    • Journal of applied mathematics & informatics
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    • v.38 no.3_4
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    • pp.221-238
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    • 2020
  • Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that subdivision of graphs admit a group S3 cordial remainder labeling.

GROUP S3 CORDIAL REMAINDER LABELING FOR PATH AND CYCLE RELATED GRAPHS

  • LOURDUSAMY, A.;WENCY, S. JENIFER;PATRICK, F.
    • Journal of applied mathematics & informatics
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    • v.39 no.1_2
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    • pp.223-237
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    • 2021
  • Let G = (V (G), E(G)) be a graph and let g : V (G) → S3 be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S3 cordial remainder labeling of G if |vg(i)-vg(j)| ≤ 1 and |eg(1)-eg(0)| ≤ 1, where vg(j) denotes the number of vertices labeled with j and eg(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S3 cordial remainder labeling is called a group S3 cordial remainder graph. In this paper, we prove that square of the path, duplication of a vertex by a new edge in path and cycle graphs, duplication of an edge by a new vertex in path and cycle graphs and total graph of cycle and path graphs admit a group S3 cordial remainder labeling.

A Proposal for the Methodology of Partition of Property by the Married Couple in the Process of Divorce -Applied to the system to division of remainder used in Germany- (부부 이혼시 재산분할액 산정과정에 대한 제안 -독일의 잉여청산제 적용을 중심으로 -)

  • 문숙재;윤소영;이윤신
    • Journal of the Korean Home Economics Association
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    • v.40 no.12
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    • pp.159-170
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    • 2002
  • This study, with a view to establishing the objective and concrete methodology of partition of properly by the married couple in the process of divorce, is to suggest the calculation method of impartial division of property by means of applying the system to division of remainder used in Germany. Generally, the process of estimating the amount of partitioned property has two steps, the first of which is to calculate the remainder of the husband and the wife each. The second step is to compare the remainders of the couple and calculate the difference in order for the spouse who has more to claim the payment of a half of the difference. This method has the advantage of dividing impartially the remainder obtained by labor in the married life.

A Study on the Quotient and Remainder in Division of Decimal (소수 나눗셈에서 몫과 나머지에 관한 소고)

  • Jeong, Sangtae
    • Education of Primary School Mathematics
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    • v.19 no.3
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    • pp.193-210
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    • 2016
  • In the $10{\div}2.4$ problem situation, we could find that curious upper and middle level students' solution. They solved $10{\div}2.4$ and wrote the result as quotient 4, remainder 4. In this curious response, we researched how students realize quotient and remainder in division of decimal. As a result, many students make errors in division of decimal especially in remainder. From these response, we constructed fraction based teaching method about division of decimal. This method provides new aspects about quotient and remainder in division of decimal, so we can compare each aspects' strong points and weak points.

A study on improper notions appeared in dealing with quotient and remainder in division for decimal numbers in Korean elementary math textbooks and its improvements (우리나라 초등학교 수학 교과서의 소수 나눗셈에서의 몫과 나머지 취급에서 나타나는 부적절한 관념과 그 개선에 관한 연구)

  • Park, Kyosik;Kwon, Seokil
    • Journal of Educational Research in Mathematics
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    • v.22 no.4
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    • pp.445-458
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    • 2012
  • Current textbooks may provide students and teachers with three improper notions related to the quotient and the remainder in division for decimal numbers as in the following. First, only the calculated results in (natural numbers)${\div}$(natural numbers) is the quotient. Second, when the quotient and the remainder are obtained in division for decimal numbers, the quotient is natural number and the remainder is unique. Third, only when the quotient cannot be divided exactly, the quotient can be rounded off. These can affect students and teachers on their notions of division for decimal numbers, so improvements are needed for to break it. For these improvements, the following measures are required. First, in the curriculum guidebook, the meaning of the quotient and the remainder in division for decimal numbers should be presented clearly, for preventing the possibility of the construction of such improper notions. Second, examples, problems, and the like should be presented in the textbooks enough to break such improper notions. Third, the didactical intention should be presented clearly with respect to the quotient and the remainder in division for decimal numbers in teacher's manual.

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A COMPUTATIONAL EXPLORATION OF THE CHINESE REMAINDER THEOREM

  • Olagunju, Amos O.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.307-316
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    • 2008
  • Real life problems can be expressed as a congruence modulus n and split into a system of congruence equations in modulus factors of n. A system of congruence equations can be combined into a congruence equation under certain conditions. This paper uniquely presents and critically reviews the generalized Chinese Remainder Theorem (CRT) for combining systems of congruence equations into single congruence equations. Sequential and parallel implementation strategies of the generic CRT are outlined. A variety of unique applications of the CRT are discussed.

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Solution of periodic notch problems in an infinite plate using BIE in conjunction with remainder estimation technique

  • Chen, Y.Z.
    • Structural Engineering and Mechanics
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    • v.38 no.5
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    • pp.619-631
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    • 2011
  • This paper provides a complex variable BIE for solving the periodic notch problems in plane plasticity. There is no limitation for the configuration of notches. For the periodic notch problem, the remainder estimation technique is suggested. In the technique, the influences on the central notch from many neighboring notches are evaluated exactly. The influences on the central notch from many remote notches are approximated by one term with a multiplying factor. This technique provides an effective way to solve the problems of periodic structures. Several numerical examples are presented, and most of them have not been reported previously.

A study of performance improvement of ASK system (ASK 시스템의 성능개선에 관한 연구)

  • Chung, Sung-Boo;Kim, Joo-Woong
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.16 no.1
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    • pp.26-32
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    • 2012
  • In this study, we proposed an intelligent algorithm for the performance improvement of ASK system for giga-bit modem in millimeter band. The proposed intelligent algorithm is a fuzzy logic system. The inputs to the fuzzy logic system are the remainder and integral of remainder that occurred counter of receiver, and the output is bandwidth of LPF. In order to verify the effectiveness of the proposed method, simulation is performed to the proposed system and the fixed bandwidth system, and is confirmed to the BER performance.