• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1357-1377
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• 2017

In this article, we first give the $L^p$ boundedness of the operator $D^2L^{-1}$ with BMO coefficients and a potential V satisfying an appropriate reverse $H{\ddot{o}}lder$ condition, then obtain global $W^{1,2}_p$ estimates for the nondivergence parabolic operator L with VMO coefficients and a potential V satisfying an appropriate reverse $H{\ddot{o}}lder$ condition.

• Advances in Traditional Medicine
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• v.10 no.4
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• pp.263-270
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• 2010

Scoparia dulcis L. is widely used in the traditional system of medicine for treating liver ailments. In the present study the terpenoids and terpenoid fractions isolated from 1:1:1 petroleum ether, diethyl ether and methanol (PDM) extract of Scoparia dulcis L. were tested for their in vitro 1, 1-Diphenyl-2-picrylhydrazyl (DPPH) radical scavenging activity. Selected samples from the assay were further tested for their in vitro hepatoprotective activity against $CCl_4$ induced hepatotoxicity in freshly isolated rat hepatocytes. In the in vitro antioxidant study, fractions 7, 11, 13, 14, and 15 and PDM extract show the DPPH radical scavenging activity. The phytochemical screening of all these fractions show the presence of terpenoids. In the in vitro hepatoprotective study all these fractions and the PDM extract significantly prevent the $CCl_4$ induced changes in the aspartate aspartate amino transferase, alanine amino transferase and alkaline phosphatase levels (p < 0.05). The above results are comparable with the standard, silymarin. The results of the study indicate that, the PDM extract of Scoparia dulcis L. possesses potential hepatoprotective activity and this may be attributed to its free radical scavenging potential, which in turn may be attributed to the presence of terpenoids.

• Journal of the Ergonomics Society of Korea
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• v.16 no.2
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• pp.15-27
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• 1997

Brain potential is described using the mesocolumnar activity defined by averaged firings of excitatory and inhibitory neuron of neocortex. Lagrangian is constructed based on SMNI(Statistical Mechanics of Neocortical Interaction) and then Euler Lagrange equation is obtained. Excitatory neuron firing is assumed to be amplitude- modulated dominantly by the sum of two modes of frequency .omega. and 2 .omega. . Time series of this neuron firing is calculated numerically by Euler Lagrangian equation. I .omega. L related to low frequency distribution of power spectrum, I .omega. H hight frequency, and Sd(standard deviation) were introduced for the effective extraction of the dynamic property in the simulated brain potential. The relative behavior of I .omega. L, I .omega. H, and Sd was found by parameters .epsilon. and .gamma. related to nonlinearity and harmonics respectively. Experimental I .omega L, I .omega. H, and Sd were obtained from EEG of human in rest state and of canine in deep sleep state and were compared with theoretical ones.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1189-1208
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• 2017

In this paper, we study vanishing properties for $L^2$ harmonic 1-forms on a gradient shrinking Ricci soliton. We prove that if (M, g, f) is a complete oriented noncompact gradient shrinking Ricci soliton with potential function f, then there are no non-trivial $L^2$ harmonic 1-forms which are orthogonal to df. Second, we show that if the scalar curvature of the metric g is greater than or equal to (n - 2)/2, then there are no non-trivial $L^2$ harmonic 1-forms on (M, g). We also show that any multiplication of the total differential df by a function cannot be an $L^2$ harmonic 1-form unless it is trivial. Finally, we derive various integral properties involving the potential function f and $L^2$ harmonic 1-forms, and handle their applications.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1382-1387
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• 2004

From the viewpoint of a macro state, there is no thermal boundary resistance (TBR) at an interface if both surfaces at an interface are perfectly contacted. However, recent molecular dynamics (MD) studies reported that there still exists the TDR at the interface in an ideal epitaxial superlttice. Our previous studies suggested the model to predict the TBR not only quantitatively also qualitatively in superlattices. The suggested model was based on the classical theory of a wave reflection, and provided highly satisfactory results for an engineering purpose. However, it was not the complete model because our previous model was derived by considering only the effects from a mass ratio and a potential ratio of two species. The interaction of two species presented by the Lennard-Jones (L-J) potential is governed by the mutual ratio of the masses, the potential well depths, and the diameters. In this study, we performed the preliminary simulations to investigate the effect resulting from the diameter ratio of two species for the completion of our model and confirmed that it was also a ruling factor to the TBR at an interface in superlattices.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1255-1268
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• 2022

We consider the Schrödinger type operator 𝓛 = (-𝚫_ℍⁿ)² + V² on the Heisenberg group ℍⁿ, where 𝚫_ℍⁿ is the sub-Laplacian and the non-negative potential V belongs to the reverse Hölder class RH_s for s ≥ Q/2 and Q ≥ 6. We shall establish the (L^p, L^q) estimates for the Riesz transforms T_𝛼,𝛽,j = V^2𝛼𝛁^j_ℍⁿ𝓛^-𝛽, j = 0, 1, 2, 3, where 𝛁_ℍⁿ is the gradient operator on ℍⁿ, 0 < α ≤ 1-j/4, j/4 < 𝛽 ≤ 1, and 𝛽 - 𝛼 ≥ j/4.

• Proceedings of the KIEE Conference
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• 1994.11a
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• pp.9-11
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• 1994

FACTS concept is the control of power flow and increase of the loading on existing lines to the thermal limuts. This paper focuses on the ability of the thyristor controlled series compensator (TCSC) to stabilize the disturbed power systems. The result shows the potential benefit of the TCSC in addition to the role of controlling the steady state power flow. In order to show the effectiveness of controlled series capacitor, power system dynamic model is augmented and the effect of the SC into the power system dynamics is included. As a control algorithm, Linear Optimal Control theory is applied.

• Proceedings of the ESK Conference
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• 1997.04a
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• pp.165-175
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• 1997

Brain potential is described by using Euler Lagrange equation derived from Lagrangian based on SMNI(Statistical Mechanics of Neocortical Interaction). It is assumed that excitatory neuron firing is amplitude-modulated dominantly by the sum of two modes of frequency ${\omega}and 2 {\omega}$ . Time series of this neuron firing is numerically calculated. $I_{L}$related to low frequency distribution of power spectrum, $I_{H}$high frequency, and S(standard deviation) are introduced for the effective extraction of the dynamic property in this simulated brain potential. $I_{L}$,$I_{H}$, and S are obtained from EEG of 4 persons in rest state and are compared with thoretical results. It is of importance in various fields related to human well-being such as comfort-pursued industrial design, psychology, medicine to characterize human emotional states by EEG analysis. The pleasant and unpleasant sensation among various emotional states would be demonstrated to be determined in terms of ${\epsilon}$ and ${\gamma}$ parameters estimated by the simulated $I_{L}$-$I_{H}$-S relations.

• Journal of ILASS-Korea
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• v.8 no.1
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• pp.16-22
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• 2003

Zeta potential measurements of colloid particles suspended in a liquid are performed by a Zeta Meter developed. There are many applications of colloid stability in spray technology, paints, wastewater treatment, and pharmaceuticalse. Zeta potentials of charged particles are obtained by measuring the electrophoretic velocities of the particles using video enhanced microscopy and image analysis program. The values of zeta potential of polystyrene latex(PSL), $silica(SiO_2)$M, polyvinylidence difluoride(PVDF), silicon nitride, and alumina particles in deionized (DI) water were measured to be -40.5, -31.9, -25.2, -15.1 and -10.1mV, respectively. The particles having high zeta potential less than -20 mV are stable in DI water, because the double layers of them have strong repulsive forces mutually, and the particles having low zeta potential over -20mV are unstable due to Van Der Waals forces. Silica(>20nm), PSL, aluminum and PVDF particles were found to be stable that would remain separate and well disperse, while silicon nitride and alumina particles were found to be unstable that would gradually agglomerate in DI water.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.999-1018
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• 1998

In this paper, we prove stability theorems for the operator-valued Feynman integral of certain functionals involving some Borel measures on (0, t) as a bounded linear operator from L$_1$(R) to $C_{0}$(R).