• Title, Summary, Keyword: Metric

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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.

FIXED POINT THEOREMS FOR GENERALIZED NONEXPANSIVE SET-VALUED MAPPINGS IN CONE METRIC SPACES

  • Kim, Seung-Hyun;Lee, Byung-Soo
    • East Asian mathematical journal
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    • v.27 no.5
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    • pp.557-564
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    • 2011
  • In 2007, Huang and Zhang [1] introduced a cone metric space with a cone metric generalizing the usual metric space by replacing the real numbers with Banach space ordered by the cone. They considered some fixed point theorems for contractive mappings in cone metric spaces. Since then, the fixed point theory for mappings in cone metric spaces has become a subject of interest in [1-6] and references therein. In this paper, we consider some fixed point theorems for generalized nonexpansive setvalued mappings under suitable conditions in sequentially compact cone metric spaces and complete cone metric spaces.

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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    • 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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(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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NOTE ON VARIOUS METRIC SPACES

  • Kim, Moon-Jeong
    • East Asian mathematical journal
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    • v.17 no.2
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    • pp.191-195
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    • 2001
  • The purpose of this note is to introduce various metrics and to prove the properties of given metric spaces.

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ON GENERALIZED SUBWAY METRIC

  • KIM, SEHUN;KIM, BYUNGJIN;KIM, JUNGON;KIM, HARAM;KIM, BYUNG HAK
    • Journal of applied mathematics & informatics
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    • v.36 no.1_2
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    • pp.69-79
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    • 2018
  • The Euclid metric is well-known and there are many results on the space with that metric. But there are many other metrics which gives more practical and useful results in the plane. In this paper, we introduce new metric function in the plane, which is more useful in city with subway. Finally we generalize to the general metric space and introduce a new metric on ${\mathbb{R}}^n$.

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.

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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