• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1996년도 춘계학술발표회논문집(1)
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• pp.131-136
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• 1996

An analytic nodal expansion method has been derived for the multigroup neutron diffusion equation in 2-D cylindrical(R-Z) coordinate. In this method we used the second order Legendre polynomials for source, and transverse leakage, and then the diffusion eqaution was solved analytically. This formalism has been applied to 2-D LWR model. $textsc{k}$$_{eff}$, power distribution, and computing time have been compared with those of ADEP code(finite difference method). The benchmark showed that the analytic nodal expansion method in R-Z coordinate has good accuracy and quite faster than the finite difference method. This is another merit of using R-Z coordinate in that the transverse integration over surfaces is better than the linear integration over length. This makes the discontinuity factor useless.s.

• Nuclear Engineering and Technology
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• 제56권3호
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• pp.772-784
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• 2024

The hexagonal nodal code RENUS has been enhanced to handle irregularly deformed hexagonal assemblies. The underlying RENUS methods involving triangle-based polynomial expansion nodal (T-PEN) and corner point balance (CPB) were extended in a way to use line and surface integrals of polynomials in a deformed hexagonal geometry. The nodal calculation is accelerated by the coarse mesh finite difference (CMFD) formulation extended to unstructured geometry. The accuracy of the unstructured nodal solution was evaluated for a group of 2D SFR core problems in which the assembly corner points are arbitrarily displaced. The RENUS results for the change in nuclear characteristics resulting from fuel deformation were compared with those of the reference McCARD Monte Carlo code. It turned out that the two solutions agree within 18 pcm in reactivity change and 0.46% in assembly power distribution change. These results demonstrate that the proposed unstructured nodal method can accurately model heterogeneous thermal expansion in hexagonal fueled cores.

• 전기학회논문지
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• 제61권6호
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• pp.885-890
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• 2012

In this study, a new blood pressure measuring system was proposed and implemented. An additional small-cuff was placed on the center of a inner cuff to measure morphological signals and new oscillometric ratio. The proposed BP-measuring system is composed of an external cuff, an inner cuff and a small-cuff. Oscillation signal from small-cuff is interpolated with 7th-order fitting polynomials and SBP, DBP ratio were 22.2% and 87.7%. Experimental data were gathered from 20 volunteers ($25{\pm}4$ years) and arterial blood pressure values were compared with auscultation, sphygmomanometers, small-cuff and inner-cuff. As a result, the difference in systolic BP between auscultation and the small-cuff was 1.93(${\pm}1.28$) mmHg, and the inner-cuff was 4.53(${\pm}4.39$) mmHg, and sphygmomanometer was 6.68(${\pm}3.99$) mmHg, and the corresponding difference in diastolic BP was 2.50(${\pm}2.04$) mmHg, 3.50(${\pm}3.19$) mmHg, 7.35(${\pm}5.62$), respectively.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.185-196
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• 2024

In this article, we investigate the growth of meromorphic solutions of $${\alpha}(z)(\frac{{\Delta}_c{\eta}}{{\eta}})^2\,+\,(b_2(z){\eta}^2(z)\;+\;b_1(z){\eta}(z)\;+\;b_0(z))\frac{{\Delta}_c{\eta}}{{\eta}} \atop =d_4(z){\eta}^4(z)\;+\;d_3(z){\eta}^3(z)\;+\;d_2(z){\eta}^2(z)\;+\;d_1(z){\eta}(z)\;+\;d_0(z),$$ where a(z), b_i(z) for i = 0, 1, 2 and d_j (z) for j = 0, ..., 4 are given functions, △_cη = η(z + c) - η(z) with c ∈ ℂ\{0}. In particular, when the a(z), the b_i(z) and the d_j(z) are polynomials, and d₄(z) ≡ 0, we shall show that if η(z) is a transcendental entire solution of finite order, and either deg a(z) ≠ deg d₀(z) + 1, or, deg a(z) = deg d₀(z) + 1 and ρ(η) ≠ ½, then ρ(η) ≥ 1.

• Korean Journal of Hydrosciences
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• 제6권
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• pp.51-66
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• 1995

Various Eulerian-Lagerangian numerical models for the one-dimensional longtudinal dispersion equation are studied comparatively. In the models studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing advection and the other dispersion. The advection equation has been solved using the method of characteristics following flud particles along the characteristic line and the result are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpo;ation po;ynomials are superor to Lagrange interpolation polynomials in reducing both dissipation and dispersion errors.

• 대한수학회보
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• 제50권1호
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• pp.263-273
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• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.267-280
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• 2009

In this paper we investigate a simple two-level additive Schwarz preconditioner for the P1 symmetric interior penalty Galerkin method of the Poisson equation on rectangular meshes. The construction is based on the decomposition of the global space of piecewise linear polynomials into the sum of local subspaces, each of which corresponds to an element of the underlying mesh, and the global coarse subspace consisting of piecewise constants. This preconditioner is a direct combination of the block Jacobi iteration and the cell-centered finite difference method, and thus very easy to implement. Explicit upper and lower bounds for the maximum and minimum eigenvalues of the preconditioned matrix system are derived and confirmed by some numerical experiments.

• Korean Journal of Geomatics
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• 제3권1호
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• pp.53-57
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• 2003

As the Korea Multi-Purpose Satellite-I (KOMPSAT-1) satellite can roll tilt up to $\pm$45$^{\circ}$, we have analyzed some KOMPSAT-1 EOC images taken at different tilt angles for this study. The required ground coordinates for bundle adjustment and geometric accuracy are obtained from the digital map produced by the National Geography Institution, at a scale of 1:5,000. Followings are the steps taken for the tilting angle of KOMPSAT-1 to be present in the evaluation of geometric accuracy of each different stereo image data: Firstly, as the tilting angle is different in each image, the characteristic of satellite dynamic must be determined by the sensor modeling. Then the best sensor modeling equation should be determined. The result of this research, the difference between the RMSE values of individual stereo images is mainly due to quality of image and ground coordinates instead of tilt angle. The bundle adjustment using three KOMPSAT-1 stereo pairs, first degree of polynomials for modeling the satellite position, were sufficient.

• 제어로봇시스템학회논문지
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• 제6권9호
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• pp.739-744
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• 2000

A robust control algorithm under disturbance and reference change is developed using a self tuning control method incorporting of the well known internal model principle and the annihilator polynomical. The types of disturbance and reference signal are assumed to be given as known difference polynomials. The algorithm is shown for a minimum phase system with parameters of unknown parameters.

• Nuclear Engineering and Technology
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• 제55권8호
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• pp.2864-2872
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• 2023

The criticality problem in this study is studied with the recently investigated the Anlı-Güngör scattering function. The scattering function depends on the Legendre polynomials as the Mika scattering function, but it includes only one scattering parameter, t, and its orders. Both Mika and Anlı-Güngör scattering are the same for only linear anisotropic scattering. The difference appears for the quadratic scattering and further. The analytical calculations are performed with the H_N method, and the numerical results are calculated with Wolfram Mathematica. Interpolation technique in Mathematica is also used to approximate the isotropic scattering results when t parameter goes to zero. Thus, the calculated results could be compared with the literature data for isotropic scattering.