• Journal of applied mathematics & informatics
• /
• 제28권3_4호
• /
• pp.679-686
• /
• 2010

This paper is concerned with the following fourth-order four-point Sturm-Liouville boundary value problem $u^{(4)}(t)=f(t,\;u(t),\;u^{\prime\prime}(t))$, $0\;{\leq}\;t\;{\leq}1$, ${\alpha}u(0)-{\beta}u^{\prime}(0)={\gamma}u(1)+{\delta}u^{\prime}(1)=0$, $au^{\prime\prime}(\xi_1)-bu^{\prime\prime\prime}(\xi_1)=cu^{\prime\prime}(\xi_2)+du^{\prime\prime\prime}(\xi_2)=0$. Some sufficient conditions are obtained for the existence of at least one positive solution to the above boundary value problem by using the well-known Guo-Krasnoselskii fixed point theorem.

• 대한수학회지
• /
• 제34권3호
• /
• pp.543-551
• /
• 1997

We prove a norm inequality of the form $\left\$\mid$ \upsilon \right\$\mid$ \leq (r - 1) \left\$\mid$ u \right\$\mid$_p, 1 < p < \infty$, between a non-negative subharmonic function u and a smooth function $\upsilon$ satisfying $$\mid$\upsilon(0)$\mid$ \leq u(0), $\mid$\nabla\upsilon$\mid$ \leq \nabla u$\mid$$ and $\mid$\Delta\upsilon$\mid$ \leq \alpha\Delta u$, where $\alpha$ is a constant with $0 \leq \alpha \leq 1$. This inequality extends Burkholder's inequality where $\alpha = 1$.

• 대한임상검사과학회지
• /
• 제56권2호
• /
• pp.125-134
• /
• 2024

본 연구는 대한민국 성인을 대상으로 대사증후군(metabolic syndrome, MetS) 유·무에 따른 빈혈과 추정 사구체여과율(estimated glomerular filtration rate, eGFR) 및 요 미세 알부민/크레아티닌 비율(urine microalbumin/creatinine ratio, uACR)의 관련성을 평가하기 위하여 2012년 국민건강 영양조사(KNHNES V-3) 자료를 활용하여 20세 이상 성인 4,943명을 대상으로 데이터를 분석하였다. 본 연구에서 몇 가지 중요한 발견이 있었다. 첫째, 비 MetS 그룹에서는 정상군(eGFR≥60 mL/min/1.73 m² 및 uACR<30 mg/g)의 빈혈(남성, 헤모글로빈[hemoglobin, Hb]<13 g/dL; 여성, Hb<12 g/dL)의 발생률에 비하여 감소된 eGFR 그룹(eGFR<60 mL/min/1.73 m²; odds ratio [OR], 3.65; 95% confidence interval [CI], 1.90~7.00) 및 감소된 eGFR+증가된 uACR 그룹(eGFR<60 mL/min/1.73 m² 및 uACR≥30 mg/g, OR, 6.00; 95% CI, 2.61~13.80)의 빈혈 발생률이 높았다. 둘째, MetS 그룹에서는 정상군에 비하여 증가된 uACR 그룹(OR, 2.18; 95% CI, 1.11~4.27), 감소된 eGFR 그룹(OR, 3.73; 95% CI, 1.09~12.75) 및 감소된 eGFR+증가된 uACR 그룹(OR, 18.17; 95% CI, 6.16~53.63)의 빈혈 발생률이 높았다. 결론적으로, 비 MetS 그룹에서는 빈혈은 eGFR의 감소와 관련이 있었고, MetS 그룹에서는 빈혈은 eGFR 감소 및 uACR 증가와 관련이 있었다. 추가적으로, 비 MetS 그룹과 MetS 그룹 모두에서 eGFR의 감소 및 uACR의 증가가 동시에 나타날 때 빈혈의 발생률이 크게 증가하였다.

• Ocean Systems Engineering
• /
• 제11권1호
• /
• pp.83-97
• /
• 2021

The submerged U-shape breakwater interaction with the solitary wave is simulated by the Boussinesq equations using the finite-difference scheme. The wave reflection, transmission, and dissipation (RTD) coefficients are used to investigate the U-shape breakwater's performance for different crest width, Lc1, and indent breakwater height, du. The results show that the submerged breakwater performance for a set of U-shape breakwater with the same cross-section area is related to the length of submerged breakwater crest, Lc1, and the distance between the crests, Lc2 (or the height of du). The breakwater has the maximum performance when the crest length is larger, and at the same time, the distance between them increases. Changing the Lc1 and du of the U-shape breakwaters result in a significant change in the RTD coefficients. Comparison of the U-shape breakwater, having the best performance, with the averaged RTD values shows that the transmission coefficients, Kt, has a better performance of up to 4% in comparison to other breakwaters. Also, the reflection coefficients KR and the diffusion coefficients, Kd shows a better performance of about 30% and 55% on average, respectively. However, the model governing equations are non-dissipative. The non-energy conserving of the transmission and reflection coefficients due to wave and breakwater interaction results in dissipation type contribution. The U-shape breakwater with the best performance is compared with the rectangular breakwater with the same cross-section area to investigate the economic advantages of the U-shape breakwater. The transmission coefficients, Kt, of the U-shape breakwater shows a better performance of 5% higher than the rectangular one. The reflection coefficient, KR, is 60% lower for U-shape in comparison to rectangular one; however, the diffusion coefficients, Kd, of U-shape breakwater is 35% higher than the rectangular breakwater. Therefore, we could say that the U-shape breakwater has a better performance than the rectangular one.

• Korean Journal of Mathematics
• /
• 제23권4호
• /
• pp.537-555
• /
• 2015

This paper is concerned with the existence of solutions to the following fractional differential inclusion $$\{-{\frac{d}{dx}}\(p_0D^{-{\beta}}_x(u^{\prime}(x)))+q_xD^{-{\beta}}_1(u^{\prime}(x))\){\in}{\partial}F_u(x,u),\;x{\in}(0,1),\\u(0)=u(1)=0,$$ where $_0D^{-{\beta}}_x$ and $_xD^{-{\beta}}_1$ are left and right Riemann-Liouville fractional integrals of order ${\beta}{\in}(0,1)$ respectively, 0 < p = 1 - q < 1 and $F:[0,1]{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is locally Lipschitz with respect to the second variable. Due to the general assumption on the constants p and q, the problem does not have a variational structure. Despite that, here we study it combining with an iterative technique and nonsmooth critical point theory, we obtain an existence result for the above problem under suitable assumptions. The result extends some corresponding results in the literatures.

• Korean Journal of Mathematics
• /
• 제16권3호
• /
• 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

• Kyungpook Mathematical Journal
• /
• 제64권1호
• /
• pp.113-131
• /
• 2024

In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term ∆_p u + 𝛼|u|^q-1u + 𝛽x.∇(|u|^q-1u) = 0 for x ∈ ℝ^N, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆_p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.

• Korean Journal of Mathematics
• /
• 제19권3호
• /
• pp.331-342
• /
• 2011

We consider the multiplicity of the solutions for a class of a system of critical growth beam equations with periodic condition on t and Dirichlet boundary condition $$\{u_{tt}+u_{xxxx}=av+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{{\alpha}-1}v_{+}^{\beta}+s{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,\\u_{tt}+v_{xxxx}=bu+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{\alpha}v_{+}^{{\beta}-1}+t{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,$$ where ${\alpha}$, ${\beta}$ > 1 are real constants, $u_+=max\{u,0\}$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_00=1$ of the eigenvalue problem $u_{tt}+u_{xxxx}={\lambda}_{mn}u$. We show that the system has a positive solution under suitable conditions on the matrix $A=\(\array{0&a\\b&0}\)$, s > 0, t > 0, and next show that the system has another solution for the same conditions on A by the linking arguments.

• 대한수학회보
• /
• 제55권4호
• /
• pp.1189-1208
• /
• 2018

The aim of this paper is to study the class of ${\Lambda}$-constacyclic codes of length $2p^s$ over the finite commutative chain ring ${\mathcal{R}}_a=\frac{{\mathbb{F}_{p^m}}[u]}{{\langle}u^a{\rangle}}={\mathbb{F}}_{p^m}+u{\mathbb{F}}_{p^m}+{\cdots}+u^{a-1}{\mathbb{F}}_{p^m}$, for all units ${\Lambda}$ of ${\mathcal{R}}_a$ that have the form ${\Lambda}={\Lambda}_0+u{\Lambda}_1+{\cdots}+u^{a-1}{\Lambda}_{a-1}$, where ${\Lambda}_0,{\Lambda}_1,{\cdots},{\Lambda}_{a-1}{\in}{\mathbb{F}}_{p^m}$, ${\Lambda}_0{\neq}0$, ${\Lambda}_1{\neq}0$. The algebraic structure of all ${\Lambda}$-constacyclic codes of length $2p^s$ over ${\mathcal{R}}_a$ and their duals are established. As an application, this structure is used to determine the Rosenbloom-Tsfasman (RT) distance and weight distributions of all such codes. Among such constacyclic codes, the unique MDS code with respect to the RT distance is obtained.

• 호남수학학술지
• /
• 제27권2호
• /
• pp.301-315
• /
• 2005

Let $\{A_u,\;u=0,\;1,\;2,\;{\cdots}\}$ be a sequence of coefficient matrices such that ${\sum}_{u=0}^{\infty}{\parallel}A_u{\parallel}<{\infty}$ and ${\sum}_{u=0}^{\infty}\;A_u{\neq}O_{m{\times}m}$, where for any $m{\times}m(m{\geq}1)$, matrix $A=(a_{ij})$, ${\parallel}A{\parallel}={\sum}_{i=1}^m{\sum}_{j=1}^m{\mid}a_{ij}{\mid}$ and $O_{m{\times}m}$ denotes the $m{\times}m$ zero matrix. In this paper, a functional central limit theorem is derived for a stationary m-dimensional linear process ${\mathbb{X}}_t$ of the form ${\mathbb{X}_t}={\sum}_{u=0}^{\infty}A_u{\mathbb{Z}_{t-u}}$, where $\{\mathbb{Z}_t,\;t=0,\;{\pm}1,\;{\pm}2,\;{\cdots}\}$ is a stationary sequence of linearly positive quadrant dependent m-dimensional random vectors with $E({\mathbb{Z}_t})={{\mathbb{O}}$ and $E{\parallel}{\mathbb{Z}_t}{\parallel}^2<{\infty}$.