• Korean Journal of Mathematics
• /
• v.16 no.3
• /
• pp.355-362
• /
• 2008

We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space

• The Pure and Applied Mathematics
• /
• v.23 no.1
• /
• pp.13-19
• /
• 2016

In this paper, we study some characterizations of unbounded domains. Among these, so-called G-domain is introduced by Cabre for the Aleksandrov-Bakelman-Pucci maximum principle of second order linear elliptic operator in a non-divergence form. This domain is generalized to wG-domain by Vitolo for the maximum principle of an unbounded domain, which contains G-domain. We study the properties of these domains and compare some other characterizations. We prove that sA-domain is wG-domain, but using the Cantor set, we are able to construct a example which is wG-domain but not sA-domain.

• Honam Mathematical Journal
• /
• v.43 no.4
• /
• pp.667-678
• /
• 2021

Blow-up phenomena for a nonlocal reaction-diffusion system with time-dependent coefficients are investigated under null Dirichlet boundary conditions. Using Kaplan's method with the comparison principle, we establish new blow-up criteria and obtain the upper bounds for the blow-up time of the solution under suitable measure sense in the whole-dimensional space.

• Korean Journal of Mathematics
• /
• v.22 no.4
• /
• pp.633-644
• /
• 2014

We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.

• Journal of the Korea Convergence Society
• /
• v.10 no.4
• /
• pp.229-236
• /
• 2019

The purpose of this paper is to analyze social phenomena and perceptions by collecting and analyzing data on public opinion, views and trends related to special case of military service in the sports community through Big KINDS operated by the Korea Press Promotion Foundation. To this end, the related keywords were derived and visualized by implementing a LDA(latent dirichlet allocation) technique to derive problems found in social phenomena based on big data analysis. The topics derived include "re-lighting special case on military service," " military service corruption controversy," "special case of military service for athletes," "alternative military service system for artists " and "parliamentary inspection of the administration" This could be used as a basic data for identifying accurate information on social controversies related to special case of military service in the sports community and drawing up practical measures that are considered in line with the principle of just and equal burden.

• Journal of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.41-49
• /
• 2009

Let $\zeta$ be a fixed complex number. In this paper, we study the quantity $S(\zeta,\;n):=mas_{f{\in}{\Lambda}_n}\;|f(\zeta)|$, where ${\Lambda}_n$ is the set of all real polynomials of degree at most n-1 with coefficients in the interval [0, 1]. We first show how, in principle, for any given ${\zeta}\;{\in}\;{\mathbb{C}}$ and $n\;{\in}\;{\mathbb{N}}$, the quantity S($\zeta$, n) can be calculated. Then we compute the limit $lim_{n{\rightarrow}{\infty}}\;S(\zeta,\;n)/n$ for every ${\zeta}\;{\in}\;{\mathbb{C}}$ of modulus 1. It is equal to 1/$\pi$ if $\zeta$ is not a root of unity. If $\zeta\;=\;\exp(2{\pi}ik/d)$, where $d\;{\in}\;{\mathbb{N}}$ and k $\in$ [1, d-1] is an integer satisfying gcd(k, d) = 1, then the answer depends on the parity of d. More precisely, the limit is 1, 1/(d sin($\pi$/d)) and 1/(2d sin($\pi$/2d)) for d = 1, d even and d > 1 odd, respectively.

• Korean Journal of Artificial Intelligence
• /
• v.11 no.2
• /
• pp.7-17
• /
• 2023

Artificial Intelligence (AI) technology has already penetrated deeply into our daily lives, and we live with the convenience of it anytime, anywhere, and sometimes even without us noticing it. However, because AI is imitative intelligence based on human Intelligence, it inevitably has both good and evil sides of humans, which is why ethical principles are essential. The starting point of this study is the AI principles for companies or organizations to develop products. Since the late 2010s, studies on ethics and principles of AI have been actively published. This study focused on AI principles declared by global companies currently developing various products through AI technology. So, we surveyed the AI principles of the Global 500 companies by market capitalization at a given specific time and collected the AI principles explicitly declared by 46 of them. AI analysis technology primarily analyzed this text data, especially LDA (Latent Dirichlet Allocation) topic modeling, which belongs to Machine Learning (ML) analysis technology. Then, we conducted a Delphi technique to reach a meaningful consensus by presenting the primary analysis results. We expect to provide meaningful guidelines in AI-related government policy establishment, corporate ethics declarations, and academic research, where debates on AI ethics and principles often occur recently based on the results of our study.