• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.323-329
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• 2022

Let $p(z)=\sum\limits_{\nu=0}^{n}a_{\nu}z^{\nu}$ be a polynomial of degree n and $p^{\prime}(z)$ its derivative. If $\max\limits_{{\mid}z{\mid}=r}{\mid}p(z){\mid}$ is denoted by M(p, r). If p(z) has all its zeros on |z| = k, k ≤ 1, then it was shown by Govil [3] that $$M(p^{\prime},\;1){\leq}\frac{n}{k^n+k^{n-1}}M(p,\;1)$$. In this paper, we first prove a result concerning the sth derivative where 1 ≤ s < n of the polynomial involving some of the co-efficients of the polynomial. Our result not only improves and generalizes the above inequality, but also gives a generalization to higher derivative of a result due to Dewan and Mir [2] in this direction. Further, a direct generalization of the above inequality for the sth derivative where 1 ≤ s < n is also proved.

• 대한수학회논문집
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• 제29권3호
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• pp.439-449
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• 2014

In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function $f(z)=z+b_{p+1}z^{p+1}+b_{p+2}z^{p+2}+{\cdots}$ defined in the unit disc, with ${\Re}\(\frac{f^{\prime}(z)}{{\lambda}f{\prime}(z)+1-{\lambda}}\)$ > ${\beta}$, $0{\leq}{\beta}$ < 1, $0{\leq}{\lambda}$ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point ${\xi}$, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.

• 대한수학회지
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• 제36권1호
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• pp.229-241
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• 1999

The fractal space is often associated with natural phenomena with many length scales and the functions defined on this space are usually not differentiable. First we define a $\sigma$-multifractal from $\sigma$-iterated function systems with probability. We introduce the measure derivative through the invariant measure of the $\sigma$-multifractal. We show that the non-differentiable function on the $\sigma$-multifractal can be differentiable with respect to this measure derivative. We apply this result to some examples of ordinary differential equations and diffusion processes on $\sigma$-multifractal spaces.

• 융합보안논문지
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• 제6권3호
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• pp.29-35
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• 2006

실제 이미지에서 에지의 속성을 찾아내고 그 정확한 위치를 지정하기 위하여 밝기 분포에 대한 국소적 미분 대신에 "적응성 방향 미분"(Adaptive Directional Derivative, ADD)이라는 비국소적 연산자를 도입함으로써 에지의 램프 폭의 변화에 무관하게 적용할 수 있는 알고리듬이 개발되었다. 본 논문에서는 이러한 알고리즘에 의한 에지 검출 시스템을 개발하고 기존의 알고리듬에 의한 것과 비교 분석한다.

• 융합보안논문지
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• 제7권3호
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• pp.39-44
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• 2007

실제 이미지에서 에지의 속성을 찾아내고 그 정확한 위치를 지정하기 위하여 밝기 분포에 대한 국소적 미분 대신에 "적응성 방향 미분"(Adaptive Directional Derivative, ADD)이라는 비국소적 연산자를 도입함으로써 에지의 램프 폭의 변화에 무관하게 적용할 수 있는 알고리듬을 개발하였다. 본 논문에서는 이미 제안한 적응성 방향 미분을 이용한 에지 검출 시스템을 현재 에지 검출을 위해 보편적으로 사용되고 있는 Canny 알고리듬과의 성능평가를 실험을 통해 보여준다.

• Structural Engineering and Mechanics
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• 제5권2호
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• pp.177-191
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• 1997

In the paper, a fractional derivative Kelvin-Voigt model describing the dynamic behavior of a special class of fluid viscous dampers, is presented. First of all, in order to verify their mechanical properties, two devices were tested the former behaving as a pure damper (PD device), whereas the latter as an elastic-damping device (ED device). For both, quasi-static and dynamic tests were carried out under imposed displacement control. Secondarily, in order to describe their cyclical behavior, a model composed by an elastic and a damping element connected in parallel was defined. The elastic force was assumed as a linear function of the displacement whereas the damping one was expressed by a fractional derivative of the displacement. By setting an appropriate numerical algorithm, the model parameters (fractional derivative order, damping coefficient and elastic stiffness) were identified by experimental results. The estimated values allowed to outline the main parameter properties on which depend both the elastic as well as the damping behavior of the considered devices.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.93.3-93
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• 2001

We propose the cascade PID type fuzzy control method for a good performance such as robustness. The one of proposed method, the first stage have two input variables of an error and a derivative error, and one output variable, and the next stage have two input variables of the output of first stage and an integral error, and one output variable, have two stages. The other, the first stage has one input of an error, and one output variable, and the second stage have two input of the output of first stage and a derivative error, and one output variable, and the third stage have two input of the output of the second stage and an integer error, and one output variable ...

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.583-590
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• 2002

Point collocation method based on the fast derivatives approximation of meshfree shape function is applied to solid mechanics in this study. Enhanced meshfree approximation with approximated derivative of shape function is reviewed, and formulation of linear elastic solid mechanics by point collocation method is presented. It implies that governing equation of solid mechanics with strong form is directly formulated without no numerical integration cells or grid. The regularity of weight function is not required due to a use of approximated derivative, so we propose the exponential type weight function that is discontinuous in first derivative. The convergence and stability of the proposed method is verified by passing the generalized patch test. Also, the efficiency and applicability of the proposed method in solid mechanics is verified by solving types of solid problems. Numerical results show that not only a use of proposed weight function leads lower error and higher convergence rate than that of the conventional weight functions, but also the improved collocation method with derivative approximation enables to compute the derivatives of shape function very fast and accurately enough to replace the classical direct derivative calculation.

• 한국토양비료학회지
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• 제37권4호
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• pp.259-265
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• 2004

사과의 영양진단에서 사과잎 분석을 신속히 하기 위한 방법을 모색하기 위해 생잎과 건조잎을 이용해 근적의 스펙트럼을 측정하고 이를 질소 함량과의 최적의 상관관계를 도출하기 위해 부분소자승(PLS)과 주성분회귀(PCR)과 같은 다변량 분석법을 이용하여 비파괴 검량식을 작성하였다. 또한 검량식 작성에서 비파괴 측정 정확도를 향상시키기 위하여 smoothing, mean normalization, multiplicative scatter correction (MSC). derivative 등의 다양한 데이터 전처리 조작을 수행하여 정확도 향상 가능성을 조사하였다. 사과 건조잎의 비파괴 측정 가능성을 조사한 결과 PLS-1 모델에서 Norris first derivate하였을 태 RMSEP가 $0.6999g\;kg^{-1}$ 로 가장 좋았으며, 생잎은 Savitzky-Golay first derivate하였을 때에 RMSEP 가 $1.202g\;kg^{-1}$으로 가장 좋았다. 건조잎의 PCR 모델은 mean normalization 처리 후 Savitzky-Golay first derivative하였을 때가 RMSEP 가 $0.553g\;kg^{-1}$, 이었으며 생잎에서도 RMSEP는 $1.047g\;kg^{-1}$로 나타났다. 이와 같은 견과로서 사과의 생잎과 건조잎의 분석이 근적외분석기술에 의해 가능할 것으로 판단된다.

• Bulletin of the Korean Chemical Society
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• 제33권8호
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• pp.2647-2650
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• 2012

The total synthesis of biologically interesting ${\beta}$-hydroxypyranochalcones, purpurenone (1), its derivative 2, praecansone B (3), and pongapinone A (4) has been accomplished starting from commercially available 2,4-dihydroxyacetophenone or 6-methoxy-2,4-dihydroxyacetophenone in 3 steps by a convergent strategy through benzopyran formations, O-methylations, and coupling reactions.