• 제목/요약/키워드: the Four conjecture

검색결과 13건 처리시간 0.02초

UNIVERSAL QUADRATIC FORMS OVER POLYNOMIAL RINGS

  • Kim, Myung-Hwan;Wang, Yuanhua;Xu, Fei
    • 대한수학회지
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    • 제45권5호
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    • pp.1311-1322
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    • 2008
  • The Fifteen Theorem proved by Conway and Schneeberger is a criterion for positive definite quadratic forms over the rational integer ring to be universal. In this paper, we give a proof of an analogy of the Fifteen Theorem for definite quadratic forms over polynomial rings, which is known as the Four Conjecture proposed by Gerstein.

ON KRAMER-MESNER MATRIX PARTITIONING CONJECTURE

  • Rho, Yoo-Mi
    • 대한수학회지
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    • 제42권4호
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    • pp.871-881
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    • 2005
  • In 1977, Ganter and Teirlinck proved that any $2t\;\times\;2t$ matrix with 2t nonzero elements can be partitioned into four sub-matrices of order t of which at most two contain nonzero elements. In 1978, Kramer and Mesner conjectured that any $mt{\times}nt$ matrix with kt nonzero elements can be partitioned into mn submatrices of order t of which at most k contain nonzero elements. In 1995, Brualdi et al. showed that this conjecture is true if $m = 2,\;k\;\leq\;3\;or\;k\geq\;mn-2$. They also found a counterexample of this conjecture when m = 4, n = 4, k = 6 and t = 2. When t = 2, we show that this conjecture is true if $k{\leq}5$.

KNOTS ADMITTING SEIFERT-FIBERED SURGERIES OVER S2 WITH FOUR EXCEPTIONAL FIBERS

  • Kang, Sungmo
    • 대한수학회보
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    • 제52권1호
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    • pp.313-321
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    • 2015
  • In this paper, we construct infinite families of knots in $S^3$ which admit Dehn surgery producing a Seifert-fibered space over $S^2$ with four exceptional fibers. Also we show that these knots are turned out to be satellite knots, which supports the conjecture that no hyperbolic knot in $S^3$ admits a Seifert-fibered space over $S^2$ with four exceptional fibers as Dehn surgery.

WEAKLY EINSTEIN CRITICAL POINT EQUATION

  • Hwang, Seungsu;Yun, Gabjin
    • 대한수학회보
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    • 제53권4호
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    • pp.1087-1094
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    • 2016
  • On a compact n-dimensional manifold M, it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, after derivng an interesting curvature identity, we show that the conjecture is true in dimension three and four when g is weakly Einstein. In higher dimensional case $n{\geq}5$, we also show that the conjecture is true under an additional Ricci curvature bound. Moreover, we prove that the manifold is isometric to a standard n-sphere when it is n-dimensional weakly Einstein and the kernel of the linearized scalar curvature operator is nontrivial.

ON PARTIAL SUMS OF FOUR PARAMETRIC WRIGHT FUNCTION

  • Din, Muhey U
    • 대한수학회논문집
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    • 제37권3호
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    • pp.681-692
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    • 2022
  • Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al. [15]. Some examples are also discussed for the sake of better understanding of this article.

7차 수학과 교육과정 작도 영역의 교과서와 수업사례 분석 (The Analysis Textbooks and Instruction Activities of Construction Contents in 7th Mathematics Curriculum)

  • 조완영;정보나
    • 대한수학교육학회지:학교수학
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    • 제4권4호
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    • pp.601-615
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    • 2002
  • This paper analyzed <7-나> and <8-나> textbooks and teacher instruction activities in classrooms, focusing on procedures used to solve construction problems. The analysis of the teachers' instruction and organization of the construction unit in <7-나> textbooks showed that the majority of the textbooks focused on the second step, i.e., the constructive step. Of the four steps for solving construction problems, teachers placed the most emphasis on the constructive order. The result of the analysis of <8-나> textbooks showed that a large number of textbooks explained the meaning of theorems that were to be proved, and that teachers demonstrated new terms by using a paper-folding activities, but there were no textbooks that tried to prove theorems through the process of construction. Here are two alternative suggestions for teaching strategies related to the construction step, a crucial means of connecting intuitive geometry with formal geometry. First, it is necessary to teach the four steps for solving construction problems in a practical manner and to divide instruction time evenly among the <7-나> textbooks' construction units. The four steps are analysis, construction, verification, and reflection. Second, it is necessary to understand the nature of geometrical figures involved before proving the problems and introducing the construction part as a tool for conjecture upon theorems used in <8-나> textbooks' demonstrative geometry units.

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남.북한 중등학교 수학 교과서의 영역별 내용 비교 분석 -대수, 통계, 해석, 기하 영역을 중심으로- (Comparative Study on Mathematics Text-book of Secondary Schools in South and North Korea -From the Viewpoint of the Region of Algebra, Statistics, Analysis and Geometry-)

  • 김삼태;이식
    • 한국수학교육학회지시리즈A:수학교육
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    • 제38권1호
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    • pp.1-14
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    • 1999
  • It has already been fifty years since the Korean peninsula was divided into two nations, South and North Korea. Owing to forming different political and social structures with each other, we can conjecture that there are much heterogeneity in education. On the assumption that education plays important role in coming to an accommodation and in restoring homogeneity of the Korean race after unification, we consider the investigation of the contents of mathematics text-book of secondary schools as a meaningful research to make provision against unification. In this paper, we shall investigate the learning contents, and the teaming substances and sequences in mathematics of secondary schools between South and North Korea by falling into four regions; algebra and statistics, analysis and geometry. By grasping the special features of terms, teaming subject matters and learning substances, and clarifying their distinctions, we shall present some reforms measure of distinctions.

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