• Korean Journal of Mathematics
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• 제16권3호
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• pp.259-269
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• 2008

The non-existence and existence of the positive solution for the generalized cooperation biological model for two species of animals $${\Delta}u+u(a-bu+g(v))=0\;in\;{\Omega}\\{\Delta}v+v(d+h(u)-cv)=0\;in\;{\Omega}\\u=v=0\;on\;{\partial}{\Omega}$$ are investigated. The techniques used in this paper are elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 1998년도 제28회 추계학술대회
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• pp.365-370
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• 1998

This paper reports on the measurement of the vane motion in a positive displacement small vane pump. The capacitive method using ceramic vane is proposed to measure the vane motion. This method enables us to measure only radial motion of the vane regardless of the motions of other directions. With simple experiments and solutions of simultaneous equations, the indirect compensation of measured signal was performed.

• 한국식품위생안전성학회지
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• 제1권1호
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• pp.13-21
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• 1986

Two short-term bioassays were employed to asses the mutagenic and clastogenic activities in browning reaction of pentose-creatine, pentose-glycine and pentose-creatine-glycine browning reaction model system. Methylene chloride extract of rhamnose-creatine-glycine browning reaction exhibited the strongest mutagenicity toward Salmonella typhimurium TA98 with S-9. Methylene chloride extract of pentose-creatine and pentose-glycine browning reaction solutions was also tested for mutagenicity, with positive responses. Methylene chloride extract of pentose-creatine-glycine browning reaction solutions induced significant increase in chromosome aberrations in the treated Chinese hamster ovary(CHO) cells. Each of pentose-creatine and pentose-glycine browning reaction solutions induced a relatively low frequency of chromosome aberrations in the treated cells.

• 통상정보연구
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• 제6권3호
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• pp.159-180
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• 2004

This paper focus on building online trust in electronic commerce between partner that have never traded with each other before, the so-called first trade situation. For this, this paper proposes the model to build trust for conduction first trade transaction in e-trade(so-ca1led Trust Matrix Model : TMM). The TMM is based on the idea that for business to business electronic trade a balance has to be found between anonymous procedural trust, i.e. procedural solutions for trust building, and personal trust based on positive past experiences within for first trade situation, because of the lack of experience in these situations. The procedural trust solutions are related in the notion of institution-based trust, because the trust in the procedural solutions depends on the trust one has in the institutions that issued or enforces the procedure. The TMM can be used as a tool to analyze and develope trust-building services to help organizations conduct first -trade electronic trade.

• Korean Journal of Mathematics
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• 제19권4호
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• pp.423-436
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• 2011

We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.

• 대한수학회논문집
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• 제16권1호
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• pp.137-152
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• 2001

Steady two-dimensional flows due to an applied pressure distribution in water of finite depth are considered. Gravity is included in the dynamic boundary condition. Gravity is included in the dynamic boundary condition. The problem is solved numerically by using the boundary integral equation technique. It is shown that, for both supercritical and subcritical flows, solutions depend on three parameters: (i) the Froude number, (ii) the magnitude of applied pressure distribution, and (iii) the span length of pressure distribution. For supercritical flows, there exist up to two solutions corresponding to the same value of Froude number for positive pressures and a unique solution for negative pressures. For subcritical flows, there are solutions with waves behind the applied pressure distribution. As the Froude number decreases, these waves when the Froude numbers approach the critical values.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.231-243
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• 2007

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearity f in the equation depends on all lower derivatives, and the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.167-182
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• 2007

The existence of solutions of the following multi-point boundary value problem $${x^{(n)}(t)=f(t,\;x(t),\;x'(t),{\cdots}, x^{(n-2)}(t))+r(t),\;0 is studied. Sufficient conditions for the existence of at least one solution of BVP(*) are established. It is of interest that the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bounds of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.

• 대한수학회보
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• 제56권1호
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• pp.245-251
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• 2019

Assume that ${\Omega}$ is a bounded domain in ${\mathbb{R}}^n$ with $n{\geq}2$. We study positive solutions to the problem, ${\Delta}u=u^p$ in ${\Omega}$, $u(x){\rightarrow}{\infty}$ as $x{\rightarrow}{\partial}{\Omega}$, where p > 1. Such solutions are called boundary blow-up solutions of ${\Delta}u=u^p$. We show that a boundary blow-up solution exists in any bounded domain if 1 < p < ${\frac{n}{n-2}}$. In particular, when n = 2, there exists a boundary blow-up solution to ${\Delta}u=u^p$ for all $p{\in}(1,{\infty})$. We also prove the uniqueness under the additional assumption that the domain satisfies the condition ${\partial}{\Omega}={\partial}{\bar{\Omega}}$.

• 대한수학회지
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• 제58권4호
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• pp.1001-1017
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• 2021

In this paper, we first apply parabolic inequalities and a maximum principle to give a new proof for symmetry and monotonicity of solutions to fractional elliptic equations with gradient term by the method of moving planes. Under the condition of suitable initial value, by maximum principles for the fractional parabolic equations, we obtain symmetry and monotonicity of positive solutions for each finite time to nonlinear fractional parabolic equations in a bounded domain and the whole space. More generally, if bounded domain is a ball, then we show that the solution is radially symmetric and monotone decreasing about the origin for each finite time. We firmly believe that parabolic inequalities and a maximum principle introduced here can be conveniently applied to study a variety of nonlocal elliptic and parabolic problems with more general operators and more general nonlinearities.