• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.491-501
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• 1998

If N is any cartesian product of a closed simply connected n-manifold $N_1$ and a closed aspherical m-manifold $N_2$, then N is a codimension 2 fibrator. Moreover, if N is any closed hopfian PL n-manifold with $\pi_iN=0$ for $2 {\leq} i < m$, which is a codimension 2 fibrator, and $\pi_i N$ is normally cohopfian and has no proper normal subroup isomorphic to $\pi_1 N/A$ where A is an abelian normal subgroup of $\pi_1 N$, then N is a codimension m PL fibrator.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.25-33
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• 2009

Let ${\pi}:E{\rightarrow}B$ be a Serre fibration with fibre F. We prove that if the inclusion map $i:F{\rightarrow}E$ has a left homotopy inverse r and ${\pi}:E{\rightarrow}B$ admits a cross section ${\rho}:B{\rightarrow}E$, then $G_n(E,F){\cong}{\pi}_n(B){\oplus}G_n(F)$. This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in [8]. Using this result, we will prove that ${\pi}_n(X^A){\cong}{\pi}_n(X){\oplus}G_n(F)$ for the function space $X^A$ from a space A to a weak $H_*$-space X where the evaluation map ${\omega}:X^A{\rightarrow}X$ is regarded as a fibration.

• Journal of Photoscience
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• v.5 no.2
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• pp.69-71
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• 1998

Electronic structures and excited states for pyrazinylquinoxalinylethylene are investigated using PM3-UHF-CI and Molecular Mechanics force field. The results indicate that pyrazinylquinoxalinylethylene has extensively mixed ($\pi$, $\pi$$^*$) and (n, $\pi$$^*$) states while the (n, $\pi$$^*$) transition band does not appear in the absorption spectrum clearly and seems to be submerged under the more intense ($\pi$, $\pi$$^*$) bands.

• Bulletin of the Korean Chemical Society
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• v.3 no.1
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• pp.1-4
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• 1982

A quantitative treatment of ${\pi}$-nonbonded and $n-{\sigma}^{\ast}$ interactions and through-bond coupling effect was attempted using n-butane, n-butyl radical, and tetramethylene diradical. Results of STO-3G level calculations showed that: (1) conformational preferences can be predicted quantitatively based solely on the additive effect of ${\pi}$-nonbonded and $n-{\sigma}^{\ast}$ interactions, the predominant effect being the ${\pi}$-nonbonded interactions, (2) $(n-{\sigma}^{\ast})_{anti}$ is destabilizing whereas $(n-{\sigma}^{\ast})_{syn}$ is weakly stabilizing, which are contrary to what we expect from the normal $n-{\sigma}^{\ast}$ interaction, (3) througb-bond coupling of the two radical lobes is destabilizing for the triplet but stabilizing for the singlet tetramethylene diradical.

• Proceedings of the Korean Vacuum Society Conference
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• 2011.02a
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• pp.264-264
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• 2011

Poly [(N, N'-oxydiphenylene) pyromellitimide], polyimide (PI) film은 기계적 강도가 매우 우수하고 열적, 화학적 안정성이 뛰어난 재료로서 전자제품의 소형화, 경령화, 고성능화를 위한 차세대 flexible electronic device에 적용하기 위하여 많은 연구가 진행되고 있다. 그러나 PI의 특성상, 매우 낮은 표면에너지로 인해 금속과의 접촉력이 좋지 않은 단점을 가지고 있다. 본 연구에서는, 금속박막과 PI film 과의 접촉력을 증가시키기 위해 remote-type modified dielectric barrier discharge (DBD) module을 이용하여 대기압 플라즈마 표면처리를 하였다. 실험에 사용된 gas composition은 각각 $N_2$/ He/ $SF_6$, $N_2$/ He/ $O_2$, $N_2$/ He/ $SF_6$/ $O_2$, $N_2$/ He/ $SF_6$/ $O_2$ 이다. $N_2$/ He/ $SF_6$/ $O_2$ gas composition을 이용하여 PI 표면을 플라즈마 처리한 경우, C=O 결합이 PI film 위에 생성됨으로써, 접촉각이 매우 낮게 형성됨을 관찰할 수 있었다. 이와는 반대로 $N_2$/ He/ $SF_6$ gas composition 을 사용하였을 경우에는 C-Fx 화학적 결합이 생성되기 때문에 가장 높은 접촉각이 형성됨을 관찰할 수 있었다. 특히, $N_2$ (40 slm)/ He (1 slm)/ $SF_6$ (1.2 slm) gas composition에 $O_2$ gas를 0.2 slm부터 1.0 slm까지 변화시켜가며 PI film 표면을 처리한 결과, $O_2$ gas를 0.9 slm 첨가하였을 때, 가장 낮은 $9.3^{\circ}$의 접촉각을 얻을 수 있었다. 이는 0.9 slm의 $O_2$ gas를 첨가하였을 때, 가장 많은 양의 $O_2$ radical이 생성되기 때문에 많은 양의 C=O 결합이 생성되기 때문이다. 최적화된 $N_2$ (40 slm)/ He (1 slm)/ $SF_6$ (1.2 slm)/ $O_2$ (0.9 slm) gas composition 조건에서 Ag film과 PI film과의 접촉력을 관찰할 결과, 111 gf/mm를 얻을 수 있었다.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.395-409
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• 2012

In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let ${\pi}$ be a group and let M ${\rightarrow}$ N be a homomorphism between projective $\mathbb{Z}[{\pi}]$-modules such that $\mathbb{Z}_p\;{\otimes}_{\mathbb{Z}[{\pi}]}M{\rightarrow}\mathbb{Z}_p{\otimes}_{\mathbb{Z}[{\pi}]}\;N$ is injective; for which other right $\mathbb{Z}[{\pi}]$-modules V is the induced map $V{\otimes}_{\mathbb{Z}[{\pi}]}\;M{\rightarrow}\;V{\otimes}_{\mathbb{Z}[{\pi}]}\;N$ also injective? Our main theorem gives a new criterion which combines and generalizes many previous results.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1269-1282
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• 2010

We in this note consider a new concept, so called $\pi$-McCoy, which unifies McCoy rings and IFP rings. The classes of McCoy rings and IFP rings do not contain full matrix rings and upper (lower) triangular matrix rings, but the class of $\pi$-McCoy rings contain upper (lower) triangular matrix rings and many kinds of full matrix rings. We first study the basic structure of $\pi$-McCoy rings, observing the relations among $\pi$-McCoy rings, Abelian rings, 2-primal rings, directly finite rings, and ($\pi-$)regular rings. It is proved that the n by n full matrix rings ($n\geq2$) over reduced rings are not $\pi$-McCoy, finding $\pi$-McCoy matrix rings over non-reduced rings. It is shown that the $\pi$-McCoyness is preserved by polynomial rings (when they are of bounded index of nilpotency) and classical quotient rings. Several kinds of extensions of $\pi$-McCoy rings are also examined.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.555-565
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• 2014

An ideal I of a ring R is strongly ${\pi}$-regular if for any $x{\in}I$ there exist $n{\in}\mathbb{N}$ and $y{\in}I$ such that $x^n=x^{n+1}y$. We prove that every strongly ${\pi}$-regular ideal of a ring is a B-ideal. An ideal I is periodic provided that for any $x{\in}I$ there exist two distinct m, $n{\in}\mathbb{N}$ such that $x^m=x^n$. Furthermore, we prove that an ideal I of a ring R is periodic if and only if I is strongly ${\pi}$-regular and for any $u{\in}U(I)$, $u^{-1}{\in}\mathbb{Z}[u]$.

• Journal of the Korean Chemical Society
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• v.21 no.6
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• pp.434-439
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• 1977

The electronic structures of 4-pyridone and lutidone are studied by the SCF MO-CI PPP method and by the configuration analysis method. The spectral data are consistent with the values calculated by the method. The polarization of $S_1({\pi},{\pi}^*)$ state is along the long molecular axis in both compounds. The lowest $({\pi},{\pi}^*)$1 state shows significant charge transfer (16∼18%) from ${\pi}$ bonding orbital of C=O moiety to ${\pi}^*$ antibonding orbital of divinyl amine moiety. The lowest triplet state shows much larger charge transfer (24∼29 %) but in opposite direction compared to that of $S_1({\pi},{\pi}^*)$ state.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.363-372
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• 2007

An element $a$ in a ring R is called left morphic if $$R/Ra{\simeq_-}1(a)$$. A ring is called left morphic if every element is left morphic. In this paper, an element $a$ in a ring R is called left ${\pi}$-morphic (resp. left G-morphic) if there exists a positive number $n$ such that $a^n$ (resp. $a^n{\neq}0$) is left morphic. A ring R is called left ${\pi}$-morphic (resp. left G-morphic) if every element is left ${\pi}$-morphic (resp. left G-morphic). The Morita invariance of left ${\pi}$-morphic (resp. left G-morphic) rings is discussed. Several relevant properties are proved. In particular, it is shown that a left Noetherian ring R with $M_4(R)$ left G-morphic or $M_2(R)$ left morphic is QF. Some known results of left morphic rings are extended to left G-morphic rings and left ${\pi}$-morphic rings.