• 대한수학회논문집
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• 제22권1호
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• pp.41-51
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• 2007

Let R be a ring with left identity e and suitably-restricted additive torsion, and Z(R) its center. Let H : $R{\times}R{\times}R{\rightarrow}R$ be a symmetric 3-additive mapping, and let h be the trace of H. In this paper we show that (i) if for each $x{\in}R$, $$n=<<\cdots,\;x>,\;\cdots,x>{\in}Z(R)$$ with $n\geq1$ fixed, then h is commuting on R. Moreover, h is of the form $$h(x)=\lambda_0x^3+\lambda_1(x)x^2+\lambda_2(x)x+\lambda_3(x)\;for\;all\;x{\in}R$$, where $\lambda_0\;{\in}\;Z(R)$, $\lambda_1\;:\;R{\rightarrow}R$ is an additive commuting mapping, $\lambda_2\;:\;R{\rightarrow}R$ is the commuting trace of a bi-additive mapping and the mapping $\lambda_3\;:\;R{\rightarrow}Z(R)$ is the trace of a symmetric 3-additive mapping; (ii) for each $x{\in}R$, either $n=0\;or\;<n,\;x^m>=0$ with $n\geq0,\;m\geq1$ fixed, then h = 0 on R, where denotes the product yx+xy and Z(R) is the center of R. We also present the conditions which implies commutativity in rings with identity as motivated by the above result.

• 한국식품과학회지
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• 제52권6호
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• pp.587-594
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• 2020

본 연구에서는 부위별 배추와 배추김치에 함유되어 있는 글루코시놀레이트류의 조성을 UPLC-MS/MS를 이용하여 탐색하고, 인돌류 대사체를 MS/MS를 이용하여 분석한 결과, 글루코시놀레이트류는 음이온 모드([M-H]-)에서 검출되었으며, glucobrassicanapin (m/z 386), glucoalyssin (m/z 450), glucobrassicin (m/z 447), 4-methoxyglucobrassicin (m/z 477), neoglucobrassicin (m/z 477)는 MS scan 모드에서, gluconapin (m/z 372→97), progoitrin (m/z 388→97), glucoiberin (m/z 422→97), 4-methoxyglucobrassicin (m/z 477→97), neoglucobrassicin (m/z 477→447)는 MS/MS MRM 모드에서 검출되었다. Glucobrassicin과 같은 인돌기 함유 글루코시놀레이트류들이 대사되어 생성되는 인돌류 대사체로는 ascorbigen (m/z 306→130)과 I3A (m/z 146→118)가 MS/MS MRM ([M+H]+) 모드에서 검출되었다. Ascorbigen은 NKC보다 IPC와 OPC에 유의적으로 많이 함유되어 있었다. I3A는 NKC에 가장 많이 함유되어 있었으나 시료 간 유의적인 차이는 없었다. 본 연구를 통하여 배추와 배추김치에 존재하는 글루코시놀레이트류와 그 대사체인 인돌류 물질을 UPLC-MS/MS를 이용하여 분석할 수 있었다.

• 대한수학회보
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• 제52권1호
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• pp.105-123
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• 2015

Let $f_{\beta}=h_{\beta}+\bar{g}_{\beta}$ and $F_a=H_a+\bar{G}_a$ be harmonic mappings obtained by shearing of analytic mappings $h_{\beta}+g_{\beta}=1/(2isin{\beta})log\((1+ze^{i{\beta}})/(1+ze^{-i{\beta}})\)$, 0 < ${\beta}$ < ${\pi}$ and $H_a+G_a=z/(1-z)$, respectively. Kumar et al. [7] conjectured that if ${\omega}(z)=e^{i{\theta}}z^n({\theta}{\in}\mathbb{R},n{\in}\mathbb{N})$ and ${\omega}_a(z)=(a-z)/(1-az)$, $a{\in}(-1,1)$ are dilatations of $f_{\beta}$ and $F_a$, respectively, then $F_a\tilde{\ast}f_{\beta}{\in}S^0_H$ and is convex in the direction of the real axis, provided $a{\in}[(n-2)/(n+2),1)$. They claimed to have verified the result for n = 1, 2, 3 and 4 only. In the present paper, we settle the above conjecture, in the affirmative, for ${\beta}={\pi}/2$ and for all $n{\in}\mathbb{N}$.

• Journal of Microbiology and Biotechnology
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• 제11권4호
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• pp.649-655
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• 2001

The kinetics of the thermolysin-catalyzed synthesis of N-(benzyloxycarbonyl)-L-phenylalanyl-L-leucine ethyl ester (Z-Phe-LeuOEt) from N-(benzyloxycarbonyl)-L-phyenylalanine (Z-Phe) and L-leucine ethyl ester (LeuOEt) in an ethyl acetate saturated aqueous system in a batch operation were studied. The kinetics for the synthesis of Z-Phe-LeuOEt were expressed using a rate equation for the rapid equilibrium random bireactant mechanism. The four kinetic constants involved in the rate equation were determined numerically by the quasi-Newton method so as to fit the calculated results with the experimental data. Within the pH and temperature range examined, the $K_{cat}$ value for the synthesis of Z-Phe-LeuOEt reached a maximum at pH 7.0 and $45^{\circ}C$, whereas the affinity between Z-Phe and thermolysin reached a maximum at pH 6.0 adn $40^{\circ}C$. The inhibitory effect of Z-Phe on the condensation reaction decreased as the pH and temperature decreased. In contrast, they affinity between LeuOEt and thermolysin remained unchanged within the pH and temperature range examined. Therefore, it was concluded that the protonation state of the carboxyl groups. of Z-Phe was more imprtant than that of the amono groups of LeuOEt for the synthesis of Z-Phe-LeuOEt in the present solvent system. The equilibrium yield at pH 6.0 and $30^{\circ}C$ was 8% higher than that at pH 7.0 and $40^{\circ}C$, although the rate was much slower. This result suggested that the affinity between the enzyme and the substrate rather than the overall rate was a more important factor affecting the equilibrium yield, when the peptide synthesis was carried out in a product-precipitation system.

• Bulletin of the Korean Chemical Society
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• 제33권9호
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• pp.3039-3042
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• 2012

Pressure tensors at the planar surface of liquid-vapor argon are evaluated from the virial theorem, Irving-Kirkwood, and Harasima versions using a test-area molecular dynamics simulation method through a Lennard-Jones intermolecular potential at two temperatures. We found that the normal and transverse components of the pressure tensor, $p_N(z)$ and $p_T(z)$, obtained from the virial theorem and Harasima version are essentially the same. The normal component of the pressure tensor from Irving-Kirkwood version, $p_N^{IK}(z)$, is shown to be a nearly constant at the lower temperature, independent of z, as agreed in a previous study, but not for $p_N^H$(z), while the transverse components, $p_T^{IK}(z)$ and $p_T^H(z)$, are almost the same. The values of surface tension for both versions computed from $p_N(z)-p_T(z)$ are also the same and are fully consistent with the experimental data.

• 대한수학회논문집
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• 제22권1호
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• pp.65-74
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• 2007

Suppose that $\mu$ is a finite positive Borel measure on bounded symmetric domain $\Omega{\subset}\mathbb{C}^n\;and\;\nu$ is the Euclidean volume measure such that $\nu(\Omega)=1$. Suppose 1 < p < $\infty$ and r > 0. In this paper, we will show that the norms $sup\{\int_\Omega{\mid}k_z(w)\mid^2d\mu(w)\;:\;z\in\Omega\}$, $sup\{\int_\Omega{\mid}h(w)\mid^pd\mu(w)/\int_\Omega{\mid}h(w)^pd\nu(w)\;:\;h{\in}L_a^p(\Omega,d\nu),\;h\neq0\}$ and $$sup\{\frac{\mu(E(z,r))}{\nu(E(z,r))}\;:\;z\in\Omega\}$$ are are all equivalent. We will also show that the inclusion mapping $ip\;:\;L_a^p(\Omega,d\nu){\rightarrow}L^p(\Omega,d\mu)$ is compact if and only if lim $w\rightarrow\partial\Omega\frac{\mu(E(w,r))}{\nu(E(w,r))}=0$.

• 대한수학회보
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• 제48권2호
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• pp.247-260
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• 2011

Let h be a meromorphic function with few poles and zeros. By Nevanlinna's value distribution theory we prove some new properties on the polynomials in h with the coefficients being small functions of h. We prove that if f is a meromorphic function and if $f^m$ is identically a polynomial in h with the constant term not vanish identically, then f is a polynomial in h. As an application, we are able to find the entire solutions of the differential equation of the type $$f^n+P(f)=be^{sz}+Q(e^z)$$, where P(f) is a differential polynomial in f of degree at most n-1, and Q($e^z$) is a polynomial in $e^z$ of degree k $\leqslant$ max {n-1, s(n-1)/n} with small functions of $e^z$ as its coefficients.

• 대한수학회보
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• 제56권4호
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• pp.911-927
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• 2019

Let $\mathscr{B}^{{\eta},{\mu}}_{p,n}\;({\alpha});\;({\eta},{\mu}{\in}{\mathbb{R}},\;n,\;p{\in}{\mathbb{N}})$ denote all functions f class in the unit disk ${\mathbb{U}}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: $$\|\[{\frac{f^{\prime}(z)}{pz^{p-1}}}\]^{\eta}\;\[\frac{z^p}{f(z)}\]^{\mu}-1\| <1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. And $\mathscr{M}^{{\eta},{\mu}}_{p,n}\;({\alpha})$ indicates all meromorphic functions h in the punctured unit disk $\mathbb{U}^*$ as $h(z)=z^{-p}+\sum_{k=n-p}^{\infty}b_kz^k$ which satisfy: $$\|\[{\frac{h^{\prime}(z)}{-pz^{-p-1}}}\]^{\eta}\;\[\frac{1}{z^ph(z)}\]^{\mu}-1\|<1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. In this paper several sufficient conditions for some classes of functions are investigated. The authors apply Jack's Lemma, to obtain this conditions. Furthermore, sufficient conditions for strongly starlike and convex p-valent functions of order ${\gamma}$ and type ${\beta}$, are also considered.

• 한국결정학회지
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• 제5권2호
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• pp.108-112
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• 1994

C19H20O5, Mr=314.337,삼사정계,PI, a=10.291(2)A, b=11.218(3)A, c=3.059(1)A, α=74.54(2)°,β=1148.84(1)°,r=109.84(2)°,V=883.283(2)A3, λ(Mo Kα)=0.71069A, μ=0.47 mm-1, F(000)=324, 296K, Z=2, Dx=1.18Mgm-3. 1637[F>3σ(F)]개 독립 반사면에 대한 최종 R=0.0580이다. α,β-diphenylsuccinic acid,C16H14O4, 분자들은 O(4)-H˙˙˙O(5)수소결합에 의하여 용체인 acetone과 결합되어 있고 중심대칭관계에 있는 dimer는 분자간의 carboxylic 수소결합 O(1)-H˙˙˙O(2)(-x,-y,-z)에 의하여 결합되어 있다. Dimer간의 가장 가까운 거리 3.288A[O(2)˙˙˙O(2)(-x,-y,-z)]은 분자들의 packing이 van der Waals 력으로 이루어졌음을 보인다.

• Journal of Microbiology
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• 제34권4호
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• pp.327-333
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• 1996

Yeast, like many other microbes, encounters large variations in ambient pH in their natural environments. Microorganisms capable of growing over a wide pH range require a versatile, efficient pH homeostatic mechanism protecting intracellular processes against extremes of pH. In several organisms, fusions to the bacterial lacZ gene have been extremely useful for the identification of genes expressed at different time during the life cycle or under different growth conditions. In this study, using the lacZ gene screening system, we surveyed a large number of yeast strains with lacZ insertion to identify genes regulated by pH. A yeast genomic library was constructed and inserted with lacZ by a shuttle mutagenesis procedure. The yeast transformants were individually picked up with a toothpick, replica-plated, and grown in alkaline pH medium. Among the 35,000 colonies screened, 10 candidate strains were identified initially by the $\beta$-gal assay. We finally confirmed two yeast strains carrying the genes whose expression are strictly dependent on pH of growth medium. One of the fusions showing a 10-fold induction in expression level in response to alkali pH was selected and further characterized. The pH-regulated gene was cloned by inverse PCR and a partial sequence of the gene was determined. Identification and characterization of the gene is currently under investigation.