• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.689-694
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• 2004

We investigate the test for model adequacy in nonlinear regression. We can expect the usual likelihood ratio statistic to be unaffected by any parametric- effect curvature; only the effect of intrinsic curvature needs to be considered. Multiplicative correction factor is derived for the limiting distribution of test statistic, which is a function of the intrinsic curvature arrays.

• Journal of the Korean Data and Information Science Society
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• v.24 no.1
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• pp.179-187
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• 2013

Bates and Watts (1981) have discussed the problems of reparameterizing nonlinear models in obtaining accurate linear approximation confidence regions for the parameters. A similar problem exists with computing confidence curves for fitted values or predictions. The statistical behavior of fitted values does not depend on the parameterization. Thus, as long as the intrinsic curvature is small, standard Wald intervals for fitted values are likely to be sufficient. Accuracy of linear approximation for fitted values is investigated using confidence curves.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.149-160
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• 2024

In this paper, we study the unicorn's Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata's theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension n ≥ 3 of non-zero scalar curvature are Riemannian spaces of constant curvature.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.913-917
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• 2009

The measures of leverage in linear regression has been extended to nonlinear regression models. We consider several curvature measures of nonlinearity in an estimation situation. The relationship between measures of leverage and statistical curvature are explored in nonlinear regression models. The circumstances under which the Jacobian leverage reduces to a tangent plane leverage are discussed in connection with the effective residual curvature of the nonlinear model.

• Communications for Statistical Applications and Methods
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• v.18 no.1
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• pp.131-136
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• 2011

The original Bates-Watts framework applies only to the complete parameter vector. Thus, guidelines developed in that framework can be misleading when the adequacy of the linear approximation is very different for different subsets. The subset curvature measures appear to be reliable indicators of the adequacy of linear approximation for an arbitrary subset of parameters in nonlinear models. Given the specific mean shift outlier model, the standard approaches to obtaining test statistics for outliers are discussed. The accuracy of outlier tests is investigated using subset curvatures.

• Korean Journal of Metals and Materials
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• v.47 no.8
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• pp.466-473
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• 2009

Our group previously observed the intrinsic stress evolution of Cu thin films during deposition by changing the deposition rate. Intrinsic stress of Cu thin films, which show Volmer-Weber growth, is reported to display three unique stress stages, initial compressive, broad tensile, and incremental compressive stress. The mechanisms of the initial compressive stress and incremental compressive stages remain subjects of debate, despite intensive research inquiries. The tensile stress stage may be related to volume contraction through grain growth and coalescence to reduce over-accumulate Cu adatoms on the film surface. The in-situ intrinsic stresses behavior in Cu thin films was investigated in the present study using a multi-beam curvature measurement system attached to a thermal evaporation device. The effect of substrate surface roughness was monitored by observed the in-situ intrinsic stress behavior in Cu thin films during deposition, using $100{\mu}m$ thick Si(111) wafer substrates with three different levels of surface roughness.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.593-607
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• 2021

The aim of the present paper is to establish an intrinsic generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1631-1647
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• 2015

In this paper, we prove two optimal inequalities involving the intrinsic scalar curvature and extrinsic Casorati curvature of submanifolds of generalized space forms endowed with a semi-symmetric metric connection. Moreover, we also characterize those submanifolds for which the equality cases hold.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.04a
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• pp.129-133
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• 2000

It is reasonable to use the stereo vision and image processing technique to digitize 3D coordinates of grid points and to evaluate surface strains on a sheet metal parts. However this method has its intrinsic problems such as the difficulty in enhancement of bad images inevitable error due to digital image resolution of camera and frame grabber unreliability of strains and thickness evaluated from coarse grid on the corner area with large curvature and the limitation of the area that can be measured at a time. Therefore it is still hard to measure strain distribution over the entire surface of a medium,- or large-sized stamped part at a time even by using an automated strain measurement system. In this study the curvature correction algorithm based on the grid refinement and the geometry assembling algorithm based on the global error minimization (GEM) scheme are suggested. Several applications are presented to show the reliability and efficiency of these algorithms.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.10 no.2
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• pp.104-109
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• 2011

I present a method of aspheric surface profile measurement using 2nd derivative of local area profile. This method is based on the principle of curvature sensor which measures the local 2nd derivative under test along a line. The profile is then reconstructed from the data on the each point. Unlike subaperture-stiching method and slope detection method, 2nd derivative method has strong points from a geometric point of view in measuring the aspheric surface profile. The second derivative terms of surface profile is an intrinsic property of the test piece, which is independent of its position and tip-tilt motion. The curvature is measured at every local area with high accuracy and high lateral resolution by using White-light scanning interferometry.