• 대한수학회지
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• 제44권4호
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• pp.787-797
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• 2007

In this paper, the following fourth-order rational difference equation $$x_{n+1}=\frac{{x_n^b}+x_n-2x_{n-3}^b+a}{{x_n^bx_{n-2}+x_{n-3}^b+a}$$, n=0, 1, 2,..., where a, b ${\in}$ [0, ${\infty}$) and the initial values $X_{-3},\;X_{-2},\;X_{-1},\;X_0\;{\in}\;(0,\;{\infty})$, is considered and the rule of its trajectory structure is described clearly out. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is $1^+,\;1^-,\;1^+,\;4^-,\;3^+,\;1^-,\;2^+,\;2^-$ in a period, by which the positive equilibrium point of the equation is verified to be globally asymptotically stable.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.369-382
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• 2016

In this paper, we investigate the global behavior of the solutions of the difference equation $x_{n+1}=\frac{A+Bx_{n-2k-1}}{C+D\prod_{i=l}^{k}x_{n-2i}^{m_i}}$, n=0, 1, ..., with non-negative initial conditions, the parameters A, B are non-negative real numbers, C, D are positive real numbers, k, l are fixed non-negative integers such that l ≤ k, and m_i, i=l, k are positive integers.

• 한국수학사학회지
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• 제17권2호
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• pp.61-72
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• 2004

본 연구에서는 문헌 연구를 통해, 수학사적 발전 과정 및 교수학적 변환을 통해 얻어진 체바 정리의 변환에 대한 구체적인 자료를 제시하였으며, 이를 통해 체바 정리가 변환되고 확장되는 패턴을 고찰하였다. 특히, 본 연구에서는 체바 정리의역, 유향선분, 삼각함수, 벡터 등의 개념과 관련된 체바 정리의 변형 및 발전을 분석하였으며, n각형에 대한 체바 정리, 사면체에 대한 체바 정리를 제시하면서 일반화 및 유추에 관련된 체바 정리의 변환과 확장을 고찰하였다.

• 한국세라믹학회지
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• 제38권6호
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• pp.499-505
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• 2001

The behaviour of ionic compound crystals under combined chemical and externally applied electrical potential gradients is discussed. Firstly, a systematic overview is given. Then a formal analysis follows. The transport equations of the ions and the electric defects predict that even with reversible electrodes demixing, and in particular decomposition of the compound will occur if the applied d.c. current density is sufficiently high. These predictions are illustrated by appropriate experiments. With the help of the solid solution (Me, Fe)O, where Fe-ions are the dilute species, we investigate experimentally the behaviour of a ternary ionic crystal under a d.c. electric current load. All the compounds were placed in a galvanic cell, and the internal reactions which then could be observed were driven by the electric field in this cell. In addition, we discuss the influence of the electric field on the classical solid state reaction AX+BX=ABX$_2$, if again the reaction couple is placed in a galvanic cell.

• 대한수학회보
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• 제52권6호
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• pp.1963-1971
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• 2015

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras. Denote by W(a) the numerical range of an element $a{\in}\mathcal{A}$. We show that the condition W(ax) = W(bx), ${\forall}x{\in}\mathcal{A}$ implies that a = b. Using this, among other results, it is proved that if ${\phi}$ : $\mathcal{A}{\rightarrow}\mathcal{B}$ is a surjective map such that $W({\phi}(a){\phi}(b){\phi}(c))=W(abc)$ for all a, b and $c{\in}\mathcal{A}$, then ${\phi}(1){\in}Z(B)$ and the map ${\psi}={\phi}(1)^2{\phi}$ is multiplicative.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 1994년도 추계학술대회 논문집
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• pp.171-174
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• 1994

The drive towards ultra-large-scale integrated circuits a continuous intermetal dielectric films for multi layer interconection. Optimum condition of remote plasma enhanced chemical vapour deposition(RPECVD) was achieved by orthogonal array method. Chracteristics of SiO$_2$ films deposited by using remote PECVD with N$_2$O gas were investigated. Etching rate of SiO$_2$ films in P-echant was about 6[A/s] that was the same as the thermal oxide. The films a showed high breakdown voltage of 7(MV/cm) and a resistivity of Bx10$\^$13/[$\Omega$cm] at 7(MV/cm). The interface Trap density of SiO$_2$ has been shown excel lent properties of 5x10$\^$10/[/$\textrm{cm}^2$eV]. It was observed that the dielectric constant dropped to a value of 4. 29 for 150 [W] RF power.

• East Asian mathematical journal
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• 제28권5호
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• pp.587-595
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• 2012

In this paper we consider the quadratic matrix equation which can be defined be $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix; A,B and C are $n{\times}n$ given matrices with real elements. Newton's method is considered to find the skew-symmetric solvent of the nonlinear matrix equations Q(X). We also show that the method converges the skew-symmetric solvent even if the Fr$\acute{e}$chet derivative is singular. Finally, we give some numerical examples.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2005년도 춘계 학술발표회 논문집
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• pp.445-456
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• 2005

The research concentrates on improving the in-hole seismic probe, which has been developed in past five years, to be used in stiffness measurements of tunnel-face materials. The probe was down-sized to be fit in 45-mm diameter holes(or BX) drilled by a jumbo-drill, which is used to drill holes to install explosives for tunneling. Also trigger system was improved by using a down-speeding motor for operating convenience and air packing system was replaced with a set of plate-springs to eliminate supply of compressed air. These modifications are to adjust the probe for the unfavourable environment inside of tunnels and to test without any further drilling cost. The probe and testing procedure were successfully adopted with horizontal holes drilled by a jumbo-drill at a tunnel-face to evaluate the stiffness of rock mass. The measured shear wave velocities can be used to estimate deformation properties of rock mass for tunnel analyses.

• Journal of Biosystems Engineering
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• 제25권1호
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• pp.25-32
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• 2000

Motivated by the need for developing the more efficient lighting system for light culture in the greenhouses, this paper aims to predict the illumination of incandescent lamp according to various levels of lighting and various kinds of the lamp. The results obtained in this experiment are summarized as follows. 1. The general equation to predict the illumination according to the kind of incandescent lamp and the installation height was suggested as {{{{y= { a + bx+ cx^2} over { 1+dx+ex^2~ + fx^3} [lx]}}}} , where , a, b, c , d, e and of were arbitrary constants. 2. Maximum illumination of hat-covered lamp of 60 W was 1.2 -1.5 times as many as uncovered lamp. 3. Maximum illumination of yellow color painted lamp of 100 W was 1.3 times as many as unpainted lamp.

• Bulletin of the Korean Chemical Society
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• 제17권1호
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• pp.50-55
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• 1996

Reaction of carbonyl compounds with diisopinocampheylhaloboranes (Ipc2BX,X=Cl, Br, I) was investigated in detail in order to establish their usefulness as selective reducing agents. The reagents reduced aldehydes and ketones to the corresponding alcohols. The reactivities are in the order of Ipc2BCl Ipc2BBr>Ipc2BI.The reagents also reduced ${\alpha}{\beta}-unsaturated$, aldehydes and ketones to the corresponding allylic alcohols without any detectable 1,4-reduction. Especially, the chloro derivative nicely achieved the selective reduction of aldehyde or ketone groups in the presence of many other functional groups. The most remarkable result of this investigation is that aldehydes and ketones can be selectively reduced in the presence of acid chlorides.