• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.1227-1233
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• 1993

In this paper we present the differential geometric approach for the analysis and design of sliding modes in nonlinear variable structure feedback systems. We also design the robust controller for the nonlinear system using variable structure control theory on the basis of differential geometric methods and feedback linearization applying Min-Max control based on the Lyapunov second method. The robustness against parameter uncertainties for robot manipulators with flexible joint is considered. Simulation results are presented and show the advantage of the proposed nonlinear control method.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1587-1598
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• 2013

In this paper, we obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation $$\frac{{\partial}u}{{\partial}t}={\triangle}u-b(x,t)u^{\sigma}$$ under general geometric flow on complete noncompact manifolds, where 0 < ${\sigma}$ < 1 is a real constant and $b(x,t)$ is a function which is $C^2$ in the $x$-variable and $C^1$ in the$t$-variable. As an application, we get an interesting Harnack inequality.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.379-386
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• 2015

The original geometric mean of two positive definite operators A and B is given by A#B = A^1/2(A^-1/2BA^-1/2)^1/2A^1/2. In this article we provide a new proof to construct from the two-variable geometric mean to the multivariable mean via symmetrization introduced by Lawson and Lim [5]. Finally we provide an algorithm to find three-variable geometric mean via symmetrization, which plays an important role to construct higher-order geometric means.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.135-141
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• 1997

In this paper, it is investigated the properties of the transformed geometric Poisson process when the intensity function of the process is a distribution of the continuous random variable. If the intensity function of the transformed geometric Poisson process is a Pareto distribution then the transformed geometric Poisson process is a strongly P-process.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.783-792
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• 2007

We consider estimation of reliability P(Y

• Steel and Composite Structures
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• v.16 no.4
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• pp.339-356
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• 2014

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.631-644
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• 2021

In the present paper, we obtain gradient estimates for positive solutions to the following nonlinear parabolic equation under general geometric flow on complete noncompact manifolds $$\frac{{\partial}u}{{\partial}t}={\Delta}u+a(x,t)u^p+b(x,t)u^q$$ where, 0 < p, q < 1 are real constants and a(x, t) and b(x, t) are functions which are C² in the x-variable and C¹ in the t-variable. We shall get an interesting Harnack inequality as an application.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.387-397
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• 2003

Generally, most of researches that need a variable-clustering process use an exploratory factor analysis technique or a divisive hierarchical variable-clustering method based on a correlation matrix. And some researchers apply a object-clustering method to a distance matrix transformed from a correlation matrix, though this approach is known to be improper. On this paper an agglomerative hierarchical variable-clustering method based on a correlation matrix itself is suggested. It is derived from a geometric concept by using variate-spaces and a characterizing variate.

• Korean Journal of Remote Sensing
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• v.19 no.3
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• pp.247-253
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• 2003

The mainly used technique to correct satellite images with geometric distortion is to develop a mathematical relationship between pixels on the image and corresponding points on the ground. Polynomial models with various transformations have been designed for defining the relationship between two coordinate systems. GCP based geometric correction has peformed overall plane to plane mapping. In the overall plane mapping, overall structure of a scene is considered, but local variation is discarded. The Region with highly variant height is rectified with distortion on overall plane mapping. To consider locally variable region in satellite image, TIN-based rectification on a satellite image is proposed in this paper. This paper describes the relationship between GCP distribution and rectification model through experimental result and analysis about each rectification model. We can choose a geometric correction model as the structural characteristic of a satellite image and the acquired GCP distribution.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.565-568
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• 1996

In this paper, a solution method is proposed to calculate the optimum solution to discrete optimal H$_{.inf}$ control problem for feedback of linear time-invariant system states and disturbance variable. From the results of this study, condition of existence and uniqueness of its solution is that transfer matrix of controlled variable to input variable is left invertible and has no invariant zeros on the unit circle of the z-domain as well as extra geometric conditions given in this paper. Through a numerical example, the noniterative solution method proposed in this paper is illustrated.