• Kyungpook Mathematical Journal
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• v.27 no.2
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• pp.187-189
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• 1987

In the present paper a result [10] of the authors has been generalized as follows: Let l, m, n be fixed positive integers and R be a semi prime ring in which $[(xy)^l,(xy)^m-(yx)^n]=0$ for all $x,y{\in}R$, then R is commutative.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.553-565
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• 2009

In this paper we prove that every generalized Jordan triple higher derivation on a 2-torsion free semiprime ring is a generalized higher derivation. This extend the main result of [9] to the case of a semiprime ring.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.1
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• pp.199-206
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• 2005

Mask manufacturing is a high COC and COO process in developing of semiconductor devices because of mask production tool with high resolution. Direct writing has been thought to be the one of the patterning method to cope with development or small-lot production of the device. This study consists two categories. One is the additional process of the direct and maskless patterning generation using SLA for easy and convenient application and the other is a removal process using wet-etching process. In this study, cured status of epoxy pattern is most important parameter because of the beer-lambert law according to the diffusion of UV light. In order to improve the contact force between patterns and substrate, prime process was performed and to remove the semi-cured resin which makes a bad effects to the pattern, spin cleaning process using TPM was also performed. At a removal process, contact force between photo-curable resin as an etching mask and Si wafer is important parameter.

• Journal of the Korean Society for Heat Treatment
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• v.4 no.3
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• pp.13-20
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• 1991

The present work was aimed to examine the variation of precipitations and mechanical properties by thermomechanical treatments (TMT) in Al-2.19 wt%Li and Al-2.0 wt%Li-0.11 wt%Zr alloys. This study was performed by TEM, SEM observation, DSC, electrical resistance measurement, hardness and tensile strength measurement. First peak of resistivity aged at $90^{\circ}C$ was caused by precipitation of ${\delta}^{\prime}$-precursor phase, and second peak was caused by precipitation of ${\delta}^{\prime}$ phase. According to this result, the precipitation process of Al-2.19 wt%Li alloy was as follow : $SSSS{\rightarrow}{\delta}^{\prime}$-precursor phase ${\rightarrow}{\delta}^{\prime}$ (Coherent ${\rightarrow}$ Semi-coherent) ${\rightarrow}{\delta}$. In a Al-2.0 wt%Li-0.11 wt%Zr ternary alloy, the first peak of resistivity was appeared at initial aging heat-treatment. It is result from exsistant of ${\delta}^{\prime}$-precursor phase. The effect acceleration in a binary alloy was not appeared and the over-aging ternary alloy was accelerated with increase of the reduction rate. It is caused by combination effect of ${\delta}^{\prime}$ and composite phase.

• Korea Journal of Hospital Management
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• v.6 no.3
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• pp.109-129
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• 2001

The purpose of this study was the acquisition of the optimum scale of the apportionment of standard & high-class bed for the maximum profit representative of the desire of customers in a General Hospital with 1,100 beds located in Seoul. This investigation was proceeded by the analysis of the result of the simulation with the survey of both the patients' needs for bed and the degree of the medical service by the grade of the ward. And finally the consequence was obtained as follows: 1. The result of the investigation of the inpatients' preference for the grade of ward classes shows that a private ward reflected 4.3 percent, a semi-private ward 1.7 percent, a three-bed ward 0.1 percent, and a ward with six beds 93.9 percent each other. 2. A questionnaire poll was paralleled of service terms of a medical doctor and a nurse by ward class, the data were used for the standard of the allotment of labor cost by the ward class. The poll shows that the service tenn of a medical doctor and a nurse based on a ward with six beds by ward class showed 1.7 times in internal medicine and 1.9 times in surgery at a private ward; 1.4 times in internal medicine and 1.7 times in surgery at a semi-private room; and 1.2 times both in internal medicine and in surgery at a three-bed ward 3. The resultant findings revealed the most profit per bed and per patient in a private ward. However, an analysis of profit with a standard of unit area by ward class represented a higher profit in both the internal medicine and the surgery semi-private ward than other ward classes. 4. The result of the analysis through simulation based on the data of the prime cost per the ward class proved the optimum scale of the distribution of beds by class as follows: sixteen beds of the internal medicine and twenty three beds of the surgery in the private ward; two hundreds and two of the internal medicine and one hundred and ninety eight of the surgery in the semi-private room; three of both the internal medicine and the surgery each other in the three-bed ward; one hundred and ninety eight of the internal medicine and two hundred and fifty two of the surgery in the ward with six beds. The result of this research exhibits that the income and expenditure of the hospital could be improved by changing parts of wards into private ones(containing the maximum profit per a unit of width) in case the scale of the number of beds is reset with the consideration of the profit per the unit width. In the near future it's strongly expected that the research for the more scientific standard of the allotment of labour cost by ward class and for definition of the optimum scale of the number of beds that actualize the maximum profit with the change of the three elements of the prime cost: cost of materials; labor costs; management expenses.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.157-161
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• 2007

Let G be a p-mixed abelian group with semi-complete torsion subgroup $G_t$ such that G is splitting or is of torsion-free rank one, and let R be a commutative unitary ring of prime characteristic p. It is proved that the group algebras RG and RH are R-isomorphic for any group H if and only if G and H are isomorphic. This isomorphism relationship extends our earlier results in (Southeast Asian Bull. Math., 2002), (Proc. Amer. Math. Soc., 2002) and (Bull. Korean Math. Soc., 2005) as well as completely settles a problem posed by W. May in (Proc. Amer. Math. Soc., 1979).

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.419-437
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• 2019

This paper investigates skew ${\Theta}-{\lambda}$-constacyclic codes over $R=F_0{\oplus}F_1{\oplus}{\cdots}{\oplus}F_{k-1}$, where $F{_i}^{\prime}s$ are finite fields. The structures of skew ${\lambda}$-constacyclic codes over finite commutative semi-simple rings and their duals are provided. Moreover, skew ${\lambda}$-constacyclic codes of arbitrary length are studied under a new definition. We also show that a skew cyclic code of arbitrary length over finite commutative semi-simple rings is equivalent to either a cyclic code over R or a quasi-cyclic code over R.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.69-76
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• 2012

Let R be a ring, and ${\alpha}$ be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left ${\alpha}$-multiplier (centralizer) if H(xy) = H(x)${\alpha}$(y) holds for all x,y $\in$ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left ${\alpha}$-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1053-1066
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• 2010

In this paper, several properties of endomorphism rings of modules are investigated. A multiplication module M over a commutative ring R induces a commutative ring $M^*$ of endomorphisms of M and hence the relation between the prime (maximal) submodules of M and the prime (maximal) ideals of $M^*$ can be found. In particular, two classes of ideals of $M^*$ are discussed in this paper: one is of the form $G_{M^*}\;(M,\;N)\;=\;\{f\;{\in}\;M^*\;|\;f(M)\;{\subseteq}\;N\}$ and the other is of the form $G_{M^*}\;(N,\;0)\;=\;\{f\;{\in}\;M^*\;|\;f(N)\;=\;0\}$ for a submodule N of M.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.553-564
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• 2008

We have a concern with the existence of solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+{\mu}g(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,2{\pi}),\\{\eta}_t=-L{\eta}+{\nu}g(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,2{\pi})\end{array}.$$ We prove the uniqueness theorem when the nonlinearity does not cross eigenvalues. We also investigate multiple solutions (${\xi}(x,t),\;{\eta}(x,t)$) for perturbations of the parabolic system with Dirichlet boundary condition when the nonlinearity f' is bounded and $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.