• Kyungpook Mathematical Journal
• /
• 제47권3호
• /
• pp.439-448
• /
• 2007

In the paper, we use the theory of normal family to study the problem on entire function that share a finite non-zero value with their derivatives and prove a uniqueness theorem which improve the result of J.P. Wang and H.X. Yi.

• 인지과학
• /
• 제28권3호
• /
• pp.173-191
• /
• 2017

The theories of cultural evolution hold subtly or clearly different stances about definition of culture, pattern of cultural evolution, biases that affect cultural evolution, and relationship between culture and organism. However, the cultural evolution theories have a common problem to solve: As the evolutionary theory of life tries to explain the early steps and the origin of life, the cultural evolution theories also must explain the early steps of the cultural evolution and the role of the human capability that makes cultural evolution possible. Therefore, explanations of the human's unique traits including the cultural ability are related to determine which one is the most plausible among many cultural evolution theories. Theories that tried to explain human uniqueness commonly depict the coevolution of gene (organism) and culture. We will explicitly call the niche construction theory and the dual inheritance theory the 'gene-culture co-evolutionary theory'. In these theories, the most important concept is the 'concept of positive feedback'. In this paper, we distinguish between core positive feedback and marginal positive feedback, according to whether the trait that the concept of positive feedback explains is the trait of human uniqueness. Both types of positive feedback effectively explain the generality of human uniqueness and the diversity of human traits driven by cultural groups. However, this positive feedback requires an end, in contrast to negative feedback which can be continued in order to maintain homeostasis. We argue that the co-evolutionary process in the gene-culture co-evolutionary theories include only the positive feedback, not covering the cultural evolution after the positive feedback. This thesis strives to define the coevolution concept more comprehensively by suggesting the potential relationships between gene and culture after the positive feedback.

• Kyungpook Mathematical Journal
• /
• 제54권4호
• /
• pp.511-519
• /
• 2014

In this paper, we prove two uniqueness theorem on meromorphic functions sharing one value which generalize a recent result of R. S. Dyavanal [2], and on the other hand, we relax the nature of sharing value from CM to IM.

• Kyungpook Mathematical Journal
• /
• 제54권3호
• /
• pp.349-363
• /
• 2014

In this paper, we shall utilize Nevanlinna value distribution theory to study the uniqueness problems on entire functions and differential polynomials sharing one value. Our theorems improve or generalize some results of Zhang and Lin, Chen, Zhang, Lin and Chen.

• 대한수학회논문집
• /
• 제39권1호
• /
• pp.105-116
• /
• 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.

• 한국해양공학회:학술대회논문집
• /
• 한국해양공학회 2002년도 춘계학술대회 논문집
• /
• pp.231-236
• /
• 2002

By using the infinite dimensional optimization[Jang and Kinoshita(2000)]. which is based on the Hilbert space theory, optimal marine propellers are studied. The mathematical uniqueness for the optimized propeller is shown in this study. As a numerical example, the MAU type propeller is considered and used as the initial guess for the optimization method. The numerical results for an optimal marine propeller is illustrated for the pitch distribution.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제19권2호
• /
• pp.103-109
• /
• 2012

The existence and uniqueness of T-periodic solutions for the following p-Laplacian equations: $$({\phi}_p(x^{\prime}))^{\prime}+{\alpha}(t)x^{\prime}+g(t,x)=e(t),\;x(0)=x(T),x^{\prime}(0)=x^{\prime}(T)$$ are investigated, where ${\phi}_p(u)={\mid}u{\mid}^{p-2}u$ with $p$ > 1 and ${\alpha}{\in}C^1$, $e{\in}C$ are T-periodic and $g$ is continuous and T-periodic in $t$. By using coincidence degree theory, some existence and uniqueness results are obtained.

• Journal of applied mathematics & informatics
• /
• 제40권5_6호
• /
• pp.995-1002
• /
• 2022

In this paper, we study the uniqueness of meromorphic functions sharing a unique range sets Ignoring multiplicities. This paper improves the result of Pulak sahoo and Anjan Sarkar [15].

• 대한수학회논문집
• /
• 제32권2호
• /
• pp.361-373
• /
• 2017

In this paper, we utilize the Nevanlinna theory and uniqueness theory of meromorphic function to investigate the differential-difference analogue of $Br{\ddot{u}}ck$ conjecture. In other words, we consider ${\Delta}_{\eta}f(z)=f(z+{\eta})-f(z)$ and f'(z) share one value or one small function, and then obtain the precise expression of transcendental entire function f(z) under certain conditions, where ${\eta}{\in}{\mathbb{C}}{\backslash}\{0\}$ is a constant such that $f(z+{\eta})-f(z){\not\equiv}0$.

• Journal of applied mathematics & informatics
• /
• 제41권4호
• /
• pp.765-780
• /
• 2023

In this paper, we explore the uniqueness property between the transcendental meromorphic functions and differential polynomial. With the notion of weighted sharing, we generalised the many previous results on uniqueness property. Here we discussed the uniqueness of [P(f)(αf^m + β)^s]^(k) - η(z) and [P(g)(αg^m + β)^s]^(k) - η(z). Meanwhile, we generalised the result of Harina P. waghamore and Rajeshwari S[1].