• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.151-184
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• 2022

In the article, we handle with the existence and controllability results for fractional impulsive neutral functional integro-differential equation in Banach spaces. We have used advanced phase space definition for infinite delay. State dependent infinite delay is the main motivation using advanced version of phase space. The results are acquired using Schaefer's fixed point theorem. Examples are given to illustrate the theory.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.119-135
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• 1994

Let $Q_{n+p-1}(\alpha)$ denote the- dass of functions $$f(z)=z^{P}-\sum_{n=0}^\infty{a_{(p+k)}z^{p+k}$$ ($a_{p+k}{\geq}0$, $p{\in}N=\left{1,2,{\cdots}\right}$) which are analytic and p-valent in the unit disc $U=\left{z:{\mid}z:{\mid}<1\right}$ and satisfying $Re\left{\frac{D^{n+p-1}f(\approx))^{\prime}}{pz^{p-a}\right}>{\alpha},0{\leq}{\alpha}<1,n>-p,z{\in}U.$ In this paper we obtain sharp results concerning coefficient estimates, distortion theorem, closure theorems and radii of p-valent close-to- convexity, starlikeness and convexity for the class $Q_{n+p-1}$ ($\alpha$). We also obtain class preserving integral operators of the form $F(z)=\frac{c+p}{z^{c}}\int_{o}^{z}t^{c-1}f(t)dt.$ c>-p $F\left(z\right)=\frac{c+p}{z^{c}}\int_{0}^{z} t^{c-1}f\left(t \right)dt. \qquad c>-p$ for the class $Q_{n+p-1}$ ($\alpha$). Conversely when $F(z){\in}Q_{n+p-1}(\alpha)$, radius of p-valence of f(z) has been determined.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.363-379
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• 2016

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we introduce here the family of the incomplete generalized ${\tau}$-hypergeometric functions $2{\gamma}_1^{\tau}(z)$ and $2{\Gamma}_1^{\tau}(z)$. The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second ${\tau}$-Appell hypergeometric functions ${\Gamma}_2^{{\tau}_1,{\tau}_2}$ and ${\gamma}_2^{{\tau}_1,{\tau}_2}$ of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2000.11a
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• pp.185-195
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• 2000

This pacer studied on the lateral motion and yaw motion of the gantry crane which is used for the automated container terminal with two driving wheel types. Though several problems are occcurred in driving of gantry crane, they are solved by the motion by the operators. But, if the gantry crane is unmanned, it is automatically controlled without any operation. There are two types, cone and flat t y pin driving wheel shape. In cone type, lateral vibration and yaw motion of crane are issued. In flat type, the collision between wheel-flange and rail or the fitting between wheel-flanges and rail is issued. Especially, the collision between wheel-flange and rail is a very critical problem in driving of unmanned gantry crane. To bring a solution to the problems, the lateral and yaw dynamic equations of the driving mechanism of gantry crane with two driving wheel types are derived. Then, we investigate the driving characteristics of gantry crane. And this study used PD(Proportional-Derivative) Controller to control the lateral displacement and yaw angle of the gantry crane. The simulation result of the driving mechanism using the Runge-Kutta Method is presented in this paper.

• Journal of the Korea Society of Computer and Information
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• v.10 no.4 s.36
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• pp.133-141
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• 2005

An edge is where the intensity of an image moves from a low value to high value or vice versa. The edges tell where objects are. their shape and size. and something about their texture. Many traditional edge operators are derivative based and perform reasonably well for simple noise-free images. In recent, statistical edge detectors for complex images with noises have been described. This paper compares and analysis the performance of statistical edge detectors based on the T test and Wilcoxon test, and mathematical edge detectors based on Sobel operator, and the well-known Canny detector and Wavelet transformation detector, and provides the implementation of these edge detectors using Java on the web.