• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.4
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• pp.475-480
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• 2004

Function approximation is one of the most important and active research fields in design optimization. Accurate function approximations can reduce the repetitive computational effort fur system analysis. So this study presents an enhanced two-point diagonal quadratic approximation method. The proposed method is based on the Two-point Diagonal Quadratic Approximation method. But unlike TDQA, the suggested method has two quadratic terms, the diagonal term and the correction term. Therefore this method overcomes the disadvantage of TDQA when the derivatives of two design points are same signed values. And in the proposed method, both the approximate function and derivative values at two design points are equal to the exact counterparts whether the signs of derivatives at two design points are the same or not. Several numerical examples are presented to show the merits of the proposed method compared to the other forms used in the literature.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.53 no.spc
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• pp.108-114
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• 2008

Near infrared spectroscopy (NIRS) is a rapid and accurate analytical method for determining the composition of agricultural products and feeds. The applicability of near infrared reflectance spectroscopic method was tested to determine the color value (L, a, b) of green tea. A total of 162 green tea calibration samples and 82 validation samples were used for NIRS equation development and validation, respectively. In the developed NIRS equation for analysis of the color value (L, a, b), the most accurate equation for L value was obtained at 2, 8, 6, 1 (2nd derivative, 8 nm gap, 6 points smoothing, and 1pointsecond smoothing), and for a, and b value were obtained at 1, 4, 4, 1 (1st derivative, 4 nm gap, 4points smoothing, and 1 point second smoothing) math treatment condition with SNVD (Standard Normal Variate and Detrend) scatter correction method and entire spectrum ($400{\sim}2,500\;nm$) by using MPLS (Modified Partial Least Squares) regression. Validation results of these NIRS equations showed very low bias (L: 0.005%, a: 0.003%, b: -0.013%) and standard error of prediction (SEP, L: 0.361%, a: 0.141%, b: 0.306%) as well as high coefficient of determination ($R^2$, L: 0.905, a: 0.986, b: 0.931). Therefore, these NIRS equations can be applicable and reliable for determination of color value (L, a, b) of green tea, and NIRS method could be used as a mass screening technique for breeding programs and quality control in the green tea industry.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1027-1041
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• 2019

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant H₂(1). Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.71.4-71
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• 2001

This paper presents swing up and stabilization control of an underactuated two-link robot called the Pendubot. This device is a two-link planar robot with an actuator at the shoulder, but no actuator at the elbow. The controller swings up first link from its open loop stable equilibrium point to the unstable equilibrium point and then, catches the unactuated second link to balance it there. Two control algorithms are used for this task. Proportional Derivative Control technique is used to design the swing up control. The linear model of Pendubot is obtained by linearizing the nonlinear dynamic equations about the desired equilibrium point and LQR technique is used to design a stabilization controller.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.3
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• pp.259-266
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• 2011

We present a new dual sequential approximate optimization (SAO) algorithm called SD-TDQAO (sequential dual two-point diagonal quadratic approximate optimization). This algorithm solves engineering optimization problems with a nonlinear objective and nonlinear inequality constraints. The two-point diagonal quadratic approximation (TDQA) was originally non-convex and inseparable quadratic approximation in the primal design variable space. To use the dual method, SD-TDQAO uses diagonal quadratic explicit separable approximation; this can easily ensure convexity and separability. An important feature is that the second-derivative terms of the quadratic approximation are approximated by TDQA, which uses only information on the function and the derivative values at two consecutive iteration points. The algorithm will be illustrated using mathematical and topological test problems, and its performance will be compared with that of the MMA algorithm.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.507-518
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• 2020

We consider a boundary version of the Schwarz Lemma on a certain class of functions which is denoted by 𝒩. For the function f(z) = z + a₂z² + a₃z³ + … which is defined in the unit disc D such that the function f(z) belongs to the class 𝒩, we estimate from below the modulus of the angular derivative of the function ${\frac{f{^{\prime}^{\prime}}(z)}{f(z)}}$ at the boundary point c with f'(c) = 0. The sharpness of these inequalities is also proved.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1323-1329
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• 2010

In this paper, a new fixed point theorem in cone is applied to obtain the existence of at least one positive pseudo-symmetric solution for the second order three-point boundary value problem {x" + f(t, x, x')=0, t $\in$ (0, 1), x(0)=0, x(1)=x($\eta$), where f is nonnegative continuous function; ${\eta}\;{\in}$ (0, 1) and f(t, u, v) = f(1+$\eta$-t, u, -v).

• The Pure and Applied Mathematics
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• v.26 no.2
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• pp.59-73
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• 2019

In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to $\mathcal{N}$(${\alpha}$) is investigated. For the function $f(z)=z+c_2z^2+C_3z^3+{\cdots}$ which is defined in the unit disc where $f(z){\in}\mathcal{N}({\alpha})$, we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with $f(b)={\frac{1}{b}}\int\limits_0^b$ f(t)dt. The sharpness of these inequalities is also proved.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.35-45
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• 2008

In cases sufficient conditions for the semilocal convergence of Newtonlike methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newtonlike method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.37-53
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• 2021

In this paper we define scaled visual curvature and visual Frenet frame that can be visually accepted for discrete space curves. Scaled visual curvature is relatively simple compared to multi-scale visual curvature and easy to control the influence of noise. We adopt scaled minimizing directions of height functions on each neighborhood. Minimizing direction at a point of a curve is a direction that makes the point a local minimum. Minimizing direction can be given by a small noise around the point. To reduce this kind of influence of noise we exmine the direction whether it makes the point minimum in a neighborhood of some size. If this happens we call the direction scaled minimizing direction of C at p ∈ C in a neighborhood Br(p). Normal vector of a space curve is a second derivative of the curve but we characterize the normal vector of a curve by an integration of minimizing directions. Since integration is more robust to noise, we can find more robust definition of discrete normal vector, visual normal vector. On the other hand, the set of minimizing directions span the normal plane in the case of smooth curve. So we can find the tangent vector from minimizing directions. This lead to the definition of visual tangent vector which is orthogonal to the visual normal vector. By the cross product of visual tangent vector and visual normal vector, we can define visual binormal vector and form a Frenet frame. We examine these concepts to some discrete curve with noise and can see that the scaled visual curvature and visual Frenet frame approximate the original geometric invariants.