• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.75-82
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• 2014

In this paper, we consider the periodic boundary value problem with sign changing nonlinearity $$u^{{\prime}{\prime}{\prime}}+{\rho}^3u=f(t,u),\;t{\in}[0,2{\pi}]$$, subject to the boundary value conditions: $$u^{(i)}(0)=u^{(i)}(2{\pi}),\;i=0,1,2$$, where ${\rho}{\in}(o,{\frac{1}{\sqrt{3}}})$ is a positive constant and f(t, u) is a continuous function. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is the nonlinear term f may change sign.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.1
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• pp.1-10
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• 1999

We consider the problem of synthesizing an internally stabilizing linear time-invariant controller for a linear tune-Invariant plant such that a given closed loop transfer function is strictly sector bounded. We show that the standard $H{\infty}$ control problem and the $\tau$ -positive real control problem are special cases of sector bounded control problem. Necessary and sufficient conditions for the existence of a controller are obtained. The state-space representation for strictly proper controllers are given in terms of solutions to ARIs or AREs.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.123-132
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• 1995

Our interest is to study the existence of positive solutions to the following elliptic system involving competing interaction $$ (1) { -\partial(x,u,\upsilon)\Delta u = uf(x,u,v) { - \psi(x,u,\upsilon)\Delta \upsilon = \upsilon g(x,u,\upsilon) { \frac{\partial n}{\partial u} + ku = 0 on \partial\Omega { \frac{\partial n}{\partial\upsilon} + \sigma\upsilon = 0 $$ in a bounded region $\Omega$ in $R^n$ with a smooth boundary, where the diffusion terms $\varphi, \psi$ are strictly positive nondecreasing function, and k, $\sigma$ are positive constants. Also we assume that the growth rates f, g are $C^1$ monotone functions. The variables u, $\upsilon$ may represent the population densities of the interacting species in problems from ecology, microbiology, immunology, etc.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1347-1372
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• 2020

We study bifurcation for the following fractional Schrödinger equation $$\{\left.\begin{eqnarray}(-{\Delta})^su+V(x)u&=&{\lambda}f(u)&&{\text{in}}\;{\Omega}\\u&>&0&&{\text{in}}\;{\Omega}\\u&=&0&&{\hspace{32}}{\text{in}}\;{\mathbb{R}}^n{\backslash}{\Omega}\end{eqnarray}\right$$ where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of ℝⁿ, (-∆)^s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is $\lim_{t{\rightarrow}+{\infty}}\;{\frac{f(t)}{t}}=a{\in}(0,+{\infty})$. We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.997-1030
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• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.561-564
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• 1998

This paper evaluated autonomic nervous system function in 23 patients with syncope and a positive tilt test result, 21 with a negative test result, and 19 healthy controls. Indexes of heart rate variability were measured during supine resting, immediately afte rtilt-up, standing rsting, immediately before syncope and immediately after tiltdown. There were no significant differences among the groups in any of the indexes of heart rate varability over the 24-hour holter recordings. In patients with a positive tilt result, tilting gaused a decrease in low-frequency (LF) immediately before syncope and incsrease in high-frequency (HF) bands immediately before. In patients with a negative tilt result, tilting caused a decrease in low-frequency (LF) immediately before syncope and decrease in high-frequency (HF) bands immediately before, different from positive tilt results. Our findings showed that patients with vasovagal syncope have no chronic differences from normal subjects in autonomic nervous system activity, but that these patients respond differently to the orthostatic stimulus.

• Journal of the Korean Ceramic Society
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• v.27 no.3
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• pp.337-344
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• 1990

As a function of sintering temperature and time, the electrical properties of ruthenium based thick film resistors were investigated with microstructure. The variatio of resistivity and TCR(temperature coefficient of resistance)trends of sintered speciman at various sintering temperature were different low resistivity paste(Du Pont 1721) from high one(Du Pont 1741). These phenomena are deeply relative to microstructure of sintered film. With increasing the sintering temperature for 1721 system, the electrical sheet resistivity decreased, but again gradually increased above 80$0^{\circ}C$. And TCR trends in 1721 system are all positive. On the other hand the electrical sheet resistivity of 1741 resistor system decreased with sintering temperature. And TCR trends variable according to sintering temperature. TCR of speciman sintered at $700^{\circ}C$ was negative value, and TCR of 80$0^{\circ}C$ sintered speciman coexisted negative and positive value. But in case of speciman sintered at 90$0^{\circ}C$, TCR was positive value. As results of this fact, it was well known that the charge carrier contributied to electrical conduction in 1741 resistor system varied with sintering temperature.

• Journal of Physiology & Pathology in Korean Medicine
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• v.23 no.2
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• pp.374-380
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• 2009

Samryungbaikchul-san(SRBCS) has been used in oriental medicine for the treatments of gastrointestinal and neurological disorders. Here, potential protective function of SRBCS was investigated in neural tissues in Alzheimer's disease(AD) mouse model. In primary cultured cells from the spinal cord of newborn rats, treatment of ${\beta}$-amyloid peptide elevated cell counts positive to glial fibrillary acidic protein(GFAP) or caspase 3 immunoreactivity, but the co-treatment of SRBCS reduced positive cell counts. In vivo administration of scopolamine, an inhibitor of muscarinic receptor, resulted in increases in the number of glial fibrillary acidic protein(GFAP) and caspase 3-positive cells in hippocampal subfields, which was then decreased by the treatment of SRBCS or acetylcholinesterase inhibitor galathamine. The present data suggest that SRBCS may play a protective role in damaged neural tissues caused by scopolamine treatments in mice.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.697-710
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• 2010

In this paper, we prove existence of infinitely many positive and concave solutions, by means of a simple approach, to $3^{th}$ order three-point singular boundary value problem {$x^{\prime\prime\prime}(t)=\alpha(t)f(t,x(t))$, 0 < t < 1, $x(0)=x'(\eta)=x^{\prime\prime}(1)=0$, (1/2 < $\eta$ < 1). Moreover with respect to multiplicity of solutions, we don't assume any monotonicity on the nonlinearity. We rely on a combination of the analysis of the corresponding vector field on the phase-space along with Knesser's type properties of the solutions funnel and the well-known Krasnosel'ski$\breve{i}$'s fixed point theorem. The later is applied on a new very simple cone K, just on the plane $R^2$. These extensions justify the efficiency of our new approach compared to the commonly used one, where the cone $K\;{\subset}\;C$ ([0, 1], $\mathbb{R}$) and the existence of a positive Green's function is a necessity.

• The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.2 no.2
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• pp.55-58
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• 1988

Electron mobility which is a basic parameter to represent gas state, is calculated for 38mm 20W fluorescent lamp. 2 Electron Group Model is u&ed for electron distribution function. To prove this result electron mobility in 38mm 20W fluorescent lamp is measured at various wall temperatures. In order to obtain electric field strength of positive column, the sum of anode and cathode fall voltages assumed to be 15(VJ) and dual slit is used to measure positive column length. The measured and calculated result is potted under $10-80^{\circ}C$ wall temperature.