• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.45-56
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• 1995

D. H. Gottlieb [1, 2] studied the subgroups $G_n(X)$ of homotopy groups $\pi_n(X)$. In [5, 7, 10], the authors introduced subgroups $G_n(X, A)$ and $G_n^{Rel}(X, A) of \pi_n(X)$ and $\pi_n(X, A)$ respectively and showed that they fit together into a sequence $$ \cdots \to G_n(A) \longrightarrow^{i_*} G_n(X, A) \longrightarrow^{j_*} G_n^{Rel}(X, A) \longrightarrow^\partial $$ $$ \cdots \to G_1^{Rel}(X, A) \to G_0(A) \ to G_0(X, A) $$ where $i_*, j_*$ and \partial$ are restrictions of the usual homomorphisms of the homotopy sequence $$ \cdot \to^\partial \pi_n(A) \longrightarrow^{i_*} \pi_n(X) \longrightarrow^{j_*} \pi_n(X, A) \to \cdot \to \pi_0(A) \to \pi_0(X) $$.

• Journal of the Microelectronics and Packaging Society
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• v.27 no.2
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• pp.33-38
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• 2020

In the photoelectrochemical (PEC) water splitting, GaN is one of the most promising photoanode materials due to high stability in electrolytes and adjustable energy band position. However, the application of GaN is limited because of low efficiency. To improve solar to hydrogen conversion efficiency, we introduce a Cobalt Phosphate (Co-pi) catalyst by photo-electrodeposition. The Co-pi deposition GaN were characterized by SEM, EDS, and XPS, respectively, which illustrated that Co-pi was successfully decorated on the surface of GaN. PEC measurement showed that photocurrent density of GaN was 0.5 mA/㎠ and that of Co-pi deposited GaN was 0.75 mA/㎠. Impedance and Mott-Schottky measurements were performed, and as a result of the measurement, polarization resistance (R_p) and increased donor concentration (N_D) values decreased from 50.35 Ω to 34.16 Ω were confirmed. As a result of analyzing the surface components before and after the water decomposition, it was confirmed that the Co-pi catalyst is stable because Co-pi remains even after the water decomposition. Through this, it was confirmed that Co-pi is effective as a catalyst for improving GaN efficiency, and when applied as a catalyst to other photoelectrodes, it is considered that the efficiency of the PEC system can be improved.

• Journal of the Korean Chemical Society
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• v.26 no.2
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• pp.65-72
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• 1982

STO-3G level computations were performed on n-propylamine, n-propylamine radical and cis-and trans-ethylene diamines in order to investigate structural contributions of (n${\pi}$/m) and (n-${\sigma}^*$) structures to the energy variations accompanying the conformational changes. It was found that (5${\pi}$/5) and (4${\pi}$/4) structures had attractive and repulsive nonbonded interactions, respectively, which were approximately additive. anti(n-${\sigma}^*$) structures had more stabilzing hyperconjugative interactions than syn(n-${\sigma}^*$) structures, but due to the large internuclear repulsion the net effect was destabilizing inthe former in contrast with the net stabilizing contribution in the latter. Moreover it was found that the stabilizing ${\pi}$-nonbond structure, (5${\pi}$/5) was always cooperatively reinforced by the more stabilizing anti(n-${\sigma}^*$) interaction, whereas the destabilizing (4${\pi}$/4) structure was accompanied by the less stabilizing syn(n-${\sigma}^*$) interaction. This type of cooperativity was found general through-bond interaction of the terminal lone pair lobes split the energy levels into two, $n_+ = \frac{1}{\sqrt{2}}(n_1 + n_2)$ and $n_- = \frac{1}{\sqrt{2}}(n_1 - n_2)$, the latter being the lower level, which can be shown using simple overlap patterns of the two lobes with a common vicinal ${\sigma}^*$ orbital.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.1-9
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• 1989

In 1980 and 1983, it was proved that P $D^{2}$-groups are surface groups ([2], [3]). Since then, topologists have been positively studying about P $D^{n}$ -groups (or $D^{n}$ -groups). For example, let a topological space X have a right .pi.-action, where .pi. is a multiplicative group. If each x.memX has an open neighborhood U such that for each u.mem..pi., u.neq.1, U.cap. $U_{u}$ =.phi., this right .pi.-action is said to be proper. In this case, if X/.pi. is compact then (1) .pi.$_{1}$(X/.pi).iden..pi.(X:connected, .pi.$_{1}$: fundamental group) ([4]), (2) if X is a differentiable orientable manifold with demension n and .rho.X (the boundary of X)=.phi. then $H^{k}$ (X;Z).iden. $H_{n-k}$(X;Z), ([6]), where Z is the set of all integers.s.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.393-401
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• 2004

In this paper, we apply the concept of the group \ulcorner(X,A) of self pair homotopy equivalences of a CW-pair (X, A) to the Postnikov system. By using a short exact sequence related to the group of self pair homotopy equivalences, we obtain the following result: for any Postnikov section X$\sub$n/ of a CW-complex X, the group \ulcorner(X$\sub$n/, A) of self pair homotopy equivalences on the pair (X$\sub$n/, X) is isomorphic to the group \ulcorner(X) of self homotopy equivalences on X. As a corollary, we have, \ulcorner(K($\pi$, n), M($\pi$, n)) ≡ \ulcorner(M($\pi$, n)) for each n$\pi$1, where K($\pi$,n) is an Eilenberg-Mclane space and M($\pi$,n) is a Moore space.

• Bulletin of the Korean Chemical Society
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• v.15 no.10
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• pp.857-860
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• 1994

We have calculated the ${\pi}$-electron density, atom self-polarizability, and free valence on each atom of N-(2-chlorobenzyl)-pyridinium, N-(benzyl)-2-chloropyridinium, and N-(2-chlorobenzyl)-2-chloropyridinium salts using a simple Huckel method in order to discuss their intramolecular photocyclization reaction in a qualitative method. Our calculation qualitatively predicts that photocyclization occurs through forming radicals as a reaction intermediate by breaking a C-Cl bond after photoexcitation into a triplet state via intersystem crossing from an initially excited singlet state. We noticed that this C-Cl bond breaking is aided by ${\pi}$-complex formation between a chlorine atom and the ${\pi}$ -electrons of the neighboring ring in the triplet state and a stronger ${\pi}$-complex bond makes C-Cl bond breaking, i.e., radical formation, much easier. A chlorine atom will form a stronger ${\pi}$ -complex bond to a benzyl ring of N-(benzyl)-2-chloropyridinium than a pyridinium ring of N-(2-chlorobenzyl)-pyridinium because the former can donate its ${\pi}$-electron more easily than the latter. The chlorine at position 15 of N-(2-chlorobenzyl)-2-chloropyridinium salt in the excited state also provides its ${\pi}$-electron to the benzyl ring. So this ${\pi}$-electron can increase the bond strength of the $\pi-complex.$ Therefore, the strength of ${\pi}$-complex follows the order of N-(2-chlorobenzyl)-2-chloropyridinium, N-(benzyl)-2-chloropyridinium, and N-(2-chlorobenzyl)-pyridinium salts and thus the radical formation rate. This provides us with an intramolecular photocyclization reaction rate of the same order as given above.

• Journal of the Korean Institute of Telematics and Electronics
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• v.13 no.4
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• pp.18-23
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• 1976

We have obtained the solution of van der Pol's equation characterized by an arctangent nonlinearity, using the perturbation method by writing periodicity conditions: $$X^{(n)}(2{\pi})-X^{(n)}(0)=0$$ $$X^{(n)'}(2{\pi})-X^{(n)'}(0)=0 (n=0,1,2......)$$ together with the starting condition: $$X^{(n)}(\frac{\pi}{2})=0,\;X^{(n)}'(\frac{\pi}{2})=-R^{(n)}$$. Our results agree with Liapunov's theorem and our calculated value is more similar to Murata's measured value than Murata's calculated value.

• Journal of the Korean Chemical Society
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• v.22 no.1
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• pp.45-51
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• 1978

The luminescence of N-methyllutidone is studied in ethanol matrix at $77^{\circ}C$K. No fluorescence is observed but a strong phosphorescence with the quantum yield of 0.1 and the lifetime of 0.2 sec is recorded. An unusually high triplet energy of 85.1 kcal/mole is determined for the compound from the O-O band of phosphorescence. The cis ${\leftrightarrow}$ trans photoisomerization of high triplet energy olefins such as 2-hexene and trans-1,4-dichlorobutene-2 is efficiently sensitized by N-methyllutidone substantiating the high triplet energy of the compound. The negative polarization of O-O band reveals the emitting triplet state to be $({\pi},{\pi}^*)^3$ state. Alkaline metal salts such as lithium chloride enhances the phosphorescence intensity through cation-N-methyllutidone coordination widening the gap between $({\pi},{\pi}^*)^3$and $(n,{\pi}^*)^3$ states.

• Journal of the Korean Chemical Society
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• v.20 no.5
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• pp.398-405
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• 1976

A new compound, 1,2-bispyrazyl ethylene,is synthesized starting from pyrazine carboxylic acid and methyl pyrazine. The compound is characterized utilizing UV-VIS, IR, NMR and mass spectra along with elemental analysis. Spectroscopic properties are studied from UV-VIS and fluorescence spectra. From unusual salt effects on fluorescence spectra, it is believed that $(n,\;{\pi}^*)$ state has about the same energy as $({\pi},\;{\pi}^*)$ state. The compound fluoresces from $({\pi},\;{\pi}^*)$ state with the quantum yield of 0.025 at $77^{\circ}K$ compared to near unity for stilbene at the same temperature indicating the efficient intersystem crossing to triplet state, because of strong $(n,\;{\pi}^*)$ and $({\pi},\;{\pi}^*)$ mixing in the lowest excited state.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.91-102
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• 2016

A chief factor H/K of G is called F-central in G provided $(H/K){\rtimes}(G/C_G(H/K)){\in}{\mathfrak{F}}$. A normal subgroup N of G is said to be ${\pi}{\mathfrak{F}}$-hypercentral in G if either N = 1 or $N{\neq}1$ and every chief factor of G below N of order divisible by at least one prime in ${\pi}$ is $\mathfrak{F}$-central in G. The symbol $Z_{{\pi}{\mathfrak{F}}}(G)$ denotes the ${\pi}{\mathfrak{F}}$-hypercentre of G, that is, the product of all the normal ${\pi}{\mathfrak{F}}$-hypercentral subgroups of G. We say that a subgroup H of G is ${\pi}{\mathfrak{F}}$-embedded in G if there exists a normal subgroup T of G such that HT is s-quasinormal in G and $(H{\cap}T)H_G/H_G{\leq}Z_{{\pi}{\mathfrak{F}}}(G/H_G)$, where $H_G$ is the maximal normal subgroup of G contained in H. In this paper, we use the ${\pi}{\mathfrak{F}}$-embedded subgroups to determine the structures of finite groups. In particular, we give some new characterizations of p-nilpotency and supersolvability of a group.