• Journal of the Korean Mathematical Society
• /
• v.43 no.6
• /
• pp.1301-1324
• /
• 2006

The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

• The Korean Journal of Applied Statistics
• /
• v.18 no.1
• /
• pp.183-196
• /
• 2005

In this paper we studied the saddlepoint approximations to the distribution of non-homogeneous quadratic forms in normal variables. The results are the extension of Kuonen's which provide the same approximations to homogeneous quadratic forms. The CGF of interested statistics and related properties are derived for applications of saddlepoint techniques. Simulation results are also provided to show the accuracy of saddlepoint approximations.

• Journal of the Korean Mathematical Society
• /
• v.41 no.6
• /
• pp.1101-1114
• /
• 2004

We generalize a result of Dror Farjoun and Zabrodsky on the relationship between fixed point sets and homotopy fixed point sets, which is related to the generalized Sullivan Conjecture. As an application, we discuss extension problems considering actions on homogeneous spaces of p-compact groups.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1377-1384
• /
• 2019

In this paper, we prove that for every surjective phase-isometry between the unit spheres of real atomic $L_p$-spaces for p > 0, its positive homogeneous extension is a phase-isometry which is phase equivalent to a linear isometry.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.658-663
• /
• 2003

A process of 3-D stereo particle image velocimetry(PIV)was developed for the measurement of an illuminated sliced section field of 3-D complex flows. The present method includes modeling of camera by a calibrator based on the homogeneous coordinate system, transformation of the oblique-angled image to the right-angled image, identification of 2-D velocity vectors by 2-D cross-correlation equation, stereo matching of 2-D velocity vectors of two cameras, accurate calculation of 3-D velocity vectors by homogeneous coordinate system, removal of error vectors by a statistical method followed by a continuity equation criteria, and finally 3-D display as the post processing. An experimental system was also used for the application of the proposed method. Two high speed digital CCD cameras and an Argon-Ion Laser for the illumination were adopted to clarify the time-dependent characteristics of the leading edge extension(LEX) in a highly swept shape applied to a delta wing found in modern air-fighters.

• Kyungpook Mathematical Journal
• /
• v.50 no.2
• /
• pp.297-306
• /
• 2010

In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree - $\lambda$ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.9 no.5
• /
• pp.47-57
• /
• 2000

In this study, a fundamental approach to make clear the mechanism of the mutual interference and coalescence of stress fields in the vicinity of two crack tips on the process of their slow growth, using boundary element method. Automatic generation of quadratic discontinuous elements along both of the crack boundaries which can be defined by an arbitrary piece-wise straight geometry. The direction of the crack-extension increment is predicted by the maximum principal stress criterion, corrected to account for the discreteness of the crack extension. Along the computed direction, the crack is extended one increment. Automatic incremental crack-extension analysis with no remeshing, computation of the stress intensity factors by J-integral. Numerical stress intensity factors for two growing cracks in plane-homogeneous regions were determined.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.1 s.173
• /
• pp.69-78
• /
• 2000

The one-parameter singular expression for stresses and displacements near a crack tip has been widely thought to be sufficiently accurate over a reasonable re ion for any geometry and loading conditions. In many cases, however subsequent terms of the series expansion are quantitatively significant, and so we now consider the evaluation of such terms and their effect on the predicted crack growth direction. For this purpose the problem of a cracked orthotropic plate subjected to a biaxial load is analysed. It is assumed that the material is ideal homogeneous anisotropic. BY considering the effect of the load applied parallel to the plane of the crack, the distribution of stresses and displacements at the crack tip is reanalyzed. In order to determine values for the angle of initial crack extension we employ the normal stress ratio criterion.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.2
• /
• pp.439-448
• /
• 2023

In this article, we are interested in studying the fractional Sadik Transform and a combination of the method of steps that will be applied together to find accurate solutions or approximations to homogeneous and non-homogeneous delayed fractional differential equations with constant-coefficient and possible extension to time-dependent delays. The results show that the process is correct, exact, and easy to do for solving delayed fractional differential equations near the origin. Finally, we provide several examples to illustrate the applicability of this method.

• Composites Research
• /
• v.23 no.5
• /
• pp.8-14
• /
• 2010

Three types of glass woven fabrics (plain, balanced twill, and unbalanced twill) having various sample sizes and aspect ratios were tested using the bias-extension tests. Real-time deformation images, force, and displacement data were collected. For the bias-extension test, the shear angle of the fabrics from the equation based on the crosshead displacement and fabric size was compared with direct manual measurements of the warp and weft angles as well as the optical measurement software. To determine the shear force, an analytical equation was introduced considering the kinematics of the bias-extension test. The obtained shear behaviors were further compared with the results by the trellis-frame test. The optical measurement methods showed that the mathematical method was reasonable before the shear angle of the fabrics reaches $30^{\circ}$ in the bias-extension tests. Also, the bias-extension test gave consistent behaviors with the trellis-frame test only for isotropic and homogeneous fabrics such as balanced plain and twill weaves.