• Korean Journal of Mathematics
• /
• v.7 no.1
• /
• pp.85-101
• /
• 1999

Let $p$ be analytic in the unit disc U and let $q$ be univalent in U. In addition, let ${\Omega}$ be a set in C and let ${\psi}:c^3{\times}U{\rightarrow}C$. The author determines conditions on ${\psi}$ so that $$\{{\psi}(p(z),zp^{\prime}(z),z^2p^{{\prime}{\prime}}(z);z){\mid}z{\in}U\}{\subset}{\Omega}{\Rightarrow}p(U){\subset}q(U)$$. Applications of this result to differential inequalities, differential subordinations and integral inequalities are presented.

• Journal of applied mathematics & informatics
• /
• v.42 no.1
• /
• pp.139-148
• /
• 2024

The purpose of this research is to investigate sufficient conditions for the existence of limit cycles of the fifth-order differential equation x⁽⁵⁾ + (p² + q²)$_{x}^{...}$ + p²q²$_{x}^{.}$ = εF(t, x, $_{x}^{.}$, $_{x}^{..}$, $_{x}^{...}$, $_{x}^{....}$), where p, q are rational numbers different from 0, p ≠ ±q, ε is a small real parameter, and F is a 2kπ-periodic function in the variable t. Also, we provide some applications.

• The Journal of Information Systems
• /
• v.14 no.2
• /
• pp.257-276
• /
• 2005

This study adopts diffusion of innovation theory and analyses product life cycle on two different information communication technology (ICT) products. One is telematics located on introduction and the other one is MP3 located on maturity. The analytical results were mixed. ordinary least square (OLS) result showed that adoption of MP3 player is affected by white noise error ($\varepsilon$) and telematics is influenced by innovation effect (p coefficient) rather than imitation effect (q coefficient) or white noise error. However, nonlinear least square (NLS) result showed that adoption of MP3 player is affected by imitation effect (q coefficient) rather than innovation effect (p coefficient). In addition, the ratio of imitation effect/innovation effect of MP3 player is larger than that of telematics.

• Kyungpook Mathematical Journal
• /
• v.46 no.2
• /
• pp.261-271
• /
• 2006

In this paper, we investigate and characterize the class of A-semirings. A characterization of the Thierrin radical of a proper ideal of an A-semiring is given. Moreover, when P is a Q-ideal in the semiring R, it is shown that P is primary if and only if R/P is nilpotent.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.983-1002
• /
• 2021

We investigate the non-existence of finite order transcendental entire solutions of Fermat-type differential-difference equations [f(z)f'(z)]ⁿ + P²(z)f^m(z + 𝜂) = Q(z) and [f(z)f'(z)]ⁿ + P(z)[∆_𝜂f(z)]^m = Q(z), where P(z) and Q(z) are non-zero polynomials, m and n are positive integers, and 𝜂 ∈ ℂ \ {0}. In addition, we discuss transcendental entire solutions of finite order of the following Fermat-type differential-difference equation P²(z) [f^(k)(z)]² + [αf(z + 𝜂) - 𝛽f(z)]² = e^r(z), where $P(z){\not\equiv}0$ is a polynomial, r(z) is a non-constant polynomial, α ≠ 0 and 𝛽 are constants, k is a positive integer, and 𝜂 ∈ ℂ \ {0}. Our results generalize some previous results.

• Korean Journal of Mathematics
• /
• v.22 no.3
• /
• pp.471-489
• /
• 2014

We investigate the number of the weak periodic solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We get one theorem which shows the existence of at least two weak periodic solutions for this system. We obtain this result by using variational method, critical point theory induced from the limit relative category theory.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.155-163
• /
• 2012

Let E be an elliptic curve over $\mathbb{Q}$. Using Iwasawa theory, we give what seems to be the first general upper bound for the order of vanishing of the p-adic L-function at s = 0, and the $\mathbb{Z}_p$-corank of the Tate-Shafarevich group for all sufficiently large good ordinary primes p.

• Korean Journal of Mathematics
• /
• v.4 no.1
• /
• pp.45-49
• /
• 1996

Let $F_0$ be the maximal real subfield of $\mathbb{Q}({\zeta}_q+{\zeta}_q^{-1})$ and $F_{\infty}={\cup}_{n{\geq}0}F_n$ be its basic $\mathbb{Z}_p$-extension. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $F_n$. The aim of this paper is to examine the injectivity of the natural $mapA_n{\rightarrow}A_m$ induced by the inclusion $F_n{\rightarrow}F_m$ when $m>n{\geq}0$. By using cyclotomic units of $F_n$ and by applying cohomology theory, one gets the following result: If $p$ does not divide the order of $A_1$, then $A_n{\rightarrow}A_m$ is injective for all $m>n{\geq}0$.

• The Journal of Korean Physical Therapy
• /
• v.15 no.3
• /
• pp.265-276
• /
• 2003

This study was to investigate the dffects of a color reversal visual perceptual training program on spastic cerebral palsied children's figure-ground discrimination disabilities and to investigate the difference between the control group and experimental group. Subjects of the study were composed of children with spastic cerebral palsy whose age varied from five to seven years old, whose I.Q. was over 70 and whose P.Q. was over 70. Implication of this study can be summarized as follows; First, Perceptual training and speech training programs should be emphasized to improve the preparative ability of spastic cerebral palsied children. Problems of perception cerebral palsied children are concerned with figure-ground discrimination disability. Second, Though it was demonstrated that color reversal visual perceptual training program can be effective through the prestudies and this study, more researches should be made to apply this kind of theory in real education environments. More interest in different color forms for training of cerebral palsied children should be taken. Third, Reprecations of the study should be considered with modified group identities(age, I.Q., P.Q.).

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.62 no.11
• /
• pp.1604-1609
• /
• 2013

When the ground fault on the power side occurs on distribution system interconnected with distributed generations, the abnormal current is generated in the neutral conductor by the connection type and the iron core structure of transformers for the interconnection of distributed power supplies due to the unbalanced voltage of the system, and subsequently the false operation of the protective relay on the load side occurs. Herein, this paper proposes the method to correct errors in the phase current to prevent the false operation of the protective relay by applying p-q theory and presents the simulation result of the error correction algorithm using PSCAD/EMTDC.