• 대한수학회지
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• 제55권6호
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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 ${\Gamma}_{sf}(K[{\Delta}])$.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1997년도 추계학술대회발표논문집; 홍익대학교, 서울; 1 Nov. 1997
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• pp.51-51
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• 1997

• 한국자동차공학회논문집
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• 제8권5호
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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.

• 한국가구학회지
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• 제20권4호
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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.

• 대한수학회보
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• 제35권2호
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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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• 제27권5호
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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.

• 대한수학회보
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• 제53권4호
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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.

• 대한수학회지
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• 제49권4호
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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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• 제22권4호
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• pp.409-418
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• 2005

자기폭풍 기간 중에는 서브스톰이 빈번히 발생한다. 그리고 서브스톰이 진행될 때 극지방에는 오로라 제트 전류가 발생하며, 이는 AU 및 AL 지수로 그 강도를 규정할 수 있다. 따라서 AU 및 AL 지수와 자기폭풍의 정도를 나타내는 Dst 지수와의 상관관계를 구해봄으로써 서브스톰이 자기폭풍의 형성에 어떻게 기여하는지 조사할 수 있다. 이를 위하여 월별 누적 AU 지수, 월별 누적 $\mid{AL}\mid$ 지수 값을 구한 뒤, 월별 누적 $\mid{Dst}\mid$ 지수와의 상관관계를 구하였다. 그 결과 월별 누적 $\mid{AL}\mid$ 지수와 월별 누적 $\mid{Dst}\mid$ 지수의 상관관계는 0.60으로 월별 누적 AU 지수와 월별 누적 $\mid{Dst}\mid$ 지수의 상관관계 0.28보다 비교적 높게 나타났다. 이는 서브스톰이 자기폭풍의 발달에 기여하고 있음을 의미한다. 한편 IMF가 남쪽을 향할 때 자기권에는 강력한 대류가 형성되어 하전입자를 내부 자기권으로 가속시키므로 자기폭풍을 야기한다는 견해가 있다. 대류를 야기하는 행성간 전기장은 $\bar{E}=-\var{V}$(태양풍 속도) $\times\bar{B}_Z$(GSM에서 IMF의 Z축 성분)으로 주어지며, 이로부터 월별 누적 행성간 전기장과 월별 누적 Dst 지수 값을 비교해 봄으로써 행성간 전기장의 강화로 인한 자기권 대류가 자기폭풍 형성에 어느 정도 기여하는지를 조사할 수 있다. 여기서 Dst 지수는 태양풍에 의한 동압을 고려한 값이며, 월별 누적 행성간 전기장은 행성간 전기장이 양일 때와 음일때를 구분한 뒤 월별 누적 Dst 지수와의 상관관계를 알아보았다. 그 결과 행성간 전기장이 음의 값을 나타낼 때 구한 월별 누적 행성간 전기장과 월별 누적 Dst 지수와의 상관관계는 0.83이고, 양일 때 월별 누적 행성간 전기장과 월별 누적 Dst 지수와의 상관관계는 0.39로 나타났다. 이것은 IMF가 남쪽으로 향할 때 발생하는 자기권 대류의 강화 역시 자기폭풍의 발달에 중요한 역할을 하고 있음을 보여 준다.

• Advances in nano research
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• 제10권2호
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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.