• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.665-684
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• 2008

Runge-Kutta-Nystr$\"{o}$m (RKN) methods provide a popular way to solve the initial value problem (IVP) for a system of ordinary differential equations (ODEs). Users of software are typically asked to specify a tolerance ${\delta}$, that indicates in somewhat vague sense, the level of accuracy required. It is clearly important to understand the precise effect of changing ${\delta}$, and to derive the strongest possible results about the behaviour of the global error that will not have regular behaviour unless an appropriate stepsize selection formula and standard error control policy are used. Faced with this situation sufficient conditions on an algorithm that guarantee such behaviour for the global error to be asympotatically linear in ${\delta}$ as ${\delta}{\rightarrow}0$, that were first derived by Stetter. Here we extend the analysis to cover a certain class of ODEs with low-order derivative discontinuities, and the class of ODEs with constant delays. We show that standard error control techniques will be successful if discontinuities are handled correctly and delay terms are calculated with sufficient accurate interpolants. It is perhaps surprising that several delay ODE algorithms that have been proposed do not use sufficiently accurate interpolants to guarantee asymptotic proportionality. Our theoretical results are illustrated numerically.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.3
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• pp.204-211
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• 1993

Boundary element method is applied to simulate nonlinear water waves using Green's identity formula in a numerical wave flume. A system of linear equations is formulated from the governing equation and free surface boundary conditions in order to calculate velocity potential and water surface elevation at each nodal point. The velocity square terms are included in the dynamic free surface boundary condition. The free surface is treated as a moving boundary. the vertical variation of velocity potential being considered in calculating the time derivative of the velocity potential at the free surface. The present method is applied to simulate solitary wave and Stokes 2nd order wave, and shows excellent agreements with their theoretical values.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.73-116
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• 2020

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.10
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• pp.4331-4338
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• 2014

$N^1$-(2, 5-dimethoxyphenyl)-$N^8$-hydroxyoctanediamide (N25) is a novel SAHA cap derivative of HDACi, with a patent (No. CN 103159646). This invention is a hydroxamic acid compound with a structural formula of $RNHCO(CH_2)6CONHOH$ (wherein R=2, 5dimethoxyaniline), a pharmaceutically acceptable salt which is soluble. In the present study, we investigated the effects of N25 with regard to drug distribution and molecular docking, and anti-proliferation, apoptosis, cell cycling, and $LD_{50}$. First, we designed a molecular approach for modeling selected SAHA derivatives based on available structural information regarding human HDAC8 in complex with SAHA (PDB code 1T69). N25 was found to be stabilized by direct interaction with the HDAC8. Anti-proliferative activity was observed in human glioma U251, U87, T98G cells and human lung cancer H460, A549, H1299 cells at moderate concentrations ($0.5-30{\mu}M$). Compared with SAHA, N25 displayed an increased antitumor activity in U251 and H460 cells. We further analyzed cell death mechanisms activated by N25 in U251 and H460 cells. N25 significantly increased acetylation of Histone 3 and inhibited HDAC4. On RT-PCR analysis, N25 increased the mRNA levels of p21, however, decreased the levels of p53. These resulted in promotion of apoptosis, inducing G0/G1 arrest in U251 cells and G2/M arrest in H460 cells in a time-dependent and dose-dependent manner. In addition, N25 was able to distribute to brain tissue through the blood-brain barrier of mice ($LD_{50}$: 240.840mg/kg). In conclusion, our findings demonstrate that N25 will provide an invaluable tool to investigate the molecular mechanism with potential chemotherapeutic value in several malignancies, especially human glioma.

• Proceedings of the PSK Conference
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• 2000.04a
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• pp.70-81
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• 2000

DA-5018 is a synthetic capsaicin derivative under development as a non-narcotic a analgesic ag$\varepsilon$nt. DA-50 18 showed a potent analgesic activity against acute and chronic pain m model(Tablel, 2.), but it had a narrow margin of safety. DA-5018 did not bind to opioid(${\kappa}, {\delta}, {\mu}$), NKl, CGRP receptors in vitro and its analgesic effect was not antagonized by naloxone, a and it did not develop analgesic tolerance. In addition DA-5018 had no inhibitory effects against c cyclooxygenase and 5-lipooxygenase activities. DA-5018 significantly increased the relcase of substance P from the slices of the rat spinal cord. These results suggest that DA-50 18 is not a narcotic nor aspirin-like analgesic and the release of substance P is one of analgesic mechanism of action of DA-5018. We found that DA-5018 was almost ten times more potent and was at l least IOO-times less irritable compared to capsaicin. Accordingly development of topical formula was adopted. Topical formula was desiged and screened by flux test of DA-5018 using hairless mouse skin and several formulas were selected. With these topical formulas we a assessed the analgesic efficacy and carried out the toxicity, skin irritation and pharmacokinetic studies. In streptozotocin-induced hyperalgesic rat and 50 % galactose-fed hyperalgesic rat as diabetic pain models, DA-5018 cream increased the pain thresh이ds up to 77.0% and 24.4% respectively, while Zostrix-HP(capsaicin cream) incr$\varepsilon$as cd by 65.9% and 21.0%. DA-5018 c cream showed a good analgesic effect as welI in FCA-induced arthritic rat. DA-5018 cream did not show any toxicological signs in acute and chronic toxicity test and had little skin irritation in car swclIing and scratching t$\varepsilon$st. Pharmacokinetics of DA-50 18 were studied after topical application of ${14}^C$-Iabelled or unlabelIed DA-5018 cream. Plasma and skin concentrations c except applied skin wcre below the dctection limit and after 7-day cummulative application, plasma concentrations were also below detection limit DA-50 18 may have an advantag$\varepsilon$ ov$\varepsilon$r c capsaicin and is now being developed as a topical agent for the treatment of pains. DA-50 18 cream was approved for Korean IND and is now under a Phase II clinical study for arthritic pain a after finising Phase I study. DA-50 18 was also liscensed out to Stiefel Company in America in

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.2
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• pp.9-15
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• 2004

We present a new unified analytical front surface potential model, which can accurately describe the transitions between the partially-depleted (PD) and the fully-depleted (FD) regimes with an analytical expression for the critical voltage V$_{c}$ delineating the PD and the FD region. It is valid in all regions of operation (from the sub -threshold to the strong inversion) and has the shorter calculation time than the iterative procedure approach. A charge sheet model based on the above explicit surface potential formulation is used to derive a single formula for the drain current valid in all regions of operation. Most of the secondary effects can be easily included in the charge sheet model and the model accurately reproduces various numerical and experimental results. No discontinuity in the derivative of the surface potential is found even though three types of smoothing functions are used. More importantly, the newly introduced parameters used in the smoothing functions do not strongly depend on the process parameter.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.9
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• pp.88-93
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• 2003

This Paper described the simulation program development for helicopter. In the design of flight control system to accomplish some special missions like UAV, it is important to minimize the execution time obtaining a linear model from nonlinear model that is used for design of controller. The first step for this kind of purpose is to complete a nonlinear model that contains full dynamic characteristics. The second step is to get the trim values that are obtained from the nonlinear model by solving an algebraic equation. And then stability and control derivatives are derived through hovering to forward flight by numerical perturbation that will be used for linear model for a specified flight condition. The software program(HeliSim) is developed by using MATLAB GUI and will provide easy modeling procedure. The suggested method in this paper is much more simpler than any other method like a fully scale helicopter model. The advantage of our suggested method will reduce the computational time due to simple formula to extract a linear model from nonlinear model that will be beneficially used for flight control system of unmanned helicopter by some reduction of computational load.

• The Transactions of the Korean Institute of Power Electronics
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• v.12 no.3
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• pp.267-275
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• 2007

This paper presents about energy input and output modeling for a flywheel energy storage system that can store and supply mechanical energy, which is emerging as one of clean energy sources, and the analysis and control of a PWM inverter system. Moreover, this paper describes flywheel's characteristics related to variations of mechanical and electrical parameters like as voltage and current versus speed characteristics formed as numerical formula and thus simulate behaviour-status of flywheel energy. Also for comparison and analysis between PI control and PDFF control, the modeling, design and analysis to the single-phase full bridge inverter with double loop feedback control is accomplished through numerical description and simulation. Finally, under load condition 0.1[pu], 1[pu]. it is validated that harmonic characteristics for voltage and current wave is controlled within 5% below even dynamics condition.

• Geophysics and Geophysical Exploration
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• v.23 no.4
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• pp.243-252
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• 2020

To share an understanding of trajectory measurement in surveys using borehole, this tutorial summarizes the relevant mathematical principles of the borehole deviation survey based on coordinate transform. For uncased or open holes, calculations of the azimuth-deviation-tool face rotation using three-component accelerometer and magnetometer measurements are summarized. For the steel-cased holes, calculations are based on the time-derivative formula of the coordinate transform matrix; yaw-pitch-roll angles through time are mathematically determined by integrating the threecomponent angular velocity measurements from the gyroscope while also removing the Earth's rotation effect. Sensor and data fusion to increase the accuracy of borehole deviation survey is explained with an example of the method. These principles of borehole deviation surveys can be adapted for attitude estimation in air-borne surveys or for positioning in tunnels where global positioning system (GPS) signals cannot be accessed. Information on the optimization filter that must be incorporated in sensor fusion is introduced to help future research.

• Journal of the Korean Chemical Society
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• v.53 no.5
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• pp.530-535
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• 2009

Dicyclohexyl telluride was obtained in a high yield by the reaction of cyclohexyl bromide with NaTeH(prepared in situ) in an aqueous ethanolic solution. A series of new organotelluronium salts of the general formula ${(cyclo-C_6H_11)}_2Te(R)X$ (where R = $CH_3$, X = I (1); R = $C_2H_5$, X = Br(2); R = $C_2H_5$, X = I (3); R = C_3H_5$, X = Br (4)) were prepared by the reaction of ${(cyclo-C_6H_11)}_2Te$ with the corresponding alkyl halide. Reaction of 1 with NaBPh4 gave compound 5 ( i.e. R = CH3, X = BPh4 ‒) in 78% yield. Reaction of ${(cyclo-C_6H_11)}_2Te$ with benzyl bromide and 4-bromophenacyl bromide gave unexpectedly dibenzylcyclohexyltelluronium bromide (6) and bis(4-bromophenacyl)cyclohexyltelluronium bromide (7), respectively. Reaction of 6 with NaBPh4 gave the corresponding tetraphenylborate derivative (8) in high yield. $^1H$ NMR studies revealed that in $CDCl_3$solution compound 1 eliminated alkyl halide. Conductivity, IR, $^1H\;and\;^{13}C$ NMR and thermal data for the new compounds are presented and discussed.