• Title/Summary/Keyword: shifts sharing values

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MEROMORPHIC FUNCTIONS SHARING FOUR VALUES WITH THEIR DIFFERENCE OPERATORS OR SHIFTS

  • Li, Xiao-Min;Yi, Hong-Xun
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1213-1235
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    • 2016
  • We prove a uniqueness theorem of nonconstant meromorphic functions sharing three distinct values IM and a fourth value CM with their shifts, and prove a uniqueness theorem of nonconstant entire functions sharing two distinct small functions IM with their shifts, which respectively improve Corollary 3.3(a) and Corollary 2.2(a) from [12], where the meromorphic functions and the entire functions are of hyper order less than 1. An example is provided to show that the above results are the best possible. We also prove two uniqueness theorems of nonconstant meromorphic functions sharing four distinct values with their difference operators.

ON PARTIAL VALUE SHARING RESULTS OF MEROMORPHIC FUNCTIONS WITH THEIR SHIFTS AND ITS APPLICATIONS

  • Noulorvang, Vangty;Pham, Duc Thoan
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.5
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    • pp.1083-1094
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    • 2020
  • In this paper, we give some uniqueness theorems of nonconstant meromorphic functions of hyper-order less than one sharing partially three or four small periodic functions with their shifts. As an application, some sufficient conditions for periodicity of meromorphic functions are given. Our results improve and extend previous results of W. Lin, X. Lin and A. Wu [11].

ON THE UNIQUENESS OF MEROMORPHIC FUNCTION AND ITS SHIFT SHARING VALUES WITH TRUNCATED MULTIPLICITIES

  • Nguyen, Hai Nam;Noulorvang, Vangty;Pham, Duc Thoan
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.3
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    • pp.789-799
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    • 2019
  • In this paper, we deal with unicity of a nonconstant zero-order meromorphic function f(z) and its shift f(qz) when they share four distinct values IM or share three distinct values with multiplicities truncated to level 4 in the extended complex plane, where $q{\in}\mathbb{C}{\setminus}\{0\}$. We also give an uniqueness result for f(z) sharing sets with its shift.

ON A UNIQUENESS QUESTION OF MEROMORPHIC FUNCTIONS AND PARTIAL SHARED VALUES

  • Imrul Kaish;Rana Mondal
    • Communications of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.105-116
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    • 2024
  • In this paper, we prove a uniqueness theorem of non-constant meromorphic functions of hyper-order less than 1 sharing two values CM and two partial shared values IM with their shifts. Our result in this paper improves and extends the corresponding results from Chen-Lin [2], Charak-Korhonen-Kumar [1], Heittokangas-Korhonen-Laine-Rieppo-Zhang [9] and Li-Yi [12]. Some examples are provided to show that some assumptions of the main result of the paper are necessary.

MEROMORPHIC FUNCTIONS PARTIALLY SHARED VALUES WITH THEIR SHIFTS

  • Lin, Weichuan;Lin, Xiuqing;Wu, Aidi
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.469-478
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    • 2018
  • We prove some uniqueness theorems of nonconstant meromorphic functions partially sharing values with their shifts. As an application, we obtain a sufficient condition on periodic meromorphic functions. Moreover, some examples are given to illustrate that the conditions are sharp and necessary.

MEROMORPHIC FUNCTIONS SHARING 1CM+1IM CONCERNING PERIODICITIES AND SHIFTS

  • Cai, Xiao-Hua;Chen, Jun-Fan
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.45-56
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    • 2019
  • The aim of this paper is to investigate the problems of meromorphic functions sharing values concerning periodicities and shifts. In this paper we prove the following result: Let f(z) and g(z) be two nonconstant entire functions, let $c{\in}{\mathbb{C}}{\setminus}\{0\}$, and let $a_1$, $a_2$ be two distinct finite complex numbers. Suppose that ${\mu}(f){\neq}1$, ${\rho}_2(f)<1$, and f(z) = f(z+c) for all $z{\in}{\mathbb{C}}$. If f(z) and g(z) share $a_1$ CM, $a_2$ IM, then $f(z){\equiv}g(z)$. Moreover, examples are given to show that all the conditions are necessary.

STUDY OF ENTIRE AND MEROMORPHIC FUNCTION FOR LINEAR DIFFERENCE-DIFFERENTIAL POLYNOMIALS

  • S. RAJESHWARI;P. NAGASWARA
    • Journal of Applied and Pure Mathematics
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    • v.5 no.5_6
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    • pp.281-289
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    • 2023
  • We investigate the value distribution of difference-differential polynomials of entire and meromorphic functions, which can be gazed as the Hayman's Conjecture. And also we study the uniqueness and existence for sharing common value of difference-differential polynomials.

Case Study on the Enterprise Microblog Usage: Focusing on Knowledge Management Strategy (기업용 마이크로블로그의 사용행태에 대한 사례연구: 지식경영전략을 중심으로)

  • Kang, Min Su;Park, Arum;Lee, Kyoung-Jun
    • Journal of Intelligence and Information Systems
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    • v.21 no.1
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    • pp.47-63
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    • 2015
  • As knowledge is paid attention as a new production factor that generates added value, studies continue to apply knowledge management to business environment. In addition, as ICT (Information Communication Technology) was engrafted in business environment, it leads to increasing task efficiency and productivity of individual workers. Accordingly, the way that a business achieves its goal has changed to one in which its individual members are willing to take part in the organization and share information to create new values (Han, 2003) and studies for the system and service to support such transition are carrying out. Of late, a new concept called 'Enterprise 2.0' newly appears. It is the extension of Wen 2.0 and its technology, which focus on participation, sharing and openness, to the work environment of a business (Jung, 2013). Enterprise 2.0 is being used as a collaborative tool to prop up individual creativity and group brain power by combining Web 2.0 technologies such as blog, Wiki, RSS and tag with business software (McAfee, 2006). As Tweeter gets popular, Enterprise Microblog (EMB), which is an example of Enterprise 2.0 for business, has been developed as equivalent to Tweeter in business circle and SaaS (Software as a Service) such as Yammer was introduced The studies of EMB mainly focus on demonstrating its usability in terms of intra-firm communication and knowledge management. However existing studies lean too much towards large-sized companies and certain departments, rather than a company as a whole. Therefore, few studies have been conducted on small and medium-sized companies that have difficulty preparing separate resources and supplying exclusive workforce to introduce knowledge management. In this respect, the present study placed its analytic focus on small-sized companies actually equipped with EMB to know how they use it. And, based on the findings, this study examined their knowledge management strategies for EMB from the point of codification and personalization. Hypothesis -"as a company grows, it shifts EMB strategy from codification to personalization'- was established on the basis of reviewing precedent studies and literature. To demonstrate the hypothesis, this study analyzed the usage of EMB by small companies that have used it from foundation. For case study, the duration of the use was divided into 2 spans and longitudinal analysis was employed to examine the contents of the blogs. Using the key findings of the analysis, this study is aimed to propose practical implications for the operation of knowledge management of small-sized company and the suitable application of knowledge management system for operation Knowledge Management Strategy can be classified by codification strategy and personalization strategy (Hansen et. al., 1999), and how to manage the two strategies were always studied. Also, current studies regarding the knowledge management strategy were targeted mostly for major companies, resulting in lack of studies in how it can be applied on SMEs. This research, with the knowledge management strategy suited for SMEs, sets an Enterprise Microblog (EMB), and with the EMB applied on SMEs' Knowledge Management Strategy, it is reviewed on the perspective of SMEs' Codification and Personalization Strategies. Through the advanced research regarding Knowledge Management Strategy and EMB, the hypothesis is set that "Depending on the development of the company, the main application of EMB alters from Codification Strategy to Personalization Strategy". To check the hypothesis, SME that have used the EMB called 'Yammer' was analyzed from the date of their foundation until today. The case study has implemented longitudinal analysis which divides the period when the EMBs were used into three stages and analyzes the contents. As the result of the study, this suggests a substantial implication regarding the application of Knowledge Management Strategy and its Knowledge Management System that is suitable for SME.