• Title/Summary/Keyword: metric

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Generalized G-Metric Spaces

  • Hayoung, Choi;Sejong, Kim;Seung Yeop, Yang
    • Kyungpook Mathematical Journal
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    • v.62 no.4
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    • pp.773-785
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    • 2022
  • In this paper, we propose the notion of a distance between n points, called a g-metric, which is a further generalized G-metric. Indeed, it is shown that the g-metric with dimension 2 is the ordinary metric and the g-metric with dimension 3 is equivalent to the G-metric.

A GENERALIZED HURWITZ METRIC

  • Arstu, Arstu;Sahoo, Swadesh Kumar
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.5
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    • pp.1127-1142
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    • 2020
  • In 2016, the Hurwitz metric was introduced by D. Minda in arbitrary proper subdomains of the complex plane and he proved that this metric coincides with the Poincaré's hyperbolic metric when the domains are simply connected. In this paper, we provide an alternate definition of the Hurwitz metric through which we could define a generalized Hurwitz metric in arbitrary subdomains of the complex plane. This paper mainly highlights various important properties of the Hurwitz metric and the generalized metric including the situations where they coincide with each other.

(A Study on Software Quality Metric Methodology and Application for Software Quality Measurement) (소프트웨어 품질측정을 위한 소프트웨어 품질매트릭 방법론과 적용 연구)

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    • Journal of the military operations research society of Korea
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    • v.22 no.2
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    • pp.90-112
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    • 1996
  • Research issues in software engineering in recent may be object oriented methodology and software quality. Since Halstead has proposed metric-software science in 1977, software quality area has been studied in steady but inactively until 1980s. As international standards such as ISO 9000-3, 9126 were enacted in 1990s early, interest in software quality is increased but many problems such as how to validate metric, measure quality or apply metric are remained. This paper proposes software quality metric methodology which software developer or project manager can use in measuring quality and validating metric during software development. The methodology is classified by several phases: establishment of quality requirement, identification of quality metric, data collection, metric implementation, metric validation. In order to show its applicability, test program, metrics and data are applied to each phase of the methodology. Consideration of this methodology as a methodology for software quality measurement similar to development methodology for software development is needed.

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Sequential Decoding of Convolutional Codes with Universal Metric over Bursty-Noise Channel (버스트잡음 채널에서 Universal Metric을 이용한 컨벌루션 부호의 축차복호)

  • Moon, Byung-Hyun;Lee, Chae-Wook
    • Proceedings of the Korea Society for Industrial Systems Conference
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    • 1997.11a
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    • pp.435-449
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    • 1997
  • In this paper, a new metric, universal metric, is Proposed for sequential decoding of convolutional decoding. The complexity of Fano metric for Fano's sequential decoding algorithm is compared with that of the proposed universal metric. Since the Fano metric assumes that it has previous knowledge of channel transition probability, the complexity of Fano metric increases as the assumed channel error probability does not coincide with the true channel error probability. However, the universal metric dose not require the previous knowledge of the channel transition probability since it is estimated on a branch by branch basis. It is shown that the complexity of universal metric is much less than that of the Fano metric for bursty noisy channel.

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CERTAIN SOLITONS ON GENERALIZED (𝜅, 𝜇) CONTACT METRIC MANIFOLDS

  • Sarkar, Avijit;Bhakta, Pradip
    • Korean Journal of Mathematics
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    • v.28 no.4
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    • pp.847-863
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    • 2020
  • The aim of the present paper is to study some solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds. We study gradient Yamabe solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds. It is proved that if the metric of a three dimensional generalized (𝜅, 𝜇)-contact metric manifold is gradient Einstein soliton then ${\mu}={\frac{2{\kappa}}{{\kappa}-2}}$. It is shown that if the metric of a three dimensional generalized (𝜅, 𝜇)-contact metric manifold is closed m-quasi Einstein metric then ${\kappa}={\frac{\lambda}{m+2}}$ and 𝜇 = 0. We also study conformal gradient Ricci solitons on three dimensional generalized (𝜅, 𝜇)-contact metric manifolds.

SOME REMARKS ON THURSTON METRIC AND HYPERBOLIC METRIC

  • Sun, Zongliang
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.2
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    • pp.399-410
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    • 2016
  • In this paper, we study the relations between the Thurston metric and the hyperbolic metric on a closed surface of genus $g{\geq}2$. We show a rigidity result which says if there is an inequality between the marked length spectra of these two metrics, then they are isotopic. We obtain some inequalities on length comparisons between these metrics. Besides, we show certain distance distortions under conformal graftings, with respect to the $Teichm{\ddot{u}}ller$ metric, the length spectrum metric and Thurston's asymmetric metrics.

DISCUSSION ON b-METRIC SPACES AND RELATED RESULTS IN METRIC AND G-METRIC SPACES

  • Bataihah, Anwar;Qawasmeh, Tariq;Shatnawi, Mutaz
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.2
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    • pp.233-247
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    • 2022
  • In the present manuscript, we employ the concepts of Θ-map and Φ-map to define a strong (𝜃, 𝜙)s-contraction of a map f in a b-metric space (M, db). Then we prove and derive many fixed point theorems as well as we provide an example to support our main result. Moreover, we utilize our results to obtain many results in the settings of metric and G-metric spaces. Our results improve and modify many results in the literature.

A Finsler space with a special metric function

  • Park, Hong-Suh;Lee, Il-Young
    • Communications of the Korean Mathematical Society
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    • v.11 no.2
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    • pp.415-421
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    • 1996
  • In this paper, we shall find the conditions that the Finsler space with a special $(\alpha,\beta)$-metric be a Riemannian space and a Berwald space.

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