• 대한수학회지
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• 제57권6호
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• pp.1573-1590
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• 2020

In this paper, we classify all solutions bounded from below to uniformly elliptic equations of second order in the form of Lu(x) = a_ij(x)D_iju(x) + b_i(x)D_iu(x) + c(x)u(x) = f(x) or Lu(x) = D_i(a_ij(x)D_ju(x)) + b_i(x)D_iu(x) + c(x)u(x) = f(x) in unbounded cylinders. After establishing that the Aleksandrov maximum principle and boundary Harnack inequality hold for bounded solutions, we show that all solutions bounded from below are linear comb_inations of solutions, which are sums of two special solutions that exponential growth at one end and exponential decay at the another end, and a bounded solution that corresponds to the inhomogeneous term f of the equation.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.517-527
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• 2016

In this paper, we consider a thermoviscoelastic equation which has one end fixed and output feedback control at the other end. We prove the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique.

• East Asian mathematical journal
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• 제34권1호
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• pp.69-84
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• 2018

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source for each independent kernels h and g with respect to Volterra terms. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• East Asian mathematical journal
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• 제32권5호
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• pp.651-658
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• 2016

In a bounded domain, we consider $$u_{tt}-{\Delta}u+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_0}^t}\;g(t-{\tau}){\Delta}ud{\tau}+u_t={\mid}u{\mid}^pu$$, where p > 0 and g is a nonnegative and decaying function. We establish a general decay result which is not necessarily of exponential or polynomial type.

• Bulletin of the Korean Chemical Society
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• 제19권4호
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• pp.471-475
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• 1998

Phase shift spectroscopy is applied to Eu(Ⅲ) luminescence from $Eu^{3+}$-exchanged Y zeolite. The phase shift and intensity modulation of luminescence following intensity-modulated excitation are measured as a function of modulation frequency and they are fitted into a double exponential decay. The fast decay component, compared with the slow one, has narrower spectral bandwidth and is emitted from the $Eu^{3+}$ that has more polar and definite environment with higher symmetry and that interacts more easily with hydrated water molecules. The fast decay component is attributed to $Eu^{3+}$ at site Ⅱ' while the slow one to $Eu^{3+}$ at sites Ⅰ' and Ⅰ.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 2004년도 요약집 춘계학술발표대회
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• pp.301.1-301.1
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• 2004

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 하계학술대회 논문집 C
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• pp.1817-1819
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• 2004

From the plasma application point of view, electron temperature and density are one of the most important parameters for plasma process. But it is only available to control plasma by adjusting external factors like gas pressure and input power. In this paper, pulse-modulated plasma is generated by modulating 13.56GHz RF power with 1, 5, 10kHz pulse. And Langmuir probe technique is used to study the distribution of electron temperature and density. When modulated pulse is off, electron temperature decreases gradually in form of exponential decay. The value t of exponential decay slope is 33.619, 13.834, 10.803 in 1kHz. 5kHz. 10kHz. This implies that this method can be used to control electron temperature and density.

• 한국전기전자재료학회논문지
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• 제11권10호
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• pp.891-896
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• 1998

The relaxation and elimination characteristics of polarization-photoinduced dichroism have been investigated in amorphous chalcogenide thin films deposited having normal(0。) and obique (80。) vapor incident angles. The dark relaxation kinetics of dichroism from a saturation point(D\ulcorner\ulcorner) to a certain relaxation point(D\ulcorner\ulcorner) grew to be longer on subsequent cycles of switching on and off of the inducing light, and these decays are changed from simple exponential decay to stretched exponential decay. The dichroism induced by a long time(~3.3 hrs) exposure exhibited the characteristics of longer time maintenance and smaller decreasing rate, in contrast with that by a short time (~min) exposure. In addition, the dichroism was eliminated by the exposure of non-polarized He-Ne laser.

• Bulletin of the Korean Chemical Society
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• 제12권1호
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• pp.47-51
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• 1991

Spin-lattice relaxation of methyl protons in 2,6-dichlorotoluene and N-methyl phthalimide, each dissolved in CDCl$_3$, has been studied at 34$^{\circ}$C and the contribution from spin-rotation interaction to the relaxation process has been separated from that due to dipole-dipole interactions among methyl protons. The results show that the spin-rotational contributions to the initial rate of relaxation in 2,6-dichlorotoluene and N-methyl phthalimide amount to 18 and 31%, respectively, of the total relaxation rate at 34$^{\circ}$C. The method of separating the spin-rotational contribution from that of dipolar interactions adopted in this paper is based on the well known fact that in an A$_3$ spin system such as methyl protons in liquid phase dipolar relaxation mechanism gives non-exponential decay of the z-component of total magnetization of protons while the random field fluctuation such as spin-rotational mechanism causes exponential decay.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.2298-2303
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• 2003

In this paper, very simple methods based on the exponential analysis are presented by which transfer function models for processes can easily be obtained. These methods employ step responses or impulse responses of the processes. These can also give a more precise transfer function model compared to the well-known graphical methods. Transfer functions are determined based on Prony method, which is one of the oldest and the most representative methods in the exponential analysis. Here, the method is reformed and applied to obtain the so-called low-order transfer function with pure time delay from the data of the step response. The effectiveness of the proposed method is examined through several numerical examples and experiments of the 2-tank level control process.