• 충청수학회지
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• 제23권3호
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• pp.495-510
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• 2010

An Einstein's connection which takes the form (2.23) is called a $^*g$-ME-connection and the corresponding vector is called a $^*g$-ME-vector. The $^*g$-ME-manifold is a generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection and we denote it by $^*g-MEX_n$. The purpose of this paper is to derive a general representation and a special representation of the $^*g$-ME-vector in $^*g-MEX_n$.

• 호남수학학술지
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• 제30권4호
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• pp.603-616
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• 2008

A generalized n-dimensional Riemannian manifold $X_n$ on which the differential geometric structure is imposed by the unified field tensor $^*g^{{\lambda}{\nu}}$, satisfying certain conditions, through the $^*g$-ME-connection which is both Einstein's equation and of the form(3.1) is called $^*g$-ME-manifold and we denote it by $^*g-MEX_n$. In this paper, we prove a necessary and sufficient condition for the existence of $^*g$-ME-connection and derive a surveyable tensorial representation of the $^*g$-ME-connection and the $^*g$-ME-vector in $^*g-MEX_n$.

• Biotechnology and Bioprocess Engineering:BBE
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• 제5권1호
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• pp.7-12
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• 2000

The expression of the mouse $\alpha-amylase$ gene in the methylotrophic yeast, P pastoris was investigated. The mouse $\alpha-amylase$ gene was inserted into the multi-cloning site of a Pichi a expression vector, pPIC9, yielding a new expression vector pME624. The plasmid pME624 was digested with SalI or BglII, and was introduced into P. pastoris strain GSl15 by the PEG1000 method. Fifty-three transformants were obtained by the transplacement of pME624 digested with SaiII or BglII into the HIS4locus $(38\;of\;Mut^+\;clone)$ or into the AOX1 locus $(15\;of\;Mut^s\;clone)$. Southern blot was carried out in 11 transformants, which showed that the mouse $\alpha-amylase$ gene was integrated into the Pichia chromosome. When the second screening was performed in shaker culture, transformant G2 showed the highest $\alpha-amylase$ activity, 290 units/ml after 3-day culture, among 53 transformants. When this expression level of the mouse $\alpha-amylase$ gene is compared with that in recombinant Saccharomyces cerevisiae harboring a plasmid encoding the same mouse $\alpha-amylase$ gene, the specific enzyme activity is eight fold higher than that of the recombinant S. cerevisiae.

• Bulletin of the Korean Chemical Society
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• 제33권12호
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• pp.4161-4164
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• 2012

Density functional MO calculations for the methylsilole anion of $[C_4H_4SiMe]^-$ and methylgermole anion of $[C_4H_4SiMe]^-$ at the B3LYP (full)/6-311+$G^*$ level (GAUSSIAN 94) were carried out and characterized by frequency analysis. The ground state structure for the methylsilole anion and methylgermole anion is that the methyl group is pyramidalized with highly localized structure. The difference between the calculated $C_{\alpha}-C_{\beta}$ and $C_{\beta}-C_{\beta}$ distances are 9.4 and 11.5 pm, respectively. The E-Me vector forms an angle of $67.9^{\circ}$ and $78.2^{\circ}$ with the $C_4E$ plane, respectively. The optimized structures of the saddle point state for the methylsilole anion and methylgermole anion have been also found as a planar with highly delocalized structure. The optimized $C_{\alpha}-C_{\beta}$ and $C_{\beta}-C_{\beta}$ distances are nearly equal for both cases. The methyl group is located in the plane of $C_4E$ ring and the angle between the E-Me vector and the $C_4E$ plane for the methylsilole anion and methylgermole anion is $2.0^{\circ}$ and $2.3^{\circ}$, respectively. The energy difference between the ground state structure and the transition state structure is only 5.1 kcal $mol^{-1}$ for the methylsilole anion. However, the energy difference of the methylgermole anion is 14.9 kcal $mol^{-1}$, which is much higher than that for the corresponding methylsilole monoanion by 9.8 kcal $mol^{-1}$. Based on MO calculations, we suggest that the head-to-tail dimer compound, 4, result from [2+2] cycloaddition of silicon-carbon double bond character in the highly delocalized transition state of 1. However, the inversion barrier for the methylgermole anion is too high to dimerize.