• Honam Mathematical Journal
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• v.2 no.1
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• pp.19-23
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• 1980

본(本) 논문(論文)은 Cohomotopy군(群)과 Cohomolopy군(群) 사이의 몇가지 관계(關係)를 구명(究明)한 것이다. 논문(論文)의 주부분(主部分)으로서 ⅰ) 어떤 조건하(條件下)에서 $${\pi}^m(X,A){\sim_=}H^m(X,A)$$ (Theorem 2, Corollary 3) ⅱ) 어떤 조건하(條件下)에서 $${\pi}^n(X,A)=0{\Leftarrow}{\Rightarrow}H^n(X,A)=0$$ (Theorem 4) ⅲ) 어떤 조건하(條件下)에서 $${\pi}^n(X){\sim_=}{\pi}^n(A){\Leftarrow}{\Rightarrow}H^n(X){\sim_=}H^n(A)$$ (Corollary 5) 가 성립(成立)함을 증명(證明)하였다.

• Proceedings of the Korea Society for Energy Engineering kosee Conference
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• 1996.10b
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• pp.34-44
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• 1996

N-machine produces more than input energy at above 3000 rpm. any space energy is absorbed when the N-machine is rotating at a very high velocity. Laws of electromagnetics verify that normal conduction is due to that electrons moves from one three-dimensional crystallizing ${\pi}-bonding$ orbital to next. The ${\pi}-far$ infrared rays are generated from the resonance and rotation of the electrons on the orbitals of three-dimensional crystallizing ${\pi}-bonding$ atoms. Material in universe is composed of ${\pi}-rays$, which have alternative outward electric field. If the alternative outward electric fields of the ${\pi}-rays$ are resonant each other they make attraction force, which is the gravity. The collection of space energy is due to a attraction force between the radially alternating electric field and the ${\pi}-far$ infrared rays in the space. Electrons flow by absorbed density difference of ${\pi}-far$ infrared rays along a conduction wire, which also verifies that normal electron conduction is due to a flow from one three-dimensional crystallizing ${\pi}-bonding$ orbital to next.

• Bulletin of the Korean Chemical Society
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• v.4 no.4
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• pp.157-161
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• 1983

Ab initio calculations were performed on systems containing various basic ${\pi}$ fragments and glycines to generalize the ${\pi}$-nonbonded interaction (${\pi}$-NBI) method of determining relative conformational and configurational stability of organic molecules. It was found that the relative stability of conformational isomers can be determined in general by the simple application of the ${\pi}$-NBI method, but the method is not applicable to the geometrical isomerism in which stronger structural factors are involved. The ${\pi}$-NBI effect of a crowded ${\pi}$-structure ($n{\pi}/m$) is maximum for the system in which n is equal to m. In crowded structures containing heteroatoms, ${P^{\pi}}_{ij}$ values of 4N+1 system may become negative, but this sign reversal does not invalidate the predictions based on the ${\pi}$-NBI method.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.875-880
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• 1995

Let $S_p(\alpha)$ denote the class of the Spirallike functions of order $\alpha, 0 < $\mid$\alpha$\mid$ < \frac{\pi}{2}$ Let $\Pi_N$ denote the subset of $S_p(\alpha)$ consisting of all products $z\Pi^N_{j=1}(1-u_j z)^{-mt_j}$ where $m = 1 + e^{-2i\alpha},$\mid$u_j$\mid$ = 1, t_j > 0$ for $j = 1, \cdots, N$ and $\sum^{N}_{j=1}{t_j = 1}$. In this paper we prove that extreme points of $S_p(\alpha)$ may be found which lie in $\Pi_N$ for some $N \geq 2$. We are let to conjecture that all exreme points of $S_p(\alpha)$ lie in $\Pi_N$ for somer $N \geq 1$ and that every such function is an extreme point.

• The Korean Journal of Ecology
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• v.8 no.1
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• pp.1-5
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• 1985

The plastochron index (PI) provides possibility on studies of the effects of various environmental factors on morphological and physiological development of plants. The PI of Erickson and Michemlini(1957) could be used merely when leaf n is longer an leaf n+1 is smaller than the references length at any time. If both the lengths of leaf n and n+1 are smaller or longer than the reference length, it could not estimated. In this study, the PI of Erickson and Michelini was complemented and the linear patterns according to leaf arrangement was represented, PI is n-(lnLR-lnLn)/(lnLn-lnLn+1). And when both the lengths of leaf n and n+1 are longer than the length of reference, PI is n+1+(ln Ln+1-lnLR)/(lnLn-lnLn+1). The linear model of PI is changed by the various environmental factors and the linear patterns are different according to leaf arrangement. According to leaf arrangement, the equation of the general regression lines is Yin-(i-j)=a-(n-1)(q1+...+qi-1)-(q1+...+qj-1)+rt+$\varepsilon$. Where Y:the logarithmic of the leaf length in question, i:leaf number hang on the one node, n:the number counting from base, q:spacing on the Y-axis, j:0, 1, 2, ..., r:slope, t:time, $\varepsilon$:error.

• Proceedings of the Korean Society of Applied Pharmacology
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• 2001.11a
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• pp.103-103
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• 2001

인간유방상피세포에서 H-ras가 침윤성과 세포 이동성을 유도한다는 것을 이 전연구에서 밝혔다. Phosphatidylinositol 3-kinase(PI3K)는 세포 이동성에서 중요한 역할을 하는 것으로 보고되고 있다. 본 연구에서 인간유방상피세포인 MCF10A에서 H-ras에 의해 유도된 침윤성에 PI3K가 어떠한 영향을 미치는지 살펴보고자 하였다. PI3K의 활성은 PI3K의 downstream molecule인 Akt의 인산화를 Western blot으로 확인하였다. Akt는 MCF10A, H-ras, N-ras MCF10A 세포에서 같은 정도로 발현되는 반면, 인산화된 Akt는 MCF10A 세포에 비해 H-ras MCF10A 세포와 N-ras MCF10A 세포에서 현저히 높게 나타났다. 이상의 결과로서 H-ras, N-ras 둘 다 PI3K를 활성화시키며, 침윤성과 세포이동성이 없는 N-ras MCF10A 세포에서도 PI3K가 활성화되었으므로, PI3K의 활성은 세포침윤성과 이동성을 유도하는데에 있어서 충분하지는 않음을 말해준다. PI3K의 저해제인 LY294002와 wortmannin을 세포에 처리하였을 때 세포침윤성과 이동성이 유의성 있게 감소되었다. 이상의 결과는 MCF10A 세포의 침윤성과 이동설에 있어서 PI3K의 활성이 충분하지는 않지만 반드시 필요하다는 것을 알 수 있었다.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.367-374
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• 2003

Let N be a Closed n-manifold with residually finite, torsion free $\pi$$_1$(N) and finite H$_1$,(N). Suppose that $\pi$$\_$k/(N)=0 for 1 < k < n-1. We show that N is a codimension-n PL fibrator if and only if N does not cover itself regularly and cyclically up to homotopy type, provided $\pi$$_1$(N) satisfies a certain condition.

• Journal of the Korean Chemical Society
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• v.25 no.2
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• pp.61-66
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• 1981

A method for calculation of the contribution of $\pi$ bonding molecular orbitals to the dipole moments for octahedral [M(III)$A_3B_3$] type complexes has been developed [M(III) = Ti(III), V(III), Cr(III), Fe(III) or Co(III); A = O or N; B = N, S or Cl]. The contribution of ${\pi}$ bonding molecular orbitals to the dipole moments is found to be smaller than that of ${\sigma}$ bonding molecular orbitals but this contribution may not be negligible even for chelate complexes in which delocalization of ${\pi}$ electron is assumed. The calculated dipole moments (u = $u_{\sigma}$ + $u_{\pi}$) are closer to the experimental values than those for the case where only ${\sigma}$ bonds are assumed to be formed.

• Journal of the Korean Chemical Society
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• v.22 no.4
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• pp.239-244
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• 1978

Spectroscopic studies of trans-1,2-bispyrazylethylene (BPE), one of the stilbene analogues, were carried out. In normal UV spectra, a distinct $n{\rightarrow}{\pi}^*$ absorption band is missing because of a strong, nearly isoenergetic ${\pi}{\rightarrow}{\pi}^*$ absorption band. The second derivative and low temperature $(77^{\circ}K)$ UV absorption spectra were taken and $n{\rightarrow}{\pi}^*$ absorption band was identified by these methods. The transition energies of ${\pi}{\rightarrow}{\pi}^*$ transitions were calculated by Pariser-Parr-Pople (PPP)-SCF-CI MO method. The calculated values showed good agreement with the observed spectral data. Luminescence studies were also carried out at low temperature. From the fluorescence spectra, fluorescence polarization studies, and PPP-SCF-CI MO calculation, the fluorescent state was determined to be a singlet $({\pi},\;{\pi}^*)$ state. This conclusion is in good agreement with the results obtained from alkaline salt effects on the fluorescence of this compound.

• Bulletin of the Korean Chemical Society
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• v.6 no.5
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• pp.277-279
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• 1985

Orbital interactions of the types, ${\sigma}-{\pi},\;{\sigma}^*-{\pi},\;{\sigma}-{\pi}^*\;and\;{\sigma}^*-{\pi}^*$ are investigated for the rotamers of ${\alpha}$-X-acetones (X = F and Cl) using STO-3G method of calculation. It was found that the interactions are possible only in gauche forms, and the ${\sigma}^*-{\pi}^*$ interactions are in general greater than the $\sigma-\pi$ interactions due to the greater overlap, in spite of the greater energy gap involved; the greater ${\sigma}^*-{\pi}^*$ interaction causes greater lowering of ${\pi}^*$ level relative to the lowering of ${\sigma}$ in the ${\sigma}-{\pi}$ interaction so that both ${\sigma}-{\pi}^*$ and $n-{\pi}^*$ interactions are enhanced in the gauche forms. The extra stability of the gauche form and the red shift in the $n-{\pi}^*$ transition are thus found to be natural corollaries of the greater ${\sigma}^*-{\pi}^*$ interaction in the gauche forms.