• 대한수학회보
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• 제57권4호
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• pp.945-956
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• 2020

We introduce the concept of S-exchange rings to unify various subclass of exchange rings, where S is a subset of the ring. Many properties on S-exchange rings are obtained. For instance, we show that a ring R is clean if and only if R is left U(R)-exchange, a ring R is nil clean if and only if R is left (N(R) - 1)-exchange, and that a ring R is J-clean if and only if R is left (J(R) - 1)-exchange. As a conclusion, we obtain a sufficient condition such that clean (nil clean property, respectively) can pass to corners and reprove that J-clean passes to corners by a different way.

• 천문학회지
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• 제34권1호
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• pp.47-57
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• 2001

In this paper we have reconstructed an armillary sphere based on the Method of an Armillary Sphere Making described in the Volume 1 of The Collection of Writings on the Scientific Instruments-Uigijipsol (儀器輯說, two volumes) edited in the 1850's by Nam Byong-Chul (南秉哲, 1817-1863) who was a famous Korean states-man-scientist. Nam achieved convenience and accuracy in the measurements of stellar positions in the manner of selective setting the equatorial, ecliptic and horizontal poles by adding a pole axis exchange ring called Jaigeukkwon (載極圈) between the Three Arrangers of Time and Four Displacements. We made use of 3-dimensional graphic software for modelling Nam's armillary sphere which consisted of five layers-eight rings. Results of simulation showed that the pole axis exchange ring functioned properly in setting the equatorial, ecliptic and horizontal coordinates simply by exchange of positions of specified holes on the ring. We ascertained that the invention of Jaigeukkwon solved inherent problems in the conventional Chinese armillary sphere in computation of real ecliptic coordinates. It was revealed that Nam Byong-Chul made great contributions in the East Asian history of armillary sphere making.

• 대한수학회보
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• 제45권1호
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

• Bulletin of the Korean Chemical Society
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• 제16권3호
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• pp.248-251
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• 1995

The crystal structure of Ba46-X, Ba46Al92Si100O384 [a= 25.297(1) Å], has been determined by single-crystal X-ray diffraction techniques in the cubic space group Fd&bar{3}at 21(1) ℃. The crystal was prepared by ion exchange in flowing stream of 0.05 M Ba(OH)2 aqueous solution for 5 days. The crystal was then dehydrated at 380 ℃ and 2 × 10-6 Torr for 2 days. The structure was refined to the final error indices R1= 0.051 and Rw= 0.054 with 369 reflections for which I > 3σ(I). In this structure, all Ba2+ ions are located at the three different crystallographic sites: fourteen Ba2+ ions are located at site Ⅰ, the centers of the double six rings, two Ba2+ ions lie at site Ⅰ', in the sodalite cavity opposite double six rings(D6R's) and another thirty Ba2+ ions are located at site Ⅱ in the supercage. Two Ba2+ ions are recessed ca. 0.27 Å into the sodalite cavity from their three O(3) oxygen plane and thirty Ba2+ ions are recessed ca. 1.11 Å into the supercage from their three O(2) oxygen planes, respectively (Ba(1)-O(3) = 2.76(1) Å, O(3)-Ba(1)-O(3) = 180(0)°, Ba(2)-O(3) = 2.45(1) Å, O(3)-Ba(2)-O(3) = 108(1)°, Ba(3)-O(2)=2.65(1) Å, and O(2)-Ba(3)-O(2)=103.9(4)°).

• Bulletin of the Korean Chemical Society
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• 제16권9호
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• pp.823-826
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• 1995

The crystal structure of a sulfur sorption complex of the dehydrated partially Co2+ exchanged zeolite A (a=12.058(2) Å) has been determined by single-crystal X-ray techniques. The crystal structure was solved and refined in cubic space group Pm3m at 21(1) ℃. Ion Exchange with aqueous 0.05 M Co(NO3)2 was done by the static method. The crystal of Na4Co4-A was dehydrated at 380 ℃ and 2 × 10-6 Torr for 2 days, followed by exposure to about 100 Torr of sulfur at 330 ℃ for 72 h. Full matrix least-squares refinement converged to R1=0.084 and Rw=0.074 with 102 reflections for which I > 3σ(I). Crystallographic analysis shows that 2.8 Co2+ ions and 4 Na+ ions per unit cell occupy 6-ring sites on the threefold axes. 1.2 Co2+ ions occupy the 8-ring sites on fourfold axes. 2.8 Co2+ ions at Co(1) are recessed 0.66 Å into the large cavity and 4 Na+ ion at Na(1) are recessed 0.77 Å into the sodalite cavity from the (111) plane of O(3)'s. Approximately 16 sulfur atoms were sorbed per unit cell. Two S8 rings, each in a butterfly form, are found in the large cavity. The bond length between S and its adjacent S is 2.27(3) Å. The distance between 6-ring Co2+ ion and its adjacent sulfur is 2.53 (2) Å and that between 8-ring Co2+ ions and its adjacent sulfur is 2.72(9) Å. The angles of S-S'-S and S'-S-S'/ in octasulfur rings are 119.0(2)°and 113.0(2)°, respectively.

• 대한수학회지
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• 제55권5호
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• pp.1193-1205
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• 2018

We focus our attention on a ring property that nilpotents are contained in the Jacobson radical. This property is satisfied by NI and left (right) quasi-duo rings. A ring is said to be NJ if it satisfies such property. We prove the following: (i) $K{\ddot{o}}the^{\prime}s$ conjecture holds if and only if the polynomial ring over an NI ring is NJ; (ii) If R is an NJ ring, then R is exchange if and only if it is clean; and (iii) A ring R is NJ if and only if so is every (one-sided) corner ring of R.

• 한국농공학회지
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• 제17권2호
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• pp.3763-3771
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• 1975

This study was attempted to investigate the changes of specific fuel consumption, compression pressure and power output, consequently to obtain basic data on farm kerosene engine. The samples which are used in this study are a 4 cycle water cooled korosene engine for the use of K6-CT83 power tiller and a 4 cycle air-cooled kerosene engine for the use of G5L-3A water pump. The Korean Industrial Standards (K.S)KS-B 6002 "Test code of small internal combustion engine" was referred in carrying out this study, and its results are as follows. 1. According to load increasing, the speific fuel consumption of the engines generally decreases, however, in case of 10% over-loading it increases. 2. As a result of full load consecutive operation, according to passing of operating time, the amount of wear generally increases, consequently the speific fuel consumption also increases, and inversly the compression pressure decreases. 3. The changes of specific fuel consumption and compression pressure were closely related with time of piston ring exchange, and periodically about 100 hours the engines show the increase of specific fuel consumption and the decrease of compression pressure. 4. After about 300 hours, although the engine had new piston rings, the specific fuel consumption increase, consequently the engine needs boring. In actual use, it is impossible to operate consecutively on full load, therefore the boring time of engine is expected to come later.

• Bulletin of the Korean Chemical Society
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• 제29권9호
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• pp.1711-1716
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• 2008

The reaction of copper(II) chloride with phenyl-N-[(pyridine-2-yl)methylene]methaneamide (ppmma) leads to a new $\mu$ -chloro bridged dimeric [Cu(ppmma)$Cl_2$]$_2$ complex, whereas a reaction of copper(II) bromide with ppmma affords a monomeric Cu(ppmma)$Br_2$ complex. Both complexes have been characterized by X-ray crystallography and electronic absorption spectroscopy. The crystal structural analysis of [Cu(ppmma)$Cl_2$]$_2$ shows that the two Cu(II) atoms are bridged by two chloride ligands, forming a dimeric copper(II) complex and the copper ion has a distorted square-pyramidal geometry ($\tau$ = 0.2). The dimer units are held through a strong intermolecular $\pi-\pi$ interactions between the nearest benzyl rings. On the other hand, Cu(ppmma)Br2 displayed a distorted square planar geometry with two types of strong intermolecular π-π interaction. EPR spectrum of [Cu(ppmma)$Cl_2$]$_2$ in frozen glas s at 77 K revealed an equilibrium between the mononuclear and binuclear species. The magnetic susceptibilities data of [Cu(ppmma)$Cl_2$]$_2$ and Cu(ppmma)$Br_2$ follow the Curie-Weiss law. No significant intermolecular magnetic interactions were examined in both complexes, and magnetic exchange interactions are discussed on the basis of the structural features.

• 대한화학회지
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• 제43권4호
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• pp.384-385
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• 1999

$Ca^{2+}$ 이온과 $Tl^+$ 이온으로 치환되고 완전히 진공 탈수된 제올라이트 X결정 $Ca_{18}Tl_{56}Si_{100}Al_{92}O_{384}$ ($Ca_{18}Tl_{56}$-X;${\alpha}=24.883(4){\AA}$)와 $Ca_{32}Tl_{28}Si_{100}Al_{92}O_{384}$ ($Ca_{32}Tl_{28}$-X;${\alpha}=24.973(4){\AA}A$)의 구조를 21(1)TEX>$^{\circ}C$에서 입방공간군 Fd3을 사용하여 단결정 X-선 회절법으로 해석하고 그 구조를 정밀화 하였다 $Ca_{18}Tl_{56}$-X 결정은 0.045 M $Ca(NO_3)_2$와 0.005 M $TINO_3$ 혼합용액으로 흐름법을 이용하여 이온 교환하였다. $Ca_{32}Tl_{28}$-X는 이와 유사하게 0.0495 M $Ca(NO_3)_2$ 와 0.0005 M $TINO_3$ 혼합용액을 사용하였다. 각 결정은 360$^{\circ}C$, $2{\times}10^{-6}$ Torr에서 탈수시켰다. $Ca_{18}Tl_{56}$-X 및 $Ca_{32}Tl_{28}$-X 결정 구조는 각각 I > 3${\sigma}$ (I)인 382 및 472개의 회절 반사점을 사용하여 각각 $R_1=0.039,\;R_2=0.036$ 및 $R_1=0.046,\;R_2=0.045$의 최종 오차 지수 값을 얻었다. 탈수된 $Ca_{18}Tl_{56}$-X 및 $Ca_{32}Tl_{28}$-X 결정 구조에서, $Ca^{2+}$ 이온과 $Tl^+$ 이온은 서로 틀리는 6개의 결정학적 자리에 위치한다. 16개의 $Ca^{2+}$ 이온은 D6R의 중심인 팔면체 자리 I을 채운다 ($Ca_{18}Tl_{56}$-X : Ca-O=2.42(1) ${\AA}$ 및 O-Ca-O=93.06(4)$^{\circ}$; $Ca_{32}Tl_{28}$-X Ca-O=2.40(1) ${\AA}$ 및 O-Ca-O=93.08(3)$^{\circ}$). $Ca_{18}Tl_{56}$-X 구조에서는 2개의 $Ca^{2+}$ 이온은 자리 II (Ca-O=2.35(2) ${\AA}$ 및 O-Ca-O=111.69(2)$^{\circ}$)를 점유하고 26개의 $Tl^+$ 이온은 큰 동공 내 마주보는 S6R의 자리 II에 점유한다. 각기 3개의 산소로 만들어지는 평면으로부터 1.493 ${\AA}$ 떨어져 있다(Tl-O=2.70(8)${\AA}$ 및 O-Tl-O=92.33(4)$^{\circ}$). 약 4개의 $Tl^+$ 이온은 세 개의 산소로 만들어지는 평면으로부터 소다라이트 동공쪽으로 1.695${\AA}$ 떨어진 자리 II에 위치해 있다(Tl-O=2.81 (1) ${\AA}$ 및 O-Tl-O=87.48(3)$^{\circ}$). 나머지 26개의 $Tl^+$ 이온들은 자리 III'에 분포된다(Tl-O=2.82 (1) ${\AA}$ 및 Tl-O=2.88(3) ${\AA}$). Ca_{32}Tl_{28}$-X 결정 구조에서는 16개의 $Ca^{2+}$ 이온과 15개의 $Tl^+$ 이온들이 자리 II를 점유하고 있다(Ca-O=2.26(1) ${\AA}$ 및 O-Ca-O=119.14(4)$^{\circ}$; Tl-O=2.70(1) ${\AA}$ 및 O-Tl-O=92.38$^{\circ}$). 한 개의 $Tl^+$ 이온들은 자리 II'를 점유한다. 나머지 12개의 $Tl^+$ 이온들은 자리IlI'에 분포된다.