• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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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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• v.14 no.1
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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.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.6
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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.

• Honam Mathematical Journal
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• v.45 no.3
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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.

• Honam Mathematical Journal
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• v.10 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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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].

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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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.

• Convergence Security Journal
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• v.8 no.4
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• pp.127-134
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• 2008

In this paper, we try to improve the accuracy of automatic measurement for analysis equipment by detecting efficiently the edge of a waterdrop with transparency. In order to detect the edge of a waterdrop with transparency, we use an edge detecting technique, MADD (Modified Adaptive Directional Derivative), which can identify the ramp edges with various widths as the perfectly sharp edges and respond effectively regardless of enlarging or reducing the image. The proposed edge detecting technique by means of perfect sharpening of ramp edges employs the modified adaptive directional derivatives instead of the usual local differential operators in order to detect the edges of image. The modified adaptive directional derivatives are defined by introducing the perfect sharpening map into the adaptive directional derivatives. Finally we apply the proposed method to contact angle arithmetic and show the effiency and validity of the proposed method.

• Kyungpook Mathematical Journal
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• v.60 no.1
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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.