• Proceedings of the Korea Information Processing Society Conference
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• 2014.11a
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• pp.597-600
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• 2014

컴퓨터 시스템의 병렬, 분산, 이동, 실시간 적인 시스템들을 명세하기 위한 여러가지 정형기법들이 존재한다. 본 논문에서는 이동 실시간 시스템의 명세를 위한 정형기법으로서 ${\delta}-Calculus$ 를 정의하였다. ${\delta}-Calculus$ 의 가장 큰 특징은 프로세스의 이동성으로써 시간의 흐름에 따라 프로세스 간의 상호작용을 통해 프로세스가 이동하는 것을 표현할 수 있다. ${\delta}-Calculus$ 를 사용하여 프로세스의 이동성을 표현함으로써 시스템의 공간정보와 시간정보를 명세하고, 프로세스의 상태에 따른 보안적 특성을 나타낼 수 있다. 본 논문에서는 ${\delta}-Calculus$ 의 문법과 의미를 설명하고 이동성에 의한 특성을 분석하였다.

• Journal of KIISE
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• v.43 no.3
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• pp.314-326
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• 2016

Some process algebras were applied to enterprise business modelling for formal specification and verification. ${\pi}$-calculus and mobile ambient can be considered for the distributed and mobile, especially to represent the movements of distributed real-time business processes. However there are some limitations to model the movements: 1) ${\pi}$-calculus passes the name of port for indirect movements, and 2) mobile ambient uses ambient to synchronize asynchronous movements forcefully. As a solution to the limitations, this paper presents a new process algebra, called ${\delta}$-calculus, to specify direct and synchronous movements of business processes over geo-temporal space. Any violation of safety or security of the systems caused by the movements can be indicated by the properties of the movements: synchrony, priority and deadline. A tool, called SAVE, was developed on ADOxx metamodelling platform to demonstrate the concept.

• Journal of KIISE
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• v.43 no.5
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• pp.541-552
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• 2016

This paper introduces the new notions of conjunctive and complement choices in process algebra, which reduce both process and system complexities significantly for distributed mobile real-time system during specification and analysis phases. The complement choice implies that two processes make cohesive choices for their synchronous partners at their own choice operations. The conjunctive choice implies choice dependency among consecutive choice operations in a process. The conjunctive choice reduces process complexity exponentially by the degree of the consecutive choice operations. The complement choice also reduces system complexity exponentially by the degree of the synchronous choice operations. Consequently, the reduction method makes the specification and analysis of the systems much easier since the complexity is reduced significantly. This notion is implemented in a process algebra, called ${\delta}$-Calculus. The efficiency and effectiveness are demonstrated with an example in a tool for the algebra, called SAVE, which is developed on ADOxx platform.

• East Asian mathematical journal
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• v.14 no.1
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• pp.107-116
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• 1998

This paper deals with functions of the form $f(z)=a_1z-{\sum}{\limits}_{n=2}^{\infty}a_nz^n(a_1>0,\;a_n{\geqslant}0)$ with $(1-{\mu})f(z_0)/z_0+{\mu}f'(z_0)=1(-1. We introduce the class $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$ with generalized fractional derivatives. Also we have obtained coefficient inequalities, distortion theorem and radious problem of functions belonging to the calss $\varphi({\mu},{\eta},{\gamma},{\delta},A,B;\;z_0)$.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.63-78
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• 2011

The purpose of this study is to explore a teaching method of limits of functions with more intuitive and visual of CAS graphing calculators rather than with the rigorous ${\epsilon}-{\delta}$ method. Texas Instruments Voyage200 CAS graphing calculators are used for studying the possibility of the use of technology in calculus course. For this, various related theoretical constructs are reviewed: concept image, concept definition, cognitive conflict, the use of visualization of technology for calculus concepts, the theory of APOS, and local straightness. Based on such theoretical constructs this study suggests a teaching method of limits of functions with embodied visualization of CAS graphing calculators.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.793-802
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• 1998

We apply the generalization of Levy's infinitesimal equation $\delta$X(t) = $\psi$(X(s), s $\leq$ t, $Y_{t}$, t, dt), $t\in R^1$, for a random field X (C) indexed by a contour C or by a more general set. Assume that the X(C) is homogeneous in x, say of degree n, then we can appeal to the classical theory of variational calculus and to the modern theory of white noise analysis in order to discuss the innovation for the X (C.)

• Journal of dental hygiene science
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• v.16 no.2
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• pp.176-182
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• 2016

The purpose of this study was to evaluate the in-vitro efficacy of the active ingredients of dentifrice following treatment time. The whitening effect was evaluated by a change in lightness value relative to the contact time of hydrogen peroxide, by using artificially stained hydroxyapatite discs. The anti-calculus effect was assessed based on the amount of calcium eluted from the human dental calculus by sodium pyrophosphate. Remineralization was evaluated by the Vickers hardness test following the application of sodium fluoride to bovine enamel. In order to view dentinal tubules occlusion, the formation of insoluble calcium salts by bovine dentin specimens was observed using scanning electron microscopy. Change in lightness value (${\Delta}L$) was $5.50{\pm}1.51$ after 1 min of treatment, $5.73{\pm}0.43$ after 3 min, $8.64{\pm}0.24$ after 10 min, $18.93{\pm}0.76$ after 30 min, and $27.35{\pm}0.54$ after 60 min. The amount of calcium eluted from the human dental calculus was $4.23{\pm}0.14ppm$ after 1 min of treatment, $4.51{\pm}0.04ppm$ after 3 min, $12.12{\pm}0.16ppm$ after 10 min, $17.85{\pm}0.81ppm$ after 30 min, and $25.15{\pm}0.32ppm$ after 60 min. The Vickers hardness change value (${\Delta}VHN$) was $1.96{\pm}1.44$ after 1 min, $1.52{\pm}1.06$ after 3 min, $9.06{\pm}0.15$ after 10 min, $10.83{\pm}5.13$ after 30 min, and $12.55{\pm}2.09$ after 60 min. Partial dentinal tubules occlusion was observed at 10 min and complete occlusion was evident at 60 min. In summary, the use of patch type dentifrices for 10, 30, or 60 min were 1.57 to 8.26 times more effective than using the paste type dentifrices for 1 to 3 min. Based on these findings, it is reasonable to expect that the use of patch type dentifrices for 10 min would lead to remineralization, anti-calculus and dentinal tubules occlusion effects, and that use for 30 min would result in a whitening effect.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.953-967
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• 2015

In this article, by making use of a linear multiplier fractional differential operator $D^{{\delta},m}_{\lambda}$, we introduce a new subclass of spiral-like functions. The main object is to provide some subordination results for functions in this class. We also find sufficient conditions for a function to be in the class and derive Fekete-$Szeg{\ddot{o}}$ inequalities.