• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.455-468
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• 2011

We introduce the notion of refinement rings, and generalize some comparability properties of regular rings to the setting of refinement rings.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1197-1211
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• 2016

Let R be a finite commutative ring with nonzero identity. We define ${\Gamma}(R)$ to be the graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u of R such that x + uy is a unit of R. This graph provides a refinement of the unit and unitary Cayley graphs. In this paper, basic properties of ${\Gamma}(R)$ are obtained and the vertex connectivity and the edge connectivity of ${\Gamma}(R)$ are given. Finally, by a constructive way, we determine when the graph ${\Gamma}(R)$ is Hamiltonian. As a consequence, we show that ${\Gamma}(R)$ has a perfect matching if and only if ${\mid}R{\mid}$ is an even number.

• Bulletin of the Korean Chemical Society
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• v.16 no.9
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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.

• Journal of the Korean Chemical Society
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• v.34 no.1
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• pp.1-9
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• 1990

Cholesteryl pentanoate $(C_{32}O_2H_{54})$ is orthorhombic, space group $P2_12_12_1$, with a = 21.930(3), b = 21.404(3), c = 6.419(5) $\AA$, Z = 4, V = 3012.8(5)$\AA$$^3$, $D_c$ = 1.04 g$cm^{-3}$, ${\lambda}(Mo\; K{\alpha}$ = 0.71069 $\AA$, $\mu$ = 0.58 $cm^{-1}$, F(000) = 1048, T = 298, R = 0.086 for 1502 unique observed reflections with I > 1.0 $\sigma$ (I). The structure was solved by direct methods and refined by cascade diagonal least-squares refinement. The C-H bond lengths and the methyl groups are fixed and refined as their ideal geometry. A comparison with other cholesteryl esters gives normal structure for the tetracyclic ring, while the tail regions of the side chain and the ester group which stands on end, show a variation from their normal values, presumably due to thermal effects. The molecules are stacked together by non-bonded van der Waals forces with the shortest intermolecular distance of 3.529 $\AA$.

• Journal of Ocean Engineering and Technology
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• v.25 no.4
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• pp.42-47
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• 2011

In this paper, wake equalizing duct (WED) form optimization was carried out using computational fluid dynamics (CFD) techniques. A WED is a ring-shaped flow vane with a foil-type cross-section fitted to a hull in front of the upper propeller area. The main advantage of a WED is the power savings resulting from the uniformity of the velocity distribution on the propeller plane, a reduction in the flow separation at the aft-body, and lift generation with a forward force component on the foil section. This paper intends to evaluate these functions and find an optimized WED form for minimizing the viscous resistance and equalizing the wake distribution. In the optimization process, the study uses four WED parameters: the angle of the section, longitudinal location, and angles of the axes for the half rings against the longitudinal and transverse planes of the ship. KRISO 300K VLCC2 (KVLCC2) is chosen as an example ship to demonstrate the WED optimization. The optimization procedure uses genetic algorithms (GAs), a gradient-based optimizer for the refinement of the solution, and Non-dominated Sorting GA-II(NSGA-II) for Multiobjective Optimization. The results show that the optimized WED can reduce the viscous resistance at the expense of the uniformity of the wake distribution.

• Bulletin of the Korean Chemical Society
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• v.15 no.11
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• pp.980-984
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• 1994

Monomeric rhodium and iridium diimine complexes $Cp^*M(HNRNH)(Cp^*$ = 1,2,3,4,5-pentamethylcyclopentadienyl : (M=lr; R=o-$C_6H_4 (1a), 4,5-(CH_3)_2-C_6H_2-1,2 (1b), 4,5-(Cl)_2-C_6H_2-1,2$ (1c), NCC=CCN-1,2 (1d): M=Rh; R=NCC=CCN-1,2 (1e)) have been synthesized from $[CP^*MCl_2]_2$ and 2 equiv. of diamine in the presence of $NEt_3$. The Crystal structure of 1a was determined by X-ray diffraction method : 1a was crystallized in the monoclinic system, space group $P2_{1/c}$, with lattice constants a=9.543 (1) ${\AA}$, b=16.286 (1) ${\AA}$, c=10.068 (1) ${\AA}$ and ${\beta}$=99.25 (1), with Z= 4. Least-squares refinement of the structure led to R factor of 0.049. The coordination sphere of rhodium and iridium can be described as a 2-legged piano-stool. All complexes are highly colored. Electrochemical studies show that 1d and 1e display quasi-reversible reduction and 1a-1c display irreversible reductions, suggesting that the acceptor orbital might be localized on the diimine ring.

• Korean Journal of Crystallography
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• v.1 no.1
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• pp.49-56
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• 1990

The crystallizied Inactions of the two metastable phases in the glasses of plagioclase compositions were estimated by x-ray diffraction method. The orthorhombic metastable phase is easily drystaliized in the composition range of 70 to 80 mol% of albite, whereas the hexagonal metastable phase is mostly crystallized in the anonhite-rich side. For the purpose of refining the orthorhombic metastable structure some single crystal fragments of the composition Na,17ca‥‥All Isi2 nn were separated Som the crystallized glasses. The cell parameters of this crystal are a=8.237(1)A. b=8.644(1)A c=4.818(1)A. The space group of this crystal is Pn,2, Final atomic coordinates give R value of 0.040 and Rw of 0.028 with anisotropic thermal parameters. The position of Na and Ca atoms statistically distributed is splitted in two points with the occupancy of 0.5. The Si and Al atoms are statistically distributed in the six-membered ring of the Immm-type framework.

• Korean Journal of Crystallography
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• v.13 no.3_4
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• pp.158-164
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• 2002

Tetrahomodioxa p-phenylcalix(4)arene dihexylether(C/sub66/H/sub68/O/sub6/) has been synthesized and structurally characterized by X-ray diffraction. Reaction of tetrahomodioxa p-phenylcalix(4)arene with hexyl halide and NaH in DMF leads to the dihexyl derivatives, 7,13,21,27-tetraphenyl-29,31-dihexyloxy- 2,3,16,17-tetrahomo-3,17-dioxacalit(4)arenes. The crystal is orthorhombic, P2₁2₁2₁, a= 9.764(2), b=16.167(2), c=32.994(3) Å, V=5208(1) Å, Z= 4, Dc = 1.221 gcm/sup -3/. The structure was solved by direct methods and refined by full-matrix least squares. Refinement converged at R = 0.070 for 2009 observed reflections. This molecule has a C-1,2-alternate conformation with pseudo-centrosymmetry and has two pairs of opposite phenyl rings, which are approximately parallel to each other. The benzene rings A and B are up, and the rings C and D rings are down with respect to the plane of the macrocyclic ring.

• Journal of Conservation Science
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• v.32 no.2
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• pp.273-291
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• 2016

Some ceramic artifacts representing time-wise from comb pattern pottery in the Neolithic Age to white porcelain in Joseon Dynasty were selected from 7 sites in the north and south area of Charyeong Mountain Range in order to making techniques interpretation and development process of ancient ceramics through physicochemical and mineralogical quantitative analysis. Studied pottery samples in the Prehistoric times showed trace of ring piling in soft-type, and pottery in the Three Kingdoms Period had both soft and hard-type but kettle-ware and storage-ware were made with ring piling, but table-ware was made by wheel spinning. Different from pottery after the Three Kingdom Period when refinement of source clay was high, pottery in the Neolithic Age and in the Bronze Age exhibited highly mineral content in sandy source clay, which showed a lot of larger temper than source clay. Groundmass of celadon and white porcelain almost did not reveal primary minerals but had high content of minerals by high temperature firing. Ceramic samples showed some different in major and minor elements according to sites irrespective of times. Geochemical behaviors are very similar indicating similar basic characteristics of source clay. However, loss-on-ignition showed 0.01 to 12.59wt.% range with a large deviation but it rapidly decreased moving from the Prehistoric times to the Three Kingdom Period. They have correlation with the weight loss due to firings, according to burning degree of source clay and detection of high temperature minerals, estimated firing temperatures are classified into 5 groups. Pottery in the Neolithic Age and in the Bronze Age belongs from 750 to $850^{\circ}C$ group; pottery in the Three Kingdom Period are variously found in 750 to $1,100^{\circ}C$ range of firing temperature; and it is believed celadon and white porcelain were baked in high temperature of 1,150 to $1,250^{\circ}C$. It seems difference between refinement of source clay and firing temperature based on production times resulted from change in raw material supply and firing method pursuant to development of production skill. However, there was difference in production methods even at the same period and it is thought that they were utilized according to use purpose and needs instead of evolved development simply to one direction.

• Journal of the Korean Chemical Society
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• v.37 no.5
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• pp.473-476
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• 1993

Dipropargyldiphenylmetane, $C_{19}H_{16}, crystallizes in a monoclinic space group $C2/_c$$ with a = 11304(3), b = 20.799(5), c = 6.622(2)${\AA}$, ${\beta} = 112.8(3)^{\circ}$, Z = 4, V = 1435.3${\AA}^3,\;F(000)\;=\;520,\;D_c\;=\;1.14g{\cdot}cm^{-3}$ and ${\mu}\;=\;0.32\;cm^{-1}$. The structure was solved by direct methods and all non-H atoms were identified in the E-map. The final refinement gave R = 0.055 from 1328 unique observed reflections with I $\geq$ -1.0 $\sigma(I).$ The molecule belongs to the point group $C_2$ of Symmetry by possessing the 2-fold axis which coincides witeh the crystallographic symmetry axis in the unit cell. The linear propargyl moiety is nearly $perpendicular(94.2)^{\circ}$ to the molecular plane of the benzene ring. The internal angle of methane carbon atoms in $108.1(1)^{\circ}$, bonding to the benzene and the propargyl moiety with the bond lengths of 1.530(2) and $1.560(2)\AA$, respectively. The shortest contant between the molecules is $3.538(2)\AA$ between C(9) and C(9) (-x, y, -1/2-z).