• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.133-146
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• 2011

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1043-1057
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• 2000

This paper is devoted to the investigation of mixed Fourier-Bessel transformation (※Equations, See Full-text) We apply the method of [6] which provides the estimate for weighted L(sub)$\infty$-norm of the spherical mean of │f│$^2$ via its weighted L$_1$-norm (generally it is wrong without the requirement of the non-negativity of f). We prove that in the case of Fourier-Bessel transformatin the mentioned method provides (in dependence on the relation between the dimension of the space of non-special variables n and the length of multiindex ν) similar estimates for weighted spherical means of │f│$^2$, the allowed powers of weights are also defined by multiindex ν. Further those estimates are applied to partial differential equations with singular Bessel operators with respect to y$_1$, …, y(sub)m and we obtain the corresponding estimates for solutions of the mentioned equations.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.195-205
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• 2022

In this paper, we provide various characterizations for the composition operator on Lorentz spaces L(p, q), 1 < p ≤ ∞, 1 ≤ q ≤ ∞ to have finite ascent (descent) in terms of its inducing measurable transformation. At the end, in order to demonstrate our outcomes, some examples are given.

• Journal of the Society of Naval Architects of Korea
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• v.37 no.2
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• pp.57-69
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• 2000

A higher order panel method based on representation for both the geometry and the velocity potential is developed for the analysis of steady flow around marine propellers. The self-influence functions due to the normal dipole and the source are desingularized through the quadratic transformation, and then the singular part is integrated analytically whereas the non-singular part is integrated using Gaussian quadrature. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution around lifting bodies with much fewer panels than existing low order panel methods.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.683-689
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• 2009

We investigate the gaps among classes of weakly hyponormal composition operators induced by Embry characterization for the subnormality. The relationship between subnormality and weak hyponormality will be discussed in a version of composition operator induced by a non-singular measurable transformation.

• Korean Institute of Interior Design Journal
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• v.17 no.1
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• pp.162-169
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• 2008

Philippe Starck is a famous french designer known for his creative works in all aspects of life from architectural space to product design. Especially, in regard to furniture, he designed more than 250 works with various design characteristics. This study therefore aims to examinate the characteristics of furniture designed by Philippe Starck through assessment of his design background and philosophy, evaluation of fifty or so of his works in terms of their function, form, material, and emotions, and lastly through a chronological analysis. As a result from this study, following various results are drawn as design characteristic through forty six representative cases: 1) possibility of fabrication and transformation 2) multi-function or optional function for user 3) pursuit of simplicity using the characteristic of singular material or mono block and immateriality 4) emotional approach in design 5) non-design method such as use of archetype or historical form.

• Communications for Statistical Applications and Methods
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• v.23 no.2
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• pp.93-103
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• 2016

In the paper, we discuss dimension reduction of predictors ${\mathbf{X}}{\in}{{\mathbb{R}}^p}$ in a regression of $Y{\mid}{\mathbf{X}}$ with a notion of sufficiency that is called sufficient dimension reduction. In sufficient dimension reduction, the original predictors ${\mathbf{X}}$ are replaced by its lower-dimensional linear projection without loss of information on selected aspects of the conditional distribution. Depending on the aspects, the central subspace, the central mean subspace and the central $k^{th}$-moment subspace are defined and investigated as primary interests. Then the relationships among the three subspaces and the changes in the three subspaces for non-singular transformation of ${\mathbf{X}}$ are studied. We discuss the two conditions to guarantee the existence of the three subspaces that constrain the marginal distribution of ${\mathbf{X}}$ and the conditional distribution of $Y{\mid}{\mathbf{X}}$. A general approach to estimate them is also introduced along with an explanation for conditions commonly assumed in most sufficient dimension reduction methodologies.