• Korean Journal of Mathematics
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• v.16 no.3
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• pp.389-402
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• 2008

We show the existence of at least two solutions for a class of systems of the critical growth nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We first show that the system has a positive solution under suitable conditions, and next show that the system has another solution under the same conditions by the linking arguments.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.445-454
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• 2006

We describe a solution to the Ornstein-Uhlenbeck equation $\frac{dI}{dt}-\frac{1}{\tau}$I(t)=cV(t) where V(t) is a constant multiple of a Gaussian white noise. Our solution is based on a discrete set of Gaussian white noise obtained by taking sample points from a sum of single frequency harmonics that have random amplitudes, random frequencies, and random phases. Hence, it is different from the solution by the standard random walk using random numbers generated by the Box-Mueller algorithm. We prove that the power of the signal has the additive property, from which we derive that the Lyapunov characteristic exponent for our solution is positive. This compares with the solution by other methods where the noise is kept to be in an error range so that its Lyapunov exponent is negative.

• Korean Journal of Mathematics
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• v.19 no.4
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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.

• East Asian mathematical journal
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• v.40 no.3
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• pp.295-306
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• 2024

We investigate the existence of multiple positive solutions of the following elliptic equation with a Schrödinger-type term: $$\begin{cases}-{\Delta}u+V(x)u={\lambda}f(u){\quad} x{\in}{\Omega},\\{\qquad}{\qquad}{\quad}u=0, {\qquad}\;x{\in}\partial{\Omega},\end{cases}$$, where 0 ∈ Ω is a bounded domain in ℝ^N , N ≥ 1, with a smooth boundary ∂Ω, f ∈ C[0, ∞), V ∈ L^∞(Ω) and λ is a positive parameter. In particular, when f(s) > 0 for 0 ≤ s < σ and f(s) < 0 for s > σ, we establish the existence of at least three positive solutions for a certain range of λ by using the method of sub and supersolutions.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.187-220
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• 2016

This paper is concerned with a kind of non-homogeneous boundary value problems for singular second order differential systems with Laplacian operators. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of boundary value problems are established. An example is presented to illustrate the main results.

• The Journal of Korean Medicine
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• v.22 no.4
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• pp.29-36
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• 2001

Objectives: This study attempted to investigate the allergic histories and the distribution of offending allergens in the general public and further to help their diagnosis and treatment with Oriental Medicine. Methods: Allergic skin tests (AST) were performed and allergic histories were taken of 359 members of the general public who visited the International Exhibition on Oriental Medicine from Sept. 1 to Sept. 5, 2000. The allergen reagents for AST were three (House dust, D. farinae, Dog hair) and the control reagent was histamine solution. Results: 1.50.1 % of the subjects (n=359) were positive to AST. The ratio between males' positivity and females' was 1.06：1. 2. The younger the subjects were, the higher the positivity was. 3. The positive subjects' (n=180) positivity to three allergens was as follows: D. farinae 98.9%, House dust 30.0%, Dog hair 1.7%. 4. The younger the positive subjects were, the higher the positivity to House dust was. In contrast, the positivity to D. farinae was high in all age groups. 5.71.1 % of the positive subjects reacted positively to monotype allergen and 28.9% reacted positively to multiple allergens (2.46：1). The most common monotype allergen was D. farinae (98.4%) and the most common combination of multiple allergens was House dust and D. farinae (94.2%). 6.52.8% of the positive subjects (n=180) and 51.4% of the negative subjects (n=179) represented the history of allergic diseases. There was no relationship between allergic skin test and allergic diseases. Conclusion: To help in diagnosis and treatment with oriental medicine, research to analyze the relationship between allergic skin test and allergic diseases should be continued on the basis of Oriental medical theories.

• Korean Journal of Microbiology
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• v.46 no.2
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• pp.152-156
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• 2010

Disposable contact lenses, which are one type of soft contact lenses, provide convenience in use, but also cause various ocular infectious diseases. Microorganisms that cause eye diseases include Acanthamoeba, bacteria, Fungi, and so on. It is impossible to prevent microorganism contamination completely due to the use of hands as wearing contact lenses. The contamination by various microorganisms leads to infectious keratitis, but it is not well known for the exact microorganisms that affect the disease. For this reason, to identify the microorganisms, two groups that are commonly used for disinfection of lenses were divided: normal saline solution and multiple purpose solution. Using these solutions the degree of microorganism contamination was observed according to the days of 1, 3, 5, 10, and 15. Twenty students by two groups from Ophthalmic Optics department at D college in Daegu Metropolitan city participated in the experiment after their ocular health conditions were checked. During they wore one-day disposable lenses for 1, 3, 5, 10, and 15 days, bacteria were cultured in media. The results, which were Gram stained by selecting the cultured colonies, show as followings: Gram positive cocci 33%, Gram-negative cocci 2%, Gram positive bacilli 34%, and the Gram negative bacilli 31%, respectively. As for the identification of potential pathogens, VITEK system and API kit methods were used. Keratitis caused by bacteria known as Staphylococcus aureus, Pseudomonas aeruginosa were detected as a result of wearing contact lenses. This study examined the distribution of bacteria as wearing one-day disposable contact lenses and pathogenic bacteria according to the duration of wearing them. In conclusion, the importance of hygiene when using contact lenses is suggested.

• Journal of Korean Institute of Industrial Engineers
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• v.26 no.3
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• pp.220-226
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• 2000

The problem (P) of optimizing a linear function $d^Tx$ over the set of efficient points for a multiple objective linear program (M) is difficult because the efficient set is nonconvex. There are some interesting properties between the objective linear vector d and the matrix of multiple objectives C and those properties lead us to establish criteria to solve (P) with a linear program. In this paper we investigate a system of the linear equations $C^T{\alpha}$ = d and construct two linearly independent positive vectors u, v such that ${\alpha}$ = u - v. From those vectors u, v, solving an weighted sum linear program for finding an efficient extreme point for the (M) is a way of getting an optimal solution of the problem (P). Therefore the theorems presented in this paper provided us an easy way of solving nonconvex program (P) with a weighted sum linear program.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.195-205
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• 2003

For the boundary value problem (BVP) of second order functional differential equations for the one-dimensional $\rho$-Laplaclan: ($\Phi$$_{\rho}$(y'))'(t)+m(t)f(t, $y^{t}$ )=0 for t$\in$[0,1], y(t)=η(t) for t$\in$[-$\sigma$,0], y'(t)=ξ(t) for t$\in$[1,d], suitable conditions are imposed on f(t, $y^{t}$ ) which yield the existence of at least two positive solutions. Our result generalizes the main result of Avery, Chyan and Henderson.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.523-537
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• 2011

A receiver operating characteristic (ROC) curve plots the true positive rate of a classier against its false positive rate, both of which are accuracy measures of the classier. The ROC curve has several interesting geometrical properties, including concavity which is a necessary condition for a classier to be optimal. In this paper, we study the nonparametric maximum likelihood estimator (NPMLE) of a concave ROC curve and its modification to reduce bias. We characterize the NPMLE as a solution to a geometric programming, a special type of a mathematical optimization problem. We find that the NPMLE is close to the convex hull of the empirical ROC curve and, thus, has smaller variance but positive bias at a given false positive rate. To reduce the bias, we propose a modification of the NPMLE which minimizes the $L_1$ distance from the empirical ROC curve. We numerically compare the finite sample performance of three estimators, the empirical ROC curve, the NMPLE, and the modified NPMLE. Finally, we apply the estimators to estimating the optimal ROC curve of the variance-threshold classier to segment a low depth of field image and to finding a diagnostic tool with multiple tests for detection of hemophilia A carrier.