• Title, Summary, Keyword: (pseudo-)metric

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PSEUDO-METRIC ON KU-ALGEBRAS

  • Koam, Ali N.A.;Haider, Azeem;Ansari, Moin A.
    • Korean Journal of Mathematics
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    • v.27 no.1
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    • pp.131-140
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    • 2019
  • In this paper we have introduced the concept of pseudo-metric which we induced from a pseudo-valuation on KU-algebras and investigated the relationship between pseudo-valuations and ideals of KU-algebras. Conditions for a real-valued function to be a pseudo-valuation on KU-algebras are provided.

On N(κ)-Contact Metric Manifolds Satisfying Certain Curvature Conditions

  • De, Avik;Jun, Jae-Bok
    • Kyungpook Mathematical Journal
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    • v.51 no.4
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    • pp.457-468
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    • 2011
  • We consider pseudo-symmetric and Ricci generalized pseudo-symmetric N(${\kappa}$) contact metric manifolds. We also consider N(${\kappa}$)-contact metric manifolds satisfying the condition $S{\cdot}R$ = 0 where R and S denote the curvature tensor and the Ricci tensor respectively. Finally we give some examples.

BCK/BCI-ALGEBRAS WITH PSEUDO-VALUATIONS

  • Doh, Myung-Im;Kang, Min-Su
    • Honam Mathematical Journal
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    • v.32 no.2
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    • pp.217-226
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    • 2010
  • Using the Bu$\c{s}$neag's model ([1, 2, 3]), the notion of pseudo-valuations (valuations) on a ${\mathbf{BCK/BCI}}$-algebra is introduced, and a pseudo-metric is induced by a pseudo-valuation on ${\mathbf{BCK/BCI}}$-algebras. Based on the notion of (pseudo) valuation, we show that the binary operation in ${\mathbf{BCK/BCI}}$-algebras is uniformly continuous.

Multidimensional Scaling Using the Pseudo-Points Based on Partition Method (분할법에 의한 가상점을 활용한 다차원척도법)

  • Shin, Sang Min;Kim, Eun-Seong;Choi, Yong-Seok
    • The Korean Journal of Applied Statistics
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    • v.28 no.6
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    • pp.1171-1180
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    • 2015
  • Multidimensional scaling (MDS) is a graphical technique of multivariate analysis to display dissimilarities among individuals into low-dimensional space. We often have two kinds of MDS which are metric MDS and non-metric MDS. Metric MDS can be applied to quantitative data; however, we need additional information about variables because it only shows relationships among individuals. Gower (1992) proposed a method that can represent variable information using trajectories of the pseudo-points for quantitative variables on the metric MDS space. We will call his method a 'replacement method'. However, the trajectory can not be represented even though metric MDS can be applied to binary data when we apply his method to binary data. Therefore, we propose a method to represent information of binary variables using pseudo-points called a 'partition method'. The proposed method partitions pseudo-points, accounting both the rate of zeroes and ones. Our metric MDS using the proposed partition method can show the relationship between individuals and variables for binary data.

A Note on the Semi-Continuity in Topological Space

  • Han, Chun Ho
    • The Mathematical Education
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    • v.22 no.1
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    • pp.31-33
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    • 1983
  • In this paper, we investigate the properties of the semi-continuous functions on the first axiom space, n-th product space, pseudo-metric space, and proximity space. Counterexample is used when the converse of the theorem is not hold.

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ON $\varepsilon$-BIRKHOFF ORTHOGONALITY AND $\varepsilon$-NEAR BEST APPROXIMATION

  • Sharma, Meenu;Narang, T.D.
    • The Pure and Applied Mathematics
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    • v.8 no.2
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    • pp.153-162
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    • 2001
  • In this Paper, the notion of $\varepsilon$-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. Mat. 29(1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Approx. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each $\varepsilon$>0 there exists a continuous $\varepsilon$-near best approximation $\phi$ : X → M of X by M then M is a chebyshev set .

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AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES

  • Park Jong-Jin;Zhang Yong
    • Communications of the Korean Mathematical Society
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    • v.21 no.2
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    • pp.355-361
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    • 2006
  • We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on $S^1$, then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.