• 대한수학회논문집
• /
• 제10권3호
• /
• pp.681-688
• /
• 1995

Fixed-point theory has an extension to coincidences. For a pair of maps $f,g:X_1 \to X_2$, a coincidence of f and g is a point $x \in X_1$ such that $f(x) = g(x)$, and $Coin(f,g) = {x \in X_1 $\mid$ f(x) = g(x)}$ is the coincidence set of f and g. The Nielsen coincidence number N(f,g) and the Lefschetz coincidence number L(f,g) are used to estimate the cardinality of Coin(f,g). The aspherical manifolds whose fundamental group has a normal solvable subgroup of finite index is called infrasolvmanifolds. We show that if $M_1,M_2$ are compact connected orientable infrasolvmanifolds, then $N(f,g) \geq $\mid$L(f,g)$\mid$$ for every $f,g : M_1 \to M_2$.

• 대한수학회지
• /
• 제32권2호
• /
• pp.171-181
• /
• 1995

Nielsen coincidence theory is concerned with the estimation of a lower bound for the number of coincidences of two maps $f,g: X \longrightarrow Y$. For this purpose the so-called Nielsen number N(f,g) is introduced, which is a lower bound for the number of coincidences ([1]). The relative Nielsen number N(f : X,A) in the fixed point theory is introduced in [3], which is a lower bound for the number of fixed points for all maps in the relative homotopy class of f:(X,A) $\longrightarrow$ (X,A), and its estimation is given in [5].

• 충청수학회지
• /
• 제10권1호
• /
• pp.87-95
• /
• 1997

In general, the positive solution to biological reaction-diffusion equations is not unique. In this paper, we state the sufficient and necessary conditions of the existence of positive solutions, and give and the proof for the uniqueness of positive solutions for a certain elliptic interacting system.

• East Asian mathematical journal
• /
• 제38권1호
• /
• pp.33-41
• /
• 2022

In this paper, we study singular Dirichlet boundary value problems involving ϕ-Laplacian. Using fixed point index theory, the existence of positive solutions is established under the assumption that the nonlinearity f = f(u) has a positive falling zero and is either superlinear or sublinear at u = 0.

• East Asian mathematical journal
• /
• 제38권5호
• /
• pp.593-601
• /
• 2022

In this paper, we consider singular 𝜑-Laplacian problems with nonlocal boundary conditions. Using a fixed point index theorem on a suitable cone, the existence results for one or two positive solutions are established under the assumption that the nonlinearity may not satisfy the L¹-Carathéodory condition.

• East Asian mathematical journal
• /
• 제40권1호
• /
• pp.85-94
• /
• 2024

In this paper we study the existence and multiplicity of positive solutions for p-Laplacian problems with a singular weight. Proofs mainly make use of Global Continuation Theorem and Fixed Point Index argument.

• 한국환경과학회지
• /
• 제24권4호
• /
• pp.371-381
• /
• 2015

In the mountain streams in Jeju Island, strong turbulence and roughness usually made it nearly impossible to utilize most of intrusive instrumentation for streamflow discharge measurements. Instead, a non-intrusive fixed electro-magnetic wave surface velocimetry (fixed EWSV: Kalesto) became alternatively popular in many representative streams to measure stream discharge seamlessly. Currently, Kalesto has shown noteworthy performance with little loss in flood discharge measurements and also has successfully provided discharge for every minute. However, Kalesto has been operated to regard its measured one-point velocity as the representative mean velocity for the given cross-section. Therefore, it could be highly possible to potentially encompass discharge measurements errors. In this study, we analyzed the difference between such Kalesto discharge measurements and other alternative concurrent discharge measurements such as Acoustic Doppler Current Profiler (ADCP) and mobile EWSV which were able to measure velocity in multi-points in the cross-section. Consequently, Kalesto discharge deviated from ADCP discharge in amount of 48% for relatively low flow, and more than 20% difference for high flow compared with mobile EWSV discharge measurements. These results indicated that the one-point velocity measured by Kalesto should be used as a cross-sectional mean velocity, rather it should be accounted for as an index-velocity in conjunction with directly measured cross-sectional mean velocity by using more reliable instrumentations. After inducing Kalesto Discharge Correction Coefficient (KDCC) that actually means relationship between index velocity and cross-sectional mean velocity, the corrected discharge from Kalesto was significantly improved. Therefore, we found that index velocity method should be applied to obtain better accuracy of discharge measurement in case of Kalesto operation.

• 한국지반환경공학회 논문집
• /
• 제10권3호
• /
• pp.37-45
• /
• 2009

대구지역에 분포하는 고유이방성 셰일(shale)의 점재하지수 및 일축․압축강도 특성을 평가하기 위한 일련의 실험실 시험을 수행하였다. 또한 시험시편의 크기효과 및 형태효과를 조사하기 위하여 축방향 및 직경방향으로 점재하지수를 측정하였다. 일반적으로 직경방향의 점재하지수는 길이/직경(L/D)비가 대략 1.0 이상일때 일정한 값을 보이고 축방향 점재하 시험 결과 L/D비의 증가에 따라 평균 점재하지수가 약간 감소하는 경향을 보였으며 L/D비가 1.0 이상이면 corner파괴가 발생하였다. 최소의 점재하지수는 층리면이 연직과 이루는 각 ($\beta$)이 $15^{\circ}{\sim}30^{\circ}$에서 나타났고 ${\beta}=30^{\circ}$에서 최소의 일축압축강도가 얻어졌다. $\beta$ 값의 범위가 $0^{\circ}{\sim}90^{\circ}$인 시편의 점재하지수와 일축압축강도를 측정하여 이들의 상호관계를 회귀분석하였다. 층리면을 $0^{\circ}$에서 $90^{\circ}$까지 변화시키면서 측정한 점재하지수는 일축압축강도와 선형적인 관계인 ${\sigma}_c=25.0 I_{s(50)}$로 나타났다. 한편, 층리각($\beta$)를 90${^{\circ}}$로 고정시킨 상태에서의 이들의 상관성은 ${\sigma}_c=14.4 I_{s(50)}$로 나타났는데, 이는 ISRM(1985)에서 추천하는 층리가 없는 무결암 시료에 대한 일반적인 상관성, ${\sigma}_c=22 I_{s(50)}$과는 많은 차이가 있음을 확인하였다. 일축압축강도의 이방성 모형은 기존의 Ramamurthy(1993)이론에 지수 'n'을 도입하여 n= 3을 적용 했을때 측정결과와 잘 부합되는 결과를 얻었다.

• 대한수학회지
• /
• 제46권2호
• /
• pp.271-279
• /
• 2009

Using an index theory for countably condensing maps, we show the existence of eigenvalues for countably k-set contractive maps and countably condensing maps in an infinite dimensional Banach space X, under certain condition that depends on the quantitative haracteristic, that is, the infimum of all $k\;{\geq}\;1$ for which there is a countably k-set-contractive retraction of the closed unit ball of X onto its boundary.

• 대한수학회논문집
• /
• 제21권4호
• /
• pp.701-717
• /
• 2006

The positive coexistence of a simple food chain model with ratio-dependent functional response and cross-diffusion is discussed. Especially, when a cross-diffusion is small enough, the existence of positive solutions of the system concerned can be expected. The extinction conditions for all three interacting species and for one or two of three species are studied. Moreover, when a cross-diffusion is sufficiently large, the extinction of prey species with cross-diffusion interaction to predator occurs. The method employed is the comparison argument for elliptic problem and fixed point theory in a positive cone on a Banach space.