• Honam Mathematical Journal
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• v.38 no.4
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• pp.693-699
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• 2016

The purpose of this note is to provide an alternative proof of two quadratic transformations contiguous to that of Kummer using a differential equation approach.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.229-243
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• 2008

This paper is intended to clarify and verify two representation algorithms computing representations of elements of free groups generated by two linear fractional transformations. Moreover in practice some parts of the two algorithms are modified for computational efficiency. In particular the justification of the algorithms has been rigorously done by showing how both algorithms work correctly and efficiently according to inputs with some properties of the two linear fractional transformations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.51-64
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• 2003

Analysis is given of construction and stability of complex symmetric analogues of Householder matrices, with applications to the eigenproblem for such matrices. We investigate numerical properties of the deflation of complex symmetric matrices by using complex symmetric Householder transformations. The proposed method is very similar to the well-known deflation technique for real symmetric matrices (Cf. [16], pp. 586-595). In this paper we present an error analysis of one step of the deflation of complex symmetric matrices.

• Bulletin of the Korean Chemical Society
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• v.14 no.4
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• pp.461-465
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• 1993

Reductive transformations of gem-bromonitro compounds and ${\alpha}$-nitro ketones were carried out conveniently with sodium dithionite by using dioctyl viologen as an electron-transfer catalyst in dichloromethane-water two-phase system:the bromine atom in gem-bromonitro compounds and the nitro group in ${\alpha}$-nitro ketones are replaced by hydrogen.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.269-277
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• 2019

Let X be a nonempty set, ${\rho}$ be an equivalence on X, T(X) be the semigroup of all transformations from X into itself, and $T_{\rho}(X)=\{f{\in}T(X)|(x,y){\in}{\rho}{\text{ implies }}((x)f,\;(y)f){\in}{\rho}\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.57-61
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• 1985

• Journal of Ocean Engineering and Technology
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• v.21 no.2 s.75
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• pp.12-21
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• 2007

As the economy grows and the population increases, we need to develop our coastal area and make use of it for various purposes. Specifically, investigation of the wave interactions on and around the vertical cylinders is very important in the design of the offshore or coastal structures. The nonlinear potential analysis developed so far, although very useful, has been found to be limited in application, as strong nonlinear waves generated by the interference between multilayered cylinders and wave impact forces by breaking waves can hardly be estimated. In this study, using a 3-Dimensional volume tracking method VOF(Volume of Fluid), based on Namer-Stokes equations, was developed to simulate highly nonlinear effects, such as breaking waves at the interface or complicated interference waves among structures. A numerical method for nonlinear interaction wave and vertical cylinders is newly proposed. The wave forces and wave transformations computed by the newly proposed numerical simulation method were compared to the other researcher's experimental results, and the results agree well. Based on the validation of this study, this numerical method is applied to the two vertical cylinders to discuss their nonlinear wave forces and wave transformations, according to the variations of separate distance of vertical cylinders.

• Journal of the Korean Society for Heat Treatment
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• v.18 no.5
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• pp.281-287
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• 2005

Titanium aluminium nitride((TiAl)N) film is anticipated as an advanced coating film with wear resistance used for drills, bites etc. and with corrosion resistance at a high temperature. In this study, (TiAl)N thin films were deposited both at room temperature and at elevated substrate temperatures of 573 to 773 K by using a two-facing-targets type DC sputtering system in a mixture Ar and $N_2$ gases. Atomic compositions of the binary Ti-Al alloy target is Al-rich (25Ti-75Al (atm%)). Process parameters such as precursor volume %, substrate temperature and Ar/$N_2$ gas ratio were optimized. The crystallization processes and phase transformations of (TiAl)N thin films were investigated by X-ray diffraction, field-emission scanning electron microscopy. The microhardness of (TiAl)N thin films were measured by a dynamic hardness tester. The films obtained with Ar/$N_2$ gas ratio of 1:3 and at 673 K substrate temperature showed the highest microhardness of $H_v$ 810. The crystallized and phase transformations of (TiAl)N thin films were $Ti_2AlN+AlN{\rightarrow}TiN+AlN$ for Ar/$N_2$ gas ratio of 1:3, $Ti_2AlN+AlN{\rightarrow}TiN+AlN{\rightarrow}Ti_2AlN+TiN+AlN$ for Ar/$N_2$ gas ratio of 1:1 and $TiN+AlN{\rightarrow}Ti_2AlN+TiN+AlN{\rightarrow}Ti_2AlN+AlN{\rightarrow}Ti_2AlN+TiN+AlN$ for Ar/$N_2$ gas ratio of 3:1. The above results are discussed in terms of crystallized phases and microhardness.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.10
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• pp.2091-2101
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• 1997

Conventional method for fractal image decoding requires high-degree computational complexity in decoding propocess, because of iterated contractive transformations applied to whole range blocks. In this paper, we propose a fast decoding algorithm of fractal image using data depence in order to reduce computational complexity for iterated contractive transformations. Range of reconstruction image is divided into a region referenced with domain, called referenced range, and a region without reference to domain, called unreferenced range. The referenced range is converged with iterated contractive transformations, and the unreferenced range can be decoded by convergence of the referenced range. Thus the unreferenced range is called data dependence region. We show that the data dependence region can be deconded by one transformation when the referenced range is converged. Consequently, the proposed method reduces computational complexity in decoding process by executing iterated contractive transformations for the referenced range only.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.20 no.1
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• pp.1-13
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• 2008

In the present work, wave transformation by vertical columns and its wave forces acting on them are discussed using a direct 3-D numerical model based on the VOF (Volume Of Fluid) method. The numerical results for wave transformations and wave forces are critically compared to an advanced experimental data, and provide the verification of the numerical model used in the present study. Overall model-data comparisons are good. After verification of the numerical model, it is used to simulate wave fields around dual vertical columns with arbitrary cross section, and the characteristics of nonlinear wave forces and wave transformations according to the variations of different cross section types of vertical columns, an interval of vertical columns and incident wave angle are discussed.