• Journal of the Korean Mathematical Society
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• v.44 no.4
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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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• v.34 no.5_6
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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.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.61-72
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• 2004

In this article we study on didactic transposition and enlargement of the Ceva theorem(if three cevians AX, BY, CZ, one through each vertex of a triangle ABC, are concurrent, then $\frac{BX}{XC}\frac{CY}{YA}\frac{AZ}{ZB}$ = 1). We suggest inverse of the Ceva theorem, some different forms of the Ceva theorem(oriented segment form, trigonometric form, vector form), enlarged the Ceva theorem of polygon and tetrahedron, and in detail propose these proofs.

• Journal of the Korean Ceramic Society
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• v.38 no.6
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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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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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.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1994.11a
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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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• v.28 no.5
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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.

• Proceedings of the Korean Geotechical Society Conference
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• 2005.03a
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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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• v.25 no.1
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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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• v.17 no.1
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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.