• Title/Summary/Keyword: set of uniqueness

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Meromorphic Functions with Weighted Sharing of One Set

  • Alzahary, Thamir C.
    • Kyungpook Mathematical Journal
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    • v.47 no.1
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    • pp.57-68
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    • 2007
  • In this article, we investigate the problem of uniqueness of meromorphic functions sharing one set and having deficient values, and obtain a result which improves some earlier results.

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UNIQUE RANGE SETS WITHOUT FUJIMOTO'S HYPOTHESIS

  • Chakraborty, Bikash
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.5
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    • pp.1247-1253
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    • 2022
  • This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give an existence of unique range sets for meromorphic functions that are the zero sets of some polynomials that do not necessarily satisfy the Fujimoto's hypothesis ([6]).

Uniqueness of Meromorphic Functions and a Question of Gross

  • Yi, Hong-Xun;Lin, Wei-Chuan
    • Kyungpook Mathematical Journal
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    • v.46 no.3
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    • pp.437-444
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    • 2006
  • In this paper, we deal with the uniqueness of meromorphic functions concerning one question of Gross (see [5, Question 6]), and obtain some results that are improvements of that of former authors. Moreover, the example shows that the result is sharp.

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A Technique for Measuring Terrain Uniqueness from Digital Terrain Elevation Data (수치 고도자료를 이용한 지형의 유일성 평가 알고리즘 연구)

  • Kim, Su-Hwan
    • Journal of the Korea Institute of Military Science and Technology
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    • v.11 no.4
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    • pp.99-106
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    • 2008
  • Digital Terrain Elevation Data is a set of numerical values that represent the heights of the terrain surface. Terrain has several properties. Among them, roughness is the most widely used one because it gives very useful information to land-based or land-reference platform. There are several ways to measure roughness of terrain. But each of them has own flaws. Moreover, it is not enough to represent the uniqueness of the terrain only by the roughness. We need another metric to measure the actual uniqueness. In this paper, we propose an improved method to measure essential characteristics, uniqueness, of terrain. It gives not only the roughness but also the unevenness. The combination of them makes up the uniqueness. And it can be applied even if there is no pre-planned path on the terrain.

UNIQUENESS OF TWO DIFFERENTIAL POLYNOMIALS OF A MEROMORPHIC FUNCTION SHARING A SET

  • Ahamed, Molla Basir
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1181-1203
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    • 2018
  • In this paper, we are mainly devoted to find out the general meromorphic solution of some specific type of differential equation. We have also answered an open question posed by Banerjee-Chakraborty [4] by extending their results in a large extent. We have provided an example showing that the conclusion of the results of Zhang-Yang [16] is not general true. Some examples have been exhibited to show that certain claims are true in our main result. Finally some questions have been posed for the future research in this direction.

Uniqueness of Meromorphic Functions That Share Three Sets

  • Banerjee, Abhijit
    • Kyungpook Mathematical Journal
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    • v.49 no.1
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    • pp.15-29
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    • 2009
  • Dealing with a question of gross, we prove some uniqueness theorems concerning meromorphic functions with the notion of weighted sharing of sets. Our results will not only improve and supplement respectively two results of Lahiri-Banerjee [9] and Qiu and Fang [13] but also improve a very recent result of the present author [1].

CONFORMAL DENSITY OF VISIBILITY MANIFOLD

  • Kim, Hyun-Jung
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.211-222
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    • 2001
  • In this paper, we prove the existence and uniqueness of a $\delta(\Gamma)$-conformal density on the limit set of $\Gamma$ acting on visibility manifold H for a Fuchsian group $\Gamma$.

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