• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1381-1388
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• 2018

Let ${\Delta}$ be a simplicial complex, $I_{\Delta}$ its Stanley-Reisner ideal and $K[{\Delta}]$ its Stanley-Reisner ring over a field K. Assume that ${\Gamma}(R)$ denotes the zero-divisor graph of a commutative ring R. Here, first we present a condition on two reduced Noetherian rings R and R', equivalent to ${\Gamma}(R){\cong}{\Gamma}(R{^{\prime}})$. In particular, we show that ${\Gamma}(K[{\Delta}]){\cong}{\Gamma}(K^{\prime}[{\Delta}^{\prime}])$ if and only if ${\mid}Ass(I_{\Delta}){\mid}={\mid}Ass(I_{{{\Delta}^{\prime}}}){\mid}$ and either ${\mid}K{\mid}$, ${\mid}K^{\prime}{\mid}{\leq}{\aleph}_0$ or ${\mid}K{\mid}={\mid}K^{\prime}{\mid}$. This shows that ${\Gamma}(K[{\Delta}])$ contains little information about $K[{\Delta}]$. Then, we define the squarefree zero-divisor graph of $K[{\Delta}]$, denoted by ${\Gamma}_{sf}(K[{\Delta}])$, and prove that ${\Gamma}_{sf}(K[{\Delta}){\cong}{\Gamma}_{sf}(K[{\Delta}^{\prime}])$ if and only if $K[{\Delta}]{\cong}K[{\Delta}^{\prime}]$. Moreover, we show how to find dim $K[{\Delta}]$ and ${\mid}Ass(K[{\Delta}]){\mid}$ from ${\Gamma}_{sf}(K[{\Delta}])$.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1997.10a
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• pp.51-51
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• 1997

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.5
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• pp.114-120
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• 2000

Friction forces of piston rings for a typical SI engine were independently measured while excluding the effects of cylinder pressure, oil starvation and piston secondary motion using a floating liner system. Friction patterns, represented by the measured friction forces, were classified into five frictional modes with regard to the combination of predominant lubrication regimes(boundary, mixed and hydrodynamic lubrication) and stroke regions(mid-stroke and dead centers). The modes were identified on the Stribeck diagram of the dimensionless bearing parameter and friction coefficients which were evaluated at the mid-stroke and at the dead centers. And the frictional modes were estimated to the full operation range. The compression rings behave in the mode where hydrodynamic lubrication is dominant at the mid-stroke and mixed lubrication is dominant at the dead centers under steady operating conditions. However, the oil control ring behave in the mode where mixed lubrication is dominant throughout the entire stroke.

• Journal of the Korea Furniture Society
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• v.20 no.4
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• pp.274-280
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• 2009

The purpose of this study was to identify the species of coffin woods excavated at Mundangdong in Gimcheon and to date this coffin by using tree-ring method. All coffin woods were identified as red pines, most possibly, Pinus densiflora S. et Z. Tree-ring dating provided absolute years of 3 among 19 coffins. Both I-9 and II-22 coffins were estimated to be made in the mid-seventeenth century, and I-65-1 in the mid-sixteenth century. Others possessed too few rings to be dated.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.259-268
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• 1998

We give several characterizations of a TV-PVMD and we show that the localization R[X;S]$_{N_{\upsilon}}$ of a semigroup ring R[X;S] is a TV-PVMD if and only if R is a TV-PVMD where $N_{\upsilon}\;=\;\{f\;{\in}\;R[X]{\mid}(A_f)_{\upsilon} = R\}$ and S is a torsion free cancellative semigroup with zero.

• Bulletin of the Korean Chemical Society
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• v.27 no.5
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• pp.679-686
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• 2006

The positions of $PbI _2$ molecule synthesized into the molecular-dimensioned cavities of $\mid K_6 (Pb _4I_2)(PbI_2) _{0.67}-(H_2O)_2\mid [Si _{12}Al _{12}O _{48}]$-LTA have been determined. A single crystal of $\mid Pb _6\mid [Si _{12}Al _{12}O _{48}]$-LTA, prepared by the dynamic ion-exchange of $\mid Na _{12}\mid [Si _{12}Al _{12}O _{48}]$-LTA with aqueous 0.05 M $Pb _(NO _3)_2$ and washed with deionized water, was placed in a stream of flowing aqueous 0.05 M KI at 294 K for three days. The resulting crystal structure of the product $( \mid K_6 (Pb _4I_2)(PbI_2) _{0.67}(H_2O)_2\mid [Si _{12}Al _{12}O _{48}]$-LTA, a = 12.353(1) $\AA$) was determined at 294 K by single-crystal X-ray diffraction in the space group Pm3 m. It was refined with all measured reflections to the final error index $R_1$ = 0.062 for 623 reflections which $F_o$ > 4$\sigma$($F_o$). 4.67 $Pb ^{2+}$ and six $K^+$ ions per unit cell are found at three crystallographically distinct positions: 3.67 $Pb ^{2+}$ and three $K^+$ ions on the 3-fold axes opposite six-rings in the large cavity, three $K^+$ ions off the plane of the eight-rings, and the remaining one $Pb ^{2+}$ ion lies opposite four-ring in the large cavity. 0.67 $Pb ^{2+}$ ions and 1.34 $I^-$ ions per unit cell are found in the sodalite units, indicating the formation of a $PbI _2$ molecule in 67% of the sodalite units. Each $PbI _2$ (Pb-I = 3.392(7) $\AA$) is held in place by the coordination of its one $Pb ^{2+}$ ion to the zeolite framework (a $Pb ^{2+}$ cation is 0.74 $\AA$ from a six-ring oxygens) and by the coordination of its two $I^-$ ions to $K^+$ ions through six-rings (I-K = 3.63(4) $\AA$). Two additional $I^-$ ions per unit cell are found opposite a four-ring in the large cavity and form $Pb _2K_2I^{5+}$ and $Pb _2K_2I^{3+}$ moieties, respectively, and two water molecules per unit cell are also found on the 3-fold axes in the large cavity.

• 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.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.687-701
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• 2012

Let $R$ be a ring and $nil(R)$ the set of all nilpotent elements of $R$. For a subset $X$ of a ring $R$, we define $N_R(X)=\{a{\in}R{\mid}xa{\in}nil(R)$ for all $x{\in}X$}, which is called a weak annihilator of $X$ in $R$. $A$ ring $R$ is called weak zip provided that for any subset $X$ of $R$, if $N_R(Y){\subseteq}nil(R)$, then there exists a finite subset $Y{\subseteq}X$ such that $N_R(Y){\subseteq}nil(R)$, and a ring $R$ is called weak symmetric if $abc{\in}nil(R){\Rightarrow}acb{\in}nil(R)$ for all a, b, $c{\in}R$. It is shown that a generalized power series ring $[[R^{S,{\leq}}]]$ is weak zip (resp. weak symmetric) if and only if $R$ is weak zip (resp. weak symmetric) under some additional conditions. Also we describe all weak associated primes of the generalized power series ring $[[R^{S,{\leq}}]]$ in terms of all weak associated primes of $R$ in a very straightforward way.

• Journal of Astronomy and Space Sciences
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• v.22 no.4
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• pp.409-418
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• 2005

Magnetospheric substorms occur frequently during magnetic storms, suggesting that the two phenomena are closely associated. We can investigate the relation between magnetospheric substorms and magnetic storms by examining the correlation between AE and Dst indices. For this purpose, we calculated the monthly cumulative AU, $\mid{AL}\mid$ and $\mid{Dst}\mid$ indices. The correlation coefficient between the monthly cumulative $\mid{AL}\mid$ and $\mid{Dst}\mid$ index is found to be 0.60, while that between monthly cumulative AU and $\mid{Dst}\mid$ index is 0.28. This result indicates that substorms seem to contribute to the development of magnetic storms. On the other hand, it has been reported that the interplanetary electric field associated with southward IMF intensifies the magnetospheric convection, which injects charged particles into the inner magnetosphere, thus developing the ring current. To evaluate the contribution of the interplanetary electric field to the development of the storm time ring current belt, we compared the monthly cumulative interplanetary electric field and the monthly cumulative Dst index. The correlation coefficient between the two cumulative indices is 0.83 for southward IMP and 0.39 for northward IMF. It indicates that magnetospheric convection induced by southward IMF is also important in developing magnetic storms. Therefore, both magnetospheric substorm and enhanced magnetospheric convection seem to contribute to the buildup of magnetic storm.

• Advances in nano research
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• v.10 no.2
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• pp.129-138
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• 2021

In present article, utilizing the Love shell theory with volume fraction laws for the cylindrical shells vibrations provides a governing equation for the distribution of material composition of material. Isotopic materials are the constituents of these rings. The position of a ring support has been taken along the radial direction. The Rayleigh-Ritz method with three different fraction laws gives birth to the shell frequency equation. Moreover, the effect of height- and length-to-radius ratio and angular speed is investigated. The results are depicted for circumferential wave number, length- and height-radius ratios with three laws. It is found that the backward and forward frequencies of exponential fraction law are sandwich between polynomial and trigonometric laws. It is examined that the backward and forward frequencies increase and decrease on increasing the ratio of height- and length-to-radius ratio. As the position of ring is enhanced for clamped simply supported and simply supported-simply supported boundary conditions, the frequencies go up. At mid-point, all the frequencies are higher and after that the frequencies decreases. The frequencies are same at initial and final stage and rust itself a bell shape. The shell is stabilized by ring supports to increase the stiffness and strength. Comparison is made for non-rotating and rotating cylindrical shell for the efficiency of the model. The results generated by computer software MATLAB.