• 제목/요약/키워드: cartesian product

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The Basis Number of the Cartesian Product of a Path with a Circular Ladder, a Möbius Ladder and a Net

  • Alzoubi, Maref Y.;Jaradat, Mohammed M.M.
    • Kyungpook Mathematical Journal
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    • 제47권2호
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    • pp.165-714
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    • 2007
  • The basis number of a graph G is the least positive integer $k$ such that G has a $k$-fold basis. In this paper, we prove that the basis number of the cartesian product of a path with a circular ladder, a M$\ddot{o}$bius ladder and path with a net is exactly 3. This improves the upper bound of the basis number of these graphs for a general theorem on the cartesian product of graphs obtained by Ali and Marougi, see [2]. Also, by this general result, the cartesian product of a theta graph with a M$\ddot{o}$bius ladder is at most 5. But in section 3 we prove that it is at most 4.

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카테시안 곱의 역 맥락에서 분수의 나눗셈 (Division of Fractions in the Contexts of the Inverse of a Cartesian Product)

  • 임재훈
    • 대한수학교육학회지:학교수학
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    • 제9권1호
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    • pp.13-28
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    • 2007
  • 학생들이 분수 나눗셈을 이해하기 어려워하는 이유 중 하나는 분수 나눗셈의 구체화가 어렵고 불충분하기 때문이다. 측정 맥락과 분할 맥락의 구체화에 비해 곱과 인수 맥락에서의 구체화는 상대적으로 부족한 실정이다. 이 연구에서는 카테시안 곱의 역 맥락에서 분수 나눗셈 알고리즘을 구체화하였다. 카테시안 곱의 역 맥락에서 이루어져 있는 기존의 분수 나눗셈 구체화의 한계를 논의하고, 세로의 길이를 고정하고 가로의 길이를 1 또는 자연수로 만드는 방법과 넓이가 1인 직사각형을 이용하는 방법으로 분수 나눗셈을 제시하였다. 이와 같은 방법은 제수의 역수의 의미, 제수를 1로 만드는 것의 중요성, 기존 학습 내용과의 연결성, 다양한 접근 가능성 면에서 장점이 있다. 이와 같은 장점을 살려 카테시안 곱의 역 맥락에서 분수 나눗셈 알고리즘을 도입하는 것을 고려할 수 있다.

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CANCELLATION OF LOCAL SPHERES WITH RESPECT TO WEDGE AND CARTESIAN PRODUCT

  • Hans Scheerer;Lee, Hee-Jin
    • 대한수학회지
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    • 제33권1호
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    • pp.15-23
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    • 1996
  • Let C be a category of (pointed) spaces. For $X, Y \in C$ we denote the wedge (or one point union) by $X \vee Y$ and the cartesian product by $X \times Y$. Let $Z \in C$; we say that Z cancels with respect to wedge (resp. cartesian product) and C, if for all $X, Y \in C$ the existence of a homotopy equivalence $X \vee Z \to Y \vee Z$ implies the existence of a homotopy equivalence $X \to Y$ (resp. for cartesian product). If this does not hold, we say that there is a non-cancellation phenomenon involving Z (and C).

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Cartesian Product Algorithm을 사용한 JavaScript-to-C++ 타입 추론 컴파일러 (JavaScript-to-c++ Type Inferencing Transcompiler Using Cartesian Product Algorithm)

  • 김재주;한환수
    • 한국정보처리학회:학술대회논문집
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    • 한국정보처리학회 2015년도 추계학술발표대회
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    • pp.910-913
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    • 2015
  • 자바스크립트는 웹 페이지를 제어하기 위한 표준적인 스크립트 언어로 오랫동안 사용되어 왔다. 최근 웹 앱이나 서버사이드 응용 프로그램을 자바스크립트로 작성하게 되면서, 자바스크립트 프로그램을 더욱 빠르게 동작하도록 만드는 것이 중요한 이슈가 되었다. 본 논문에서는 암시적인 동적 타입 시스템을 사용하는 자바스크립트 언어에 Cartesian Product Algorithm을 적용하여 타입을 추론하고, 이 정보를 바탕으로 정적 타입 시스템인 C++ 코드로 변환하는 컴파일러의 구조와 알고리즘을 제시한다.

하이브리드 수의 조건부 기대값 (Conditional Expectation of Hybrid Number)

  • ;최규탁;한성일
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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    • pp.18-21
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    • 2003
  • We propose some properties of fuzzy conditional expectation of hybrid number the addition of fuzzy number and random variable using Cartesian product distance for ${\alpha}$-level sets.

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NOTE ON THE MULTIFRACTAL MEASURES OF CARTESIAN PRODUCT SETS

  • Attia, Najmeddine;Guedri, Rihab;Guizani, Omrane
    • 대한수학회논문집
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    • 제37권4호
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    • pp.1073-1097
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    • 2022
  • In this paper, we shall be concerned with evaluation of multifractal Hausdorff measure 𝓗q,t𝜇 and multifractal packing measure 𝓟q,t𝜇 of Cartesian product sets by means of the measure of their components. This is done by investigating the density result introduced in [34]. As a consequence, we get the inequalities related to the multifractal dimension functions, proved in [35], by using a unified method for all the inequalities. Finally, we discuss the extension of our approach to studying the multifractal Hewitt-Stromberg measures of Cartesian product sets.

REVERSE EDGE MAGIC LABELING OF CARTESIAN PRODUCT, UNIONS OF BRAIDS AND UNIONS OF TRIANGULAR BELTS

  • REDDY, KOTTE AMARANADHA;BASHA, S. SHARIEF
    • Journal of applied mathematics & informatics
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    • 제40권1_2호
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    • pp.117-132
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    • 2022
  • Reverse edge magic(REM) labeling of the graph G = (V, E) is a bijection of vertices and edges to a set of numbers from the set, defined by λ : V ∪ E → {1, 2, 3, …, |V| + |E|} with the property that for every xy ∈ E, constant k is the weight of equals to a xy, that is λ(xy) - [λ(x) + λ(x)] = k for some integer k. We given the construction of REM labeling for the Cartesian Product, Unions of Braids and Unions of Triangular Belts. The Kotzig array used in this paper is the 3 × (2r + 1) kotzig array. we test the konow results about REM labelling that are related to the new results we found.

DEGREE OF VERTICES IN VAGUE GRAPHS

  • BORZOOEI, R.A.;RASHMANLOU, HOSSEIN
    • Journal of applied mathematics & informatics
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    • 제33권5_6호
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    • pp.545-557
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    • 2015
  • A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G1 and G2 using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

THE λ-NUMBER OF THE CARTESIAN PRODUCT OF A COMPLETE GRAPH AND A CYCLE

  • Kim, Byeong Moon;Song, Byung Chul;Rho, Yoomi
    • Korean Journal of Mathematics
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    • 제21권2호
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    • pp.151-159
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    • 2013
  • An $L(j,k)$-labeling of a graph G is a vertex labeling such that the difference of the labels of any adjacent vertices is at least $j$ and that of any vertices of distance two is at least $k$ for given $j$ and $k$. The minimum span of all L(2, 1)-labelings of G is called the ${\lambda}$-number of G and is denoted by ${\lambda}(G)$. In this paper, we find a lower bound of the ${\lambda}$-number of the Cartesian product $K_m{\Box}C_n$ of the complete graph $K_m$ of order $m$ and the cycle $C_n$ of order $n$. In fact, we show that when $n{\geq}3$, ${\lambda}(K_4{\Box}C_n){\geq}7$ and the equality holds if and only if n is a multiple of 8. Moreover when $m{\geq}5$, ${\lambda}(K_m{\Box}C_n){\geq}2m-1$ and the equality holds if and only if $n$ is even.