• 대한수학회논문집
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• 제14권1호
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• pp.147-156
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• 1999

This paper deals with a class H(A,B,$\alpha$) of analytic functions and we obtain coefficient estimates and related results.

• 대한수학회보
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• 제55권1호
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• pp.165-173
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• 2018

In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^*({\alpha})$ of starlike functions of order ${\alpha}$ and $\mathcal{K}({\alpha}$) of convex functions of order ${\alpha}$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.

• 충청수학회지
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• 제19권2호
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• pp.133-139
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• 2006

By combining the classical Newton's method with the pseudo-secant method, pseudo-secant-Newton's method is constructed and its order and rate of convergence are investigated. Given a function $f:\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$ and is sufficiently smooth in a small neighborhood of ${\alpha}$, the convergence behavior is analyzed near ${\alpha}$ for pseudo-secant-Newton's method. The order of convergence is shown to be cubic and the rate of convergence is proven to be $\(\frac{f^{{\prime}{\prime}}(\alpha)}{2f^{\prime}(\alpha)}\)^2$. Numerical experiments show the validity of the theory presented here and are confirmed via high-precision programming in Mathematica.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1395-1408
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• 2010

In this paper, a pair of Wolfe type second-order nondifferentiable multiobjective symmetric dual program over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order (F, $\alpha$, $\rho$, d)-convexity assumptions. An illustration is given to show that second-order (F, $\alpha$, $\rho$, d)-convex functions are generalization of second-order F-convex functions. Several known results including many recent works are obtained as special cases.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2017년도 추계학술대회
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• pp.145-147
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• 2017

Tracking filter plays a key role in accurate estimation and prediction of maneuvering vessel's dynamics. The third-order ${\alpha}-{\beta}-{\gamma}$ filter is one of the special cases of the general solution provided by the Kalman filter. Fading memory algorithm performs a better performance in numerous of ${\alpha}-{\beta}-{\gamma}$ filter algorithms. This study aims to optimize the fourth-order fading memory algorithm ${\alpha}-{\beta}-{\gamma}-{\eta}$ filter, which is extended form ${\alpha}-{\beta}-{\gamma}$ filter, to get much more accurate position of high dynamic target on the condition that the own ship is also high dynamic.

• Bulletin of the Korean Chemical Society
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• 제6권3호
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• pp.124-127
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• 1985

The kinetic study on the bromine-exchange reaction of antimony tribromide with ${\alpha}$-phenylethyl bromide in nitrobenzene has been carried out, using Br-82 labelled antimony tribromide. The results show that the exchange reaction is first order with respect to ${\alpha}$-phenylethyl bromide, and either second or first order with respect to antimony tribromide depending on its concentration. It is also concluded that ${\alpha}$-phenylethyl bromide exchanges bromine atom with antimony tribromide much faster than other organic bromides previously examined. Reaction mechanisms for the exchange reaction are discussed.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1165-1176
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• 2009

This paper is concerned with the interval oscillation of the second order nonlinear ordinary differential equation (r(t)|y'(t)|$^{{\alpha}-1}$ y'(t))'+p(t)|y'(t)|$^{{\alpha}-1}$ y'(t)+q(t)f(y(t))g(y'(t))=0. By constructing ageneralized Riccati transformation and using the method of averaging techniques, we establish some interval oscillation criteria when f(y) is not differetiable but satisfies the condition $\frac{f(y)}{|y|^{{\alpha}-1}y}$ ${\geq}{\mu}_0$ > 0 for $y{\neq}0$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권2호
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• pp.119-130
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• 2024

In this paper we discuss on the growth properties of composite entire and meromorphic functions on the basis of generalized (α, β, γ) order and generalized (α, β, γ) type comparing to their corresponding left and right factors.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.355-376
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• 2021

In this paper we wish to establish the integral representations of generalized relative order (𝛼, 𝛽) and generalized relative type (𝛼, 𝛽) of entire and meromorphic functions where 𝛼 and 𝛽 are continuous non-negative functions defined on (-∞, +∞). We also investigate their equivalence relation under some certain condition.

• 대한수학회보
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• 제25권2호
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• pp.179-183
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• 1988

In this paper we study a $C^{*}$-dynamical system (A, G, .alpha.) where A is a UHF-algebra, G is a finite abelian group and .alpha. is a *-automorphic action of product type of G on A. In [2], A. Kishimoto considered the case G= $Z_{n}$, the cyclic group of order n and investigated a condition in order that the fixed point algebra $A^{\alpha}$ of A under the action .alpha. is UHF. In later N.J. Munch studied extremal tracial states on $A^{\alpha}$ by employing the method of A. Kishimoto [3], where G is a finite abelian group. Generally speaking, when G is compact (not necessarily discrete and abelian), $A^{\alpha}$ is an AF-algebra and its ideal structure was well analysed by N. Riedel [4]. Here we obtain some conditions for $A^{\alpha}$ to be UHF, where G is a finite abelian group, which is an extension of the result of A. Kishimoto.oto.