• Korean Journal of Mathematics
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• v.21 no.3
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• pp.345-350
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• 2013

Some results on the sensitivity of the solution of the generalized Lyapunov equation $$A^{n-1}X+A^{n-2}XA^*+{\cdots}+X(A^*)^{n-1}=B$$ are shown follow easily from well-known theorems in functional analysis.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.45-61
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• 2009

We consider finite time blowup solutions of the $L^2$-critical focusing Hartree equation on $\mathbb{R}^n$, $n{\geq}3$ below $H^1$.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.1
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• pp.1-11
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• 1998

For the analysis of phonon heat transfer within short time and spatial scales, conventional macroscopic heat conduction equations with jump boundary conditions are tried and the results are compared to those of equation of phonon radiative transport(EPRT), which is one of microscopic transport equation. In transient state the macroscopic temperatures show far different behavior from EPRT. In steady state the hyperbolic temperatures with temperature jump at the wall from time relaxation model agrees well with EPRT temperatures. Since EPRT is also an approximate form of microscopic transport equation and there are no experimental results to verify the proposed model in this study, we can not conclude whether the approaching method from this study is valid or not. To the authors' knowledge, there are no experimental results available which can be used to test the validity of these models. Such an experiment, while difficult to conduct, would be invaluable.

• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.927-928
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• 2006

In this paper, we propose a dynamic emotion system involving the state equation and the output equation from the control theory. In our emotion system, the state equation accepts external stimulus and generates emotions. And the output equation modifies the intensity of emotions in accordance with personalities and circumstances. The validity of the proposed emotion system is shown by two simulation works which express emotions according to personalities and circumstances.

• Journal of the Korean Chemical Society
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• v.48 no.3
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• pp.243-248
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• 2004

Brake theory of viscosity, which can sucessfully calculate the viscosity of real gases, dense gases and liquids, is extended to the binary gas mixture. Adjustable parameters are not involved, but the calculated results are good agreements with the experimental values at high pressure as well as low pressure. Corresponding state equation for viscosity can be obtained by using the Redlich-Kwong equation, so that we hope this equation may be useful for the supercritical fluid in engineering applications at high pressure around the critcal point.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.8
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• pp.1355-1361
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• 2016

The inter-turn fault (ITF) causes the negative sequence components in the d -q voltage equation due to an increase in the unbalance of three-phase input currents. For this reason, d -q voltage equation become complicate as the voltage equation is classified into positive and negative components. In this study, we propose a simplified d -q equivalent circuit of an interior permanent magnet synchronous motor under ITF state. First, we proposed modeling method for d -q current based on the finite element method simulation results. Then, we developed the simplified d -q equivalent circuit by applying the proposed d -q current modeling.

• Macromolecular Research
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• v.11 no.1
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• pp.53-61
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• 2003

A molecular-thermodynamic model is developed for the salt-induced protein precipitation. The protein molecules interact through four intermolecular potentials. An equation of state is derived based on the statistical mechanical perturbation theory with the modified Chiew's equation for the fluid phase, Young's equation for the solid phase as the reference system and a perturbation based on the protein-protein effective two body potential. The equation of state provides an expression for the chemical potential of the protein. In a single protein system, the phase separation is represented by fluid-fluid equilibria. The precipitation behaviors are simulated with the partition coefficient at various salt concentrations and degree of pre-aggregation effect for the protein particles. In a binary protein system, we regard the system as a fluid-solid phase equilibrium. At equilibrium, we compute the reduced osmotic pressure-composition diagram in the diverse protein size difference and salt concentrations.

• Structural Engineering and Mechanics
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• v.81 no.2
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• pp.179-194
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• 2022

The bending, buckling and free vibration responses of functionally graded material (FGM) beams are investigated semi-analytically by the scaled boundary finite element method (SBFEM) in this paper. In the concepts of the SBFEM, the dimension of computational domain can be reduced by one, therefore only the axial dimension of the beam is discretized using the higher order spectral element, which reduces the amount of calculation and greatly improves the calculation efficiency. The governing equation of FGM beams is derived in detail by the means of the principle of virtual work. Compared with the higher-order beam theory, fewer parameters and simpler control equations are used. And the governing equation is transformed into a first-order ordinary differential equation by introducing intermediate variables. Analytical solutions of the governing equation can be obtained by pade series expansion in the direction of thickness. Numerical example are compared with the numerical solutions provided by the previous researchers to verify the accuracy and applicability of the proposed method. The results show that the proposed formulations can quickly converge to the reference solutions by increasing the order of higher order spectral elements, and high accuracy can be achieved by using a small number of the elements. In addition, the influence of the structural sizes, material properties and boundary conditions on the mechanical behaviors of FG beams subjected to different load types is discussed.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.487-500
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• 1997

In this paper we introduce a multigrid method for solving the nonliear Urysohn integral equation. The algorithm is derived from a discrete resolvent equation which approximates the continuous resolvent equation of the nonlinear Urysohn integral equa-tion. The algorithm is mathematically equivalent to Atkinson's adap-tive twogrid iteration. But the two are different computationally. We show the convergence of the algorithm and its equivalence to Atkinson's adaptive twogrid iteration. in our numerical example we compare our algorithm to other multigrid methods for solving the nonliear Urysohn integral equation including the nonlinear multigrid nethod introduced by hackbush.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.791-804
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• 2006

This paper is concerned with a second-order iterated differential equation of the form $c_0x'(Z)+c_1x'(z)+c_2x(z)=x(az+bx(z))+h(z)$ with the distinctive feature that the argument of the unknown function depends on the state. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained.