• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1371-1385
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• 2022

For setting a general weight function on n dimensional complex space ℂⁿ, we expand the classical Fock space. We define Fock type space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ of entire functions with a mixed norm, where 0 < p, q < ∞ and t ∈ ℝ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$. As a result of this application, the space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ is especially characterized by a Lipschitz type condition.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.184-197
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• 2023

For the numerous uses and significance of the Whittaker function in the diverse research areas of mathematical sciences and engineering sciences, This paper aims to introduce an extension of the Whittaker function by using a new extended confluent hypergeometric function of the first kind in terms of the Mittag-Leffler function. We also drive various valuable results like integral representation, integral transform and derivative formula. Further, we also analyze specific known results as a particular case of the main result.

• Journal of the Korean Magnetic Resonance Society
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• v.27 no.4
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• pp.35-41
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• 2023

From a marine sponge Dysidea species, four new furanosesquiterterpenoids were isolated and characterized. Their structural elucidation was achieved through an extensive analysis employing NMR, MS data, and DFT method. Notably, all compounds shared as identical molecular formula. Compound 2 was identified as a derivative of compound 1, while compounds 3 and 4 exhibited an identical planar structure. Determination of the configurations of chiral centers in compounds 1 and 2 involved a comparative analysis between measured and calculated ECD spectra, along with the application of DP4+ probability analysis. Distinctly, the configurations of isomers 3 and 4 were established by scrutinizing proton chemical shifts based on the NOE correlation.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.93-115
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• 2024

In this paper, the Gauge-Uzawa methods for the Darcy-Brinkman equations driven by temperature and salt concentration (DBTC) are proposed. The first order backward difference formula is adopted to approximate the time derivative term, and the linear term is treated implicitly, the nonlinear terms are treated semi-implicit. In each time step, the coupling elliptic problems of velocity, temperature and salt concentration are solved, and then the pressure is solved. The unconditional stability and error estimations of the first order semi-discrete scheme are derived, at the same time, the unconditional stability of the first order fully discrete scheme is obtained. Some numerical experiments verify the theoretical prediction and show the effectiveness of the proposed methods.

• Journal of the Korean earth science society
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• v.30 no.7
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• pp.834-844
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• 2009

Two-dimensional magnetotelluric (MT) inversion algorithm using minimum support (MS) stabilizer functional was implemented in this study to enhance the contrast of inverted images. For this implementation, this study derived a formula in discrete form for creeping model updates in the least-squares linearized inversion. A spatially varying regularization parameter determination algorithm, which is known as ACB (Active Constraint Balancing), was also adopted to stabilize the inversion process when using MS stabilizer as a model constraint. Inversion experiments for a simple isolated body model show well the feature of MS stabilizer in concentrating the anomalous body compared with the second-order derivative model constraint. This study also compared MS stabilizer and the second-order derivative model constraints for a model having multiple anomalous bodies to show the applicability of the algorithm into field data.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.1
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• pp.141-152
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• 1993

A generalized method is presented for shape design sensitivity analysis of axisymmetric thermal conducting solids. The shape sensitivity formula of a general performance functional arising in shape optimal design problem is derived using the material derivative concept and the adjoint variable method. The method for deriving the formula is based on standard axisymmetric boundary integral equation formulation. It is then applied to obtain the sensitivity formulas for temperature and heat flux constraints imposed over a small segment of the boundary. To show the accuracy of the sensitivity analysis, numerical implementations are done for three examples. Sensitivities calculated by the presented method are compared with analytic sensitivities for two examples with analytic solutions, and compared with sensitivies by finite difference for a cooling fin example.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.414-418
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• 2005

A finite element model is developed for the numerical simulation of bed elevation change in a curved channel. The SU/PG (Streamline-Upwind/Petrov-Galerkin) method is used to solve 2D shallow water equations and the BG (Bubnov-Galerkin) method is used for the Exner equation. For the time derivative terms, the Crank-Nicolson scheme is used. The developed model is a decoupled model in a sense that the bed elevation does not change simultaneously with the flow during the computational time step. The total load formula with is used for the sediment transport model. The slip conditions are described along the lateral boundaries. The effects of gravity force due to geometry change and the secondary flows in a curved channel are considered in the model. For the verification, the model is applied to two laboratory experiments. The first is $140^{\circ}$ bended channel data at Delft Hydraulics Laboratory and the second is $140^{\circ}$ bended channel data at Laboratory of Fluid Mechanics of the Delft University of Technology. The finite element grid is constructed with linear quadrilateral elements. It is found that the computed results are in good agreement with measured data, showing a point bar at the inner bank and a pool at the outer bank.

• Journal of Applied Biological Chemistry
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• v.48 no.1
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• pp.38-41
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• 2005

Structurally new antioxidative metabolite was isolated from mycelial culture of mushroom Stereum hirsutum. Culture broth was subjected to Diaion HP-20 column chromatography, and 70% aqueous MeOH eluent was extracted with EtOAc. EtOAc extract was purified through silica gel and Sephadex LH-20 column chromatographies, and reversed phase $C_{18}$ HPLC. Compound was revealed to be new dihydroxylated derivative of sterin B with molecular formula of $C_{12}H_{16}O_5$(MW 240) by MS and various NMR spectral data analyses, and designated as sterin C. Sterin C showed superoxide radical-scavenging activity with $EC_{50}$ value of 0.31 mM.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.288-291
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• 1999

The PID (Proportional-Integral-Derivative) controller is widely used in the industries for more than fifty years with the well known Ziegler-Nichols tuning method and others varieties. However, most of the PID controller being used in the real practice still require trial and error adjustment for each process after the tuning method is done, which is consuming of time and needs the operator experiences to obtain the best results for the controller parameter. In order to reduce the inconvenience in the controller tuning, this paper presents a design of an automatic PID controller parameter analyzer being used as a support instrument in the industrial process control. This analyzer is designed based on the tuning formula of Dahlin to synthesize the PID controller parameter. Using this analyzer, the time to be spent in the trial and error procedures and its complexity can be neglected. Experimental results using PID controller parameter synthesized from this analyzer to the liquid level control plant model and the fluid flow control plant model show that the responses of the controlled systems can be efficiently controlled without any difficulty in mathemathical computation.

• 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.