• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1993년도 추계학술대회 논문집
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• pp.395-401
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• 1993

The purpose of this paper is to develop an automatic measuring system based on the digital image processing which can be applied to the in-process measurement of the characteristics of the thin thickness. The derivative operators is used for edge detection in gray level image. This concept can be easiliy illustrated with the aid of object shows an image of a simple light object on a dark background, the gray level profile along a horizontal scan line of the image, and the first and second derivatives of the profile. The first derivative of an edge modeled in this manner is () in all regions of constant gray level, and assumes a constant value during a gray level transition. The experimental results indicate that the developed qutomatic inspection system can be applied in real situation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권1호
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• pp.43-56
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• 2010

The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

• 한국정밀공학회지
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• 제12권6호
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• pp.72-79
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• 1995

The purpose of this paper is to develop an automatic measuring system based on the digital image processing which can be applied to the in-process measurment of the characteristics of the thin thickness. The derivative operators is used for edge detection in gray level image. This concept can be easily illustrated with the aid of object shows an image of a simple light object on a dark background, the gray level profile along a horizontal scan line of the image, and the first and second derivatives of the profile. The first derivative of an edge modeled in this manner is 0 in all regions of constant gray level, and assumes a constant value during a gray level transition. The experimental results indicate that the developed automatic inspection system can be applied in real situation.

• 호남수학학술지
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• 제45권3호
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• pp.433-456
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• 2023

This paper deals with differentiability of solutions of neutral stochastic differential equations with respect to the initial data in the G-framework. Since the initial data belongs to the space BC ([-r, 0] ; ℝⁿ) of bounded continuous ℝⁿ-valued functions defined on [-r, 0] (r > 0), the derivative belongs to the Banach space 𝓛_BC (ℝⁿ) of linear bounded operators from BC ([-r, 0] ; ℝⁿ) to ℝⁿ. We give the neutral stochastic differential equation of the derivative. In addition, we exhibit two examples confirming the accuracy of the obtained results.

• 호남수학학술지
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• 제10권1호
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• pp.23-30
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• 1988

Let C[C, D] and $S^{*}[C,\;D]$ denote the classes of functions g, g(0)=1-g'(0)0=0, analytic in the unit disc E such that $\frac{(zg{\prime}(z)){\prime}}{g{\prime}(z)}$ and $\frac{zg{\prime}(z)}{g(z)}$ are subordinate to $\frac{1+Cz}{1+Dz{\prime}}$ $z{\in}E$, respectively. In this paper, the classes K[A,B;C,D] and $C^{*}[A,B;C,D]$, $-1{\leq}B<A{\leq}1$; $-1{\leq}D<C{\leq}1$, are defined. The functions in these classes are close-to-convex. Using the properties of convolution operators, we deal with some problems for our classes.

• 대한수학회논문집
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• 제35권1호
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• pp.161-184
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• 2020

In this article, we establish some new weighted Hardy-type inequalities involving some variants of extended Riemann-Liouville fractional derivative operators, using convex and increasing functions. As special cases of the main results, we obtain the results of [18,19]. We also prove the boundedness of the k-fractional integral operator on L_p[a, b].

• 대한수학회보
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• 제48권1호
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• pp.169-182
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• 2011

The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc $\mathbb{U}$, which generalize the familiar class of k-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.

• 대한수학회보
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• 제55권5호
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• pp.1351-1370
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• 2018

In the first part of this paper we show that, under some conditions, a polynomially demicompact operator can be demicompact. An example involving the Caputo fractional derivative of order ${\alpha}$ is provided. Furthermore, we give a refinement of the left and the right Weyl essential spectra of a closed linear operator involving the class of demicompact ones. In the second part of this work we provide some sufficient conditions on the inputs of a closable block operator matrix, with domain consisting of vectors which satisfy certain conditions, to ensure the demicompactness of its closure. Moreover, we apply the obtained results to determine the essential spectra of this operator.

• 융합보안논문지
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• 제8권4호
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• pp.127-134
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• 2008

본 연구는 투명 성질을 가진 물방울의 윤곽선에 대한 효율적인 검출을 통해 분석 장비의 자동 측정에 대한 정확성을 향상시키는 것을 목적으로 한다. 투명성질을 가지는 원의 윤곽선 검출을 위해 밝기 분포에 대한 국소적 미분 대신에 적응성 방향 미분(Adaptive Directional Derivative；ADD)이라는 비국소적 연산자를 도입함으로써 에지의 램프 폭의 변화에 무관하게 에지 검출에 적용할 수 있는 MADD(Modified Adaptive Directional Derivative) 알고리즘을 사용한다. 이 방법은 램프 구간 내에서 방향 미분 값을 가중치로 사용하여 픽셀들의 위치를 평균한 방향 미분의 국소 중심(Local Center of Directional Derivative；LCDD)등의 위치를 찾는 추가적인 과정없이, 정확한 에지 픽셀의 위치가 완전 선명화 사상에 의한 단순 계단 함수의 위치로 자연스럽게 결정될 수 있다. 제시된 에지 검출 방법을 표면분석 기술인 접촉각 연산에 적용하여 실험 및 결과 분석을 통해 제안 기법의 타당성 및 효율성을 검증한다.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.73-116
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• 2020

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.