• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.8
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• pp.440-444
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• 2002

This paper presents an efficient and robust algorithm to compute the isophote of a surface of revolution. A surface of revolution can be decomposed to a set of cross-sectional circles. The surface normals along each cross-sectional circle form a cone. Using the characteristics of the normal vectors and the symmetric property of the surface of revolution, we propose a method to find the connected components of an isophote, which requires intersecting a planar curve(and its reflection) with two rays. Moreover, we propose a closed-form representation of an isophote as a parametric curve.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.10a
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• pp.312-333
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• 2006

This paper presents the results of an analysis of the excess porewater pressure distribution due to piezocone penetration in overconsolidated clays. From piezocone test results for moderately and heavily overconsolidated clays, it was observed that the excess porewater pressure increases monotonically from the piezocone surface to the outer boundary of the shear zone and then decreases logarithmically to the outer boundary of the plastic zone. It was also found that the size of the shear zone decreases from approximately 2.2 to 1.5 times the cone radius with increasing OCR, while the plastic radius is about 11 times the piezocone radius, regardless of the OCR. The equation developed in this study based on the modified Cam clay model and the cylindrical cavity expansion theory, which take into consideration the effects of the strain rate and stress anisotropy, provide a good prediction of the initial porewater pressure at the piezocone location. The method of predicting the spatial distribution of excess porewater pressure proposed in this study is based on a linearly increasing ${\Delta}u_{shear}$. In the shear zone and a logarithmically decreasing ${\Delta}u_{oct}$, and is verified by comparing with the excess porewater pressure measured in overconsolidated specimens at the calibration chamber.

• Journal of Korean Ophthalmic Optics Society
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• v.8 no.2
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• pp.163-168
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• 2003

The eye sensitivity in the difference conditions of a light source intensity consists of two functions by the receptor of cone and rod according to a wavelength. We derived a distribution function of $P{\lambda}=A{\cdot}e^{-({\lambda}-{\lambda}_u)^2/2W^2}$ using a respond probability of the receptor of cone-rod for a photon. It was well applied for a CIE eye's sensitivity curve of a wavelength. When there is lens In front of eye, luminous efficiency should be corrected. Transmission light which permeate to depends on absorption wavelength, and relationship of final luminous efficiency's estimation method is expressed by multiplication of luminous efficiency and transmittance intensity of lens. $$Pf({\lambda})=T({\lambda}){\cdot}P({\lambda})$$. The theory was applied to photopic and scopic vision with brown color lens.

• Proceedings of the Korean Geotechical Society Conference
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• 2008.10a
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• pp.1328-1339
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• 2008

For a commonly used piezocone with a shoulder filter element, dilatory dissipation behavior, which shows an initial temporary increase in pore pressure, has been observed in overconsolidated cohesive soils. However, there is no appropriate way to estimate a consolidation parameter from a dilatory dissipation curve because currently available interpretation methods were developed based on the monotonic decrease of the excess pore pressure. In this study, the interpretation method for evaluation of coefficient of consolidation from a dilatory dissipation result of piezocone test was developed by performing the finite difference analysis on the dissipation after cone penetration. The distribution of the initial excess pore pressure induced by cone penetration, which is the core of the analysis, was estimated from the empirical modification of a solution proposed by cavity expansion theory and critical state concept. And the proposed interpretation method was applied to the field piezocone data and the results were compared to those obtained from laboratory tests. Its reliability was confirmed by the insignificant difference between the values of coefficient of consolidation from piezocone tests and laboratory consolidation tests.

• Journal of Welding and Joining
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• v.27 no.5
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• pp.88-93
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• 2009

While the pinch instability theory (PIT) has been widely employed to analyze the spray transfer mode in the gas metal arc welding (GMAW), it cannot predict the detaching drop size accurately. The PIT is modified in this work to increase the accuracy of prediction and to simulate the molten tip geometry to be more physically acceptable. Since the molten tip becomes a cone shape in the spray mode, the effective wire diameter is formulated that the effective diameter is inversely proportional to current square. Modifications are also made to consider the finite length of the liquid column and current leakage through the arc. While the effective diameter influences drop transfer significantly, the current leakage has negligible effects. The effects of modifications on drop transfer are analyzed, and the predicted drop diameters show good agreements with the experimental data of the steel wire.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.298-309
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• 1990

In this paper, a new method is suggested to analyze impulsive stresses at loading poing of concentrated impact load under certain impact conditions determined by impact velocity, stiffness of plate and mass of impact body, etc. The impulsive stresses are analyzed by using the three dimensional dynamic theory of elasticity so as to analytically clarify the generation phenomenon of cone crack at the impact fracture of fragile materials (to be discussed if the second paper). The Lagrange's plate theory and Hertz's law of contact theory are used for the analysis of impact load, and the approximate equation of impact load is suggested to analyze the impulsive stresses at the impact point to decide the ranage of impact load factor. When impact load factors are over and under 0.263, approximate equations are suggested to be F(t)=Aexp(-Bt)sinCt and F(t)=Aexp(-bt) {1-exp(Ct)} respectively. Also, the inverse Laplace transformation is done by using the F.F.T.(fast fourier transform) algorithm. And in order to clarity the validity of stress analysis method, experiments on strain fluctuation at impact point are performed on a supported square glass plate. Finally, these analytical results are shown to be in close agreement with experimental results.

• Proceedings of the KWS Conference
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• 2009.11a
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• pp.44-44
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• 2009

While the pinch instability theory (PIT) has been widely employed to analyze the spray transfer mode in the gas metal arc welding (GMAW), it cannot predict the detaching drop size accurately. The PIT is modified in this work to increase the accuracy of prediction and to simulate the molten tip geometry to be more physically acceptable. Since the molten tip becomes a cone shape in the spray mode, the effective wire diameter is formulated that the effective diameter is inversely proportional to current square. Modifications are also made to consider the finite length of the liquid column and current leakage through the arc. While the effective diameter influences drop transfer significantly, the current leakage has negligible effects. The effects of modifications on drop transfer are analyzed, and the predicted drop diameters show good agreements with the experimental data of the steel wire.

• Composites Research
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• v.16 no.4
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• pp.1-9
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• 2003

2 ply laminated composite is regarded to simulate the interply behavior of the belt layer of the tire. It was cone with 3 dimensional FE(Finite Element) analysis to determine interply shear stress and strain. Widthwise, the shear strain was measured by the pin method. These results are compared with those of CLT(classical lamination theory) in center region and those of Kassapoglou's and Kelsey's theory in edge region. In the FE analysis. rubber is assumed as linear elastic material. and rubber/cord laminate as the orthotropic material composed of cord and rubber In the FE result, interlaminar shear stress causing the interlaminar delamination has the largest value in the edge region of the inner rubber layer. Numerical results obtained coincides with CLT well in the center region, and agrees with other theoretical result little in the edge region.

• Journal of the Korean Statistical Society
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• v.30 no.2
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• pp.179-192
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• 2001

When a statistical model has a hierarchical structure such as multilayer perceptrons in neural networks or Gaussian mixture density representation, the model includes distribution with unidentifiable parameters when the structure becomes redundant. Since the exact structure is unknown, we need to carry out statistical estimation or learning of parameters in such a model. From the geometrical point of view, distributions specified by unidentifiable parameters become a singular point in the parameter space. The problem has been remarked in many statistical models, and strange behaviors of the likelihood ratio statistics, when the null hypothesis is at a singular point, have been analyzed so far. The present paper studies asymptotic behaviors of the maximum likelihood estimator and the Bayesian predictive estimator, by using a simple cone model, and show that they are completely different from regular statistical models where the Cramer-Rao paradigm holds. At singularities, the Fisher information metric degenerates, implying that the cramer-Rao paradigm does no more hold, and that he classical model selection theory such as AIC and MDL cannot be applied. This paper is a first step to establish a new theory for analyzing the accuracy of estimation or learning at around singularities.