• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.185-223
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• 2022

The classical equation of Jonathan Homer Lane and Robert Emden, a nonlinear second-order ordinary differential equation, models the isothermal spherical clouded gases under the influence of the mutual attractive interaction between the gases' molecules. In this paper, the Adomian decomposition method (ADM) is presented to obtain highly accurate and reliable analytical solutions of a class of generalised Lane-Emden equations with strong nonlinearities. The nonlinear term f(y(x)) of the proposed problem is given by the integer powers of a continuous real-valued function h(y(x)), that is, f(y(x)) = h^m(y(x)), for integer m ≥ 0, real x > 0. In the end, numerical comparisons are presented between the analytical results obtained using the ADM and numerical solutions using the eighth-order nested second derivative two-step Runge-Kutta method (NSDTSRKM) to illustrate the reliability, accuracy, effectiveness and convenience of the proposed methods. The special cases h(y) = sin y(x), cos y(x); h(y) = sinh y(x), cosh y(x) are considered explicitly using both methods. Interestingly, in each of these methods, a unified result is presented for an integer power of any continuous real-valued function - compared with the case by case computations for the nonlinear functions f(y). The results presented in this paper are a generalisation of several published results. Several examples are given to illustrate the proposed methods. Tables of expansion coefficients of the series solutions of some special Lane-Emden type equations are presented. Comparisons of the two results indicate that both methods are reliably and accurately efficient in solving a class of singular strongly nonlinear ordinary differential equations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.1
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• pp.117-124
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• 2009

The p-convergent boundary element method has been proposed to analyze two-dimensional potential problem on the basis of high order Legendre shape functions that have different property comparing with the shape functions in conventional boundary element method. The location of nodes corresponding to high order shape function are not defined along the boundary, called by nodeless node, similar to the p-convergent finite element method. As the order of shape function increases, the collocation point method is used to solve linear simultaneous equations. The collocation patterns of p-convergent boundary element method consist of non-symmetric hierarchial or symmetric non-hierarchical. As the order of shape function increases, the number of collocation point increases. The singular integral that appears in p-convergent boundary element has been calculated by special numeric quadrature technique and semi-analytical integration technique. The L-shape domain problem including singularity in the vicinity of reentrant comer is analyzed and the numerical results show that the relative error is smaller than $10^{-2}%$ range as compared with other results in literatures. In case of same condition, the symmetric p-collocation point pattern shows high accuracy of solution.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.7
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• pp.617-623
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• 2013

Accurate prediction of the radiated noise is important to reduce the noise of the washing machine. It is also necessary to predict the excitation force accurately because excitation force can induce noise. In order to predict the excitation force acting on the washing machine, this paper conducts source identification method by use of phase reference spectrum. In this method, the transfer function between the cabinet and the motor through FEM and the measured response from the surface of the cabinet is used. The analysis of the radiation noise from the identified exciting force has been investigated. The comparison between the predicted SPL and the measured SPL at 1m apart from the front side of the washing machine showed good tendency.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.77.3-77.3
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• 2019

Aims. The evolution of scaling relations between SMBHs and their host galaxies becomes uncertain at high redshifts. The HULQ project proposes to use gravitational lensing to measure the masses of QSO host galaxies, an otherwise difficult goal. SMBH masses of QSOs are relatively easy to determine using either reverberation mapping or the single-epoch method. These measurements, if made for a substantial number of QSOs at various redshifts, will allow us to study the co-evolution of SMBHs and their host galaxies. To determine the feasibility of this study, we present how to estimate the number of sources lensed by QSO hosts, i.e. the number of deflector QSO host galaxies (hereafter QSO lenses). Method and results. Using SMBH masses measured from SDSS DR14 spectra, and the M_BH - Sigma relation, the Einstein radii are calculated as a function of source redshift, assuming singular isothermal sphere mass distributions. Using QSOs and galaxies as sources, the probability of a QSO host galaxy being a QSO lens is calculated, depending on the limiting magnitude. The expected numbers of QSO lenses are estimated for ongoing and future wide-imaging surveys, and additional factors that may affect these numbers are discussed.

• Korea-Australia Rheology Journal
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• v.15 no.3
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• pp.131-150
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• 2003

A new numerical algorithm of finite element methods is presented to solve high Deborah number flow problems with geometric singularities. The steady inertialess planar 4 : 1 contraction flow is chosen for its test. As a viscoelastic constitutive equation, we have applied the globally stable (dissipative and Hadamard stable) Leonov model that can also properly accommodate important nonlinear viscoelastic phenomena. The streamline upwinding method with discrete elastic-viscous stress splitting is incorporated. New interpolation functions classified as rational interpolation, an alternative formalism to enhance numerical convergence at high Deborah number, are implemented not for the whole set of finite elements but for a few elements attached to the entrance comer, where stress singularity seems to exist. The rational interpolation scheme contains one arbitrary parameter b that controls the singular behavior of the rational functions, and its value is specified to yield the best stabilization effect. The new interpolation method raises the limit of Deborah number by 2∼5 times. Therefore on average, we can obtain convergent solution up to the Deborah number of 200 for which the comer vortex size reaches 1.6 times of the half width of the upstream reservoir. Examining spatial violation of the positive definiteness of the elastic strain tensor, we conjecture that the stabilization effect results from the peculiar behavior of rational functions identified as steep gradient on one domain boundary and linear slope on the other. Whereas the rational interpolation of both elastic strain and velocity distorts solutions significantly, it is shown that the variation of solutions incurred by rational interpolation only of the elastic strain is almost negligible. It is also verified that the rational interpolation deteriorates speed of convergence with respect to mesh refinement.

• Journal of the Korean Institute of Landscape Architecture
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• v.33 no.4 s.111
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• pp.97-107
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• 2005

This study was carried out to construct accurate and scientific system of assessment indicators in selection of National Trust conservation areas, which was new concept of domestic environment movement and offer the raw data of new analytic method by introducing the fuzzy theory and weight for overcoming the uncertainty of ranking decision. To transform the Likert's scale granted to assessment indicators into the type of triangular fuzzy number(a, b, c), there was conversion to each minimum(a), median(b), and maximum(c) in applying membership function, and in using the center of gravity and eigenvalue, there was to decide the ranking. The rankings of converted values applied a mean importance and weight were confirmed that they were generally changed. Therefore, the ranking decision was better to accomplish objective and rational ranking decision by applying weight that was calculated in grouping of indicator than to judge the singular concept and to be useful in assessment of diverse National Trust site. In the future, because AHP, which was general method of calculating weight, was lacked, there was to understand the critical point to fix a pertinent weight, and to carry out the study applying engineering concept like fuzzy integral using $\lambda-measure$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.10
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• pp.1029-1037
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• 2009

Recently, the technologies of mobile robots have been growing rapidly in the fields such as cleaning robot, explosive ordnance disposal robot, patrol robot, etc. However, the researches about the autonomous underwater robots have not been done so much, and they still remain at the low level of technology. This paper describes a model of 3-joint (4 links) fish robot type. Then we calculate the dynamic motion equation of this fish robot and use Singular Value Decomposition (SVD) method to reduce the divergence of fish robot's motion when it operates in the underwater environment. And also, we analysis response characteristic of fish robot according to the parameters of input torque function and compare characteristic of fish robot with 3 joint and fish robot with 2 joint. Next, fish robot's maximum velocity is optimized by using the combination of Hill Climbing Algorithm (HCA) and Genetic Algorithm (GA). HCA is used to generate the good initial population for GA and then use GA is used to find the optimal parameters set that give maximum propulsion power in order to make fish robot swim at the fastest velocity.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.839-865
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• 2013

We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v&gt;0\;in\;\mathbb{R}^N,}$$ where ${\varepsilon}$ is a small positive parameter; $V_1$, $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$-homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$, where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$.

• International Journal of Control, Automation, and Systems
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• v.5 no.5
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• pp.547-558
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• 2007

This paper proposes a simpler solution to the stabilization problem of a special class of nonlinear underactuated mechanical systems which includes widely studied benchmark systems like Inertia Wheel Pendulum, TORA and Acrobot. Complex internal dynamics and lack of exact feedback linearizibility of these systems makes design of control law a challenging task. Stabilization of these systems has been achieved using Energy Shaping and damping injection and Backstepping technique. Former results in hybrid or switching architectures that make stability analysis complicated whereas use of backstepping some times requires closed form explicit solutions of highly nonlinear equations resulting from partial feedback linearization. It also exhibits the phenomenon of explosions of terms resulting in a highly complicated control law. Exploiting recently introduced Dynamic Surface Control technique and using control Lyapunov function method, a novel nonlinear controller design is presented as a solution to these problems. The stability of the closed loop system is analyzed by exploiting its two-time scale nature and applying concepts from Singular Perturbation Theory. The design procedure is shown to be simpler and more intuitive than existing designs. Design has been applied to important benchmark systems belonging to the class demonstrating controller design simplicity. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and performance is verified using numerical simulations.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.5
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• pp.442-449
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• 2009

A two-dimensional cross-section analysis program based on the finite element method has been developed for composite blades with solid, thin-walled and compound cross-sections. The weighted-modulus method is introduced to determine the laminated composite material properties. The shear center and the torsion constant for any given section are calculated according to the Trefftz' definition and the St. Venant torsion theory, respectively. The singular value problem of cross-section stiffness properties faced during the section analysis has been solved by performing an eigenvalue analysis to remove the rigid body mode. Numerical results showing the accuracy of the program obtained for stiffness, offset and inertia properties are compared in this analysis. The current analysis results are validated with those obtained by commercial software and published data available in the literature and a good correlation has generally been achieved through a series of validation study.