• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.559-568
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• 2003

We introduce the notion of two-scale convergence for partial differential equations with random coefficients that gives a very efficient way of finding homogenized differential equations with random coefficients. For an application, we find the homogenized matrices for linear second order elliptic equations with random coefficients. We suggest a natural way of finding the two-scale limit of second order equations by considering the flux term.

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.665-674
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• 2015

Lack of a general matrix formula hampers implementation of the semi-partial correlation, also known as part correlation, to the higher-order coefficient. This is because the higher-order semi-partial correlation calculation using a recursive formula requires an enormous number of recursive calculations to obtain the correlation coefficients. To resolve this difficulty, we derive a general matrix formula of the semi-partial correlation for fast computation. The semi-partial correlations are then implemented on an R package ppcor along with the partial correlation. Owing to the general matrix formulas, users can readily calculate the coefficients of both partial and semi-partial correlations without computational burden. The package ppcor further provides users with the level of the statistical significance with its test statistic.

• Advances in aircraft and spacecraft science
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• v.2 no.4
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• pp.427-443
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• 2015

The present paper is the follow-on of a former work in which the influence of the gas-surface interaction models was evaluated on the aerodynamic coefficients of an aero-space-plane and on a section of its wing. The models by Maxwell and by Cercignani-Lampis-Lord were compared by means of Direct Simulation Monte Carlo (DSMC) codes. In that paper the diffusive, fully accommodated, semi-specular and specular accommodation coefficients were considered. The results pointed out that the influence of the interaction models, considering the above mentioned accommodation coefficients, is pretty strong while the Cercignani-Lampis-Lord and the Maxwell models are practically equivalent. In the present paper, the comparison of the same models is carried out considering the dependence of the accommodation coefficients on the angle of incidence (or partial accommodation coefficients). More specifically, the normal and the tangential momentum partial accommodation coefficients, obtained experimentally by Knetchel and Pitts, have been implemented. Computer tests on a NACA-0012 airfoil have been carried out by the DSMC code DS2V-64 bits. The airfoil, of 2 m chord, has been tested both in clean and flapped configurations. The simulated conditions were those at an altitude of 100 km where the airfoil is in transitional regime. The results confirmed that the two interaction models are practically equivalent and verified that the use of the Knetchel and Pitts coefficients involves results very close to those computed considering a diffusive, fully accommodated interaction both in clean and flapped configurations.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1509-1533
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• 2020

We provide detailed proofs for local gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients in a ball and a half ball.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.865-875
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• 2020

We provide detailed proofs for local gradient estimates for weak solutions to elliptic equations in divergence form with partial Dini mean oscillation coefficients subject to conormal derivative boundary conditions.

• Journal for History of Mathematics
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• v.23 no.1
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• pp.53-66
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• 2010

This study concerns with partial sum of Fourier series, Fourier coefficients and the $L^1$-convergence of Fourier series. First, we introduce the $L^1$-convergence results. We consider equivalence relations of the partial sum of Fourier series from the early 20th century until the middle of. Second, we investigate the minor lineage of $L^1$-convergence theorem from W. H. Young to G. A. Fomin. Finally, we compare and reinterpret the $L^1$-convergence theorems.

• Journal of Information Processing Systems
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• v.14 no.5
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• pp.1068-1074
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• 2018

In this paper, we consider the delay partial differential equation of three dimensions with constant coefficients. We established the alternating direction difference scheme by the standard finite difference method, gave the order of convergence of the format and the expression of the difference scheme truncation errors.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.397-402
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• 2022

The mathematical expression of the p-value calculation for the semi-partial correlation coefficient differs between Kim (2015) and Cohen et al. (2003). These two expressions were compared and the advantages of Kim (2015)'s approach over Cohen et al. (2003) were discussed.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.333-346
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• 1996

Let $A(\zeta, \partial)$ be a second order uniformly elliptic operator $$ A(\zeta, \partial )u = -\sum_{j, k = 1}^{n} \frac{\partial\zeta_i}{\partial}(a_{jk}(\zeta)\frac{\partial\zeta_k}{\partial u}) + \sum_{j = 1}^{n}b_j(\zeta)\frac{\partial\zeta_j}{\partial u} + c(\zeta)u $$ with real, smooth coefficients $a_{j, k}, b_j$, c defined on $\zeta \in \Omega, \Omega$ a bounded domain in $R^n$ with a sufficiently smooth boundary $\Gamma$.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.57-66
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• 2024

In this paper, we study how the Hilbert polynomial, associated with a reduced closed subscheme X of codimension 2 in ℙ^N, reveals geometric information about X. Although it is known that the Hilbert polynomial can tell us about the scheme's degree and arithmetic genus, we find additional geometric information it can provide for smooth varieties of codimension 2. To do this, we introduce the concept of Gotzmann coefficients, which helps to extract more information from the Hilbert polynomial. These coefficients are based on the binomial expansion of values of the Hilbert function. Our method involves combining techniques from initial ideals and partial elimination ideals in a novel way. We show how these coefficients can determine the degree of certain geometric features, such as the singular locus appearing in a generic projection, for smooth varieties of codimension 2.