• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.355-376
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• 2021

In this paper we wish to establish the integral representations of generalized relative order (𝛼, 𝛽) and generalized relative type (𝛼, 𝛽) of entire and meromorphic functions where 𝛼 and 𝛽 are continuous non-negative functions defined on (-∞, +∞). We also investigate their equivalence relation under some certain condition.

• Bulletin of the Korean Chemical Society
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• v.30 no.6
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• pp.1293-1296
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• 2009

A new series of N-substituted 2-n-butyl-3-fluoropyrroles were prepared by a simple one-pot reaction designed of retrosynthesis. $\alpha,\alpha-Difluoro-\gamma-iodo-\gamma$-(trimethylsilyl)propyl n-butyl ketone, a component precursor molecule to 2-n-butyl-3-fluoropyrroles, was prepared with Cu(0) catalyst. It reacted with various primary amines to yield N-substituted 2-n-butyl-3-fluoropyrroles. The products were synthesized via a one-pot reaction scheme between $\alpha,\alpha-Difluoro-\gamma-iodo-\gamma$-(trimethylsilyl) propyl n-butyl ketone and primary amines in excess ( $\geq$ 5 molar equivalence), which eliminate the need of KF required in obtaining n-butyl-1H-3-fluoropyrrole. The yield of products depended reversely on spatial bulkness around N-binding carbon.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.193-199
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• 1993

A hereditary $C^{*}$-subalgebra B of a $C^{*}$-algebra A is said to be full if B is not contained in any proper closed two-sided ideal in A, so each hereditary $C^{*}$-subalgebra of a simple $C^{*}$-algebra is always full. It is well known that every $C^{*}$-algebra is strong Morita equivalent to its full hereditary $C^{*}$-subalgebra, but the strong Morita equivalence of a $C^{*}$-algebra A and its hereditary $C^{*}$-subalgebra B does not imply the fullness of B, ingeneral. We present the following lemma for our computational convenience in the course of the proof of the main theorem. Note that $L_{B}$, $L_{B}$$^{*}$ and $L_{B}$ $L_{B}$$^{*}$ are all .alpha.-invariant whenever B is .alpha.-invariant under the action .alpha. of G.a. of G.a. of G.a. of G.f G.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.367-379
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• 1996

Let $V = {(z, y) : f(z, y) = z^n + Ay^\alpha z^p + y^\beta z^q + y^k = 0}$ and $W = {(z, y) : g(z, y) = z^n + By^\gamma z^s + y^\delta z^t + y^k = 0}$ be germs of analytic irreducible subvarieties of a polydisc near the origin in $C^2$ with n < k and (n, k) = 1 where A and B are complex numbers. Assume that V and W are topologically equivalent near the origin.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.63-78
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• 2008

We generalize several integral inequalities for analytic functions on the open unit polydisc $U^n={\{}z{\in}C^n||zj|<1,\;j=1,...,n{\}}$. It is shown that if a holomorphic function on $U^n$ belongs to the mixed norm space $A_{\vec{\omega}}^{p,q}(U^n)$, where ${\omega}_j(\cdot)$,j=1,...,n, are admissible weights, then all weighted derivations of order $|k|$ (with positive orders of derivations) belong to a related mixed norm space. The converse of the result is proved when, p, q ${\in}\;[1,\;{\infty})$ and when the order is equal to one. The equivalence of these conditions is given for all p, q ${\in}\;(0,\;{\infty})$ if ${\omega}_j(z_j)=(1-|z_j|^2)^{{\alpha}j},\;{\alpha}_j>-1$, j=1,...,n (the classical weights.) The main results here improve our results in Z. Anal. Anwendungen 23 (3) (2004), no. 3, 577-587 and Z. Anal. Anwendungen 23 (2004), no. 4, 775-782.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.10
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• pp.1303-1310
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• 2001

In order to be applicable to the combustion modelling of stratified charged combustion like that of - lean burn and GDI engine, the correlations of laminar burring velocities fur several hydrocarbon fuels and methanol are needed over a wide range of equivalence ratio, pressure and temperature. In this study, these correlations are modeled in the 1311owing form based on the experimental and Muller\`s modeling results for several fuels, where $\alpha$, ξ, and ξ are functions of pressure and temperature, $S_{L}$ =$\alpha$ exp[-ξ($\Phi$-$\Phi$$_{m}$)$^{2}$ -exp {-ζ($\Phi$-$\Phi$$_{m}$)}-ζ($\Phi$-$\Phi$$_{m}$)]. By using the results calculated by PREMIX code with Sloane\`s detailed chemical reaction mechanism for propane, it is verified that the coefficients of the abode modeling can be determined by considering laminar burning velocity data only in a range of equivalence ratio less than $\Phi$$_{m}$. Therefore, Muller\`s modeling results can be adopted leer modeling of the pressure and temperature dependency. Compared with the results of the existing Keck'and Gulder's models, those of the present one showed the good agreement of the recent experimental data, especially in the range of lean and rich sides.s.des.s.

• Korean Journal of Adult Nursing
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• v.27 no.4
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• pp.472-479
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• 2015

Few instruments are available to measure nurses' perceptions of cultural competence in South Korea. Furthermore, the equivalence of factors between original and translated instruments has not been evaluated. The specific aims of this study were to identify the validity and reliability of a Korean version of the Cultural Awareness Scale (K-CAS) and to evaluate the equivalence of factors between the original CAS and the K-CAS. A total of 515 nursing students completed the 26-item K-CAS, 28-item Caffrey Cultural Competence in Healthcare Scale (CCCHS), and eight-item Openness to Diversity and Challenge Scale (ODCS). The K-CAS exhibited good reliability (${\alpha}=.83$) and construct validity by correlating with the CCCHS (r=.344, p<.001) and ODCS (r=.394, p<.001). Confirmatory factor analysis results of the K-CAS confirmed the same factor structure as the original CAS. The K-CAS could be a useful tool to assess the concept of cultural competence among nursing students and nurses.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.809-823
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• 2020

Let C[0, T] denote the space of continuous, real-valued functions on the interval [0, T] and let C₀[0, T] be the space of functions x in C[0, T] with x(0) = 0. In this paper, we introduce a Banach algebra ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ on C[0, T] and its equivalent space ${\bar{\mathcal{F}}}({\mathcal{H}}) $, a space of transforms of equivalence classes of measures, which generalizes Fresnel class 𝓕(𝓗), where 𝓗 is an appropriate real separable Hilbert space of functions on [0, T]. We also investigate their properties and derive an isomorphism between ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ and ${\bar{\mathcal{F}}}({\mathcal{H}}) $. When C[0, T] is replaced by C₀[0, T], ${\bar{\mathcal{F}}}({\mathcal{H}}) $ and ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ reduce to 𝓕(𝓗) and Cameron-Storvick's Banach algebra 𝓢, respectively, which is the space of generalized Fourier-Stieltjes transforms of the complex-valued, finite Borel measures on L²[0, T].

• Biomolecules & Therapeutics
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• v.11 no.1
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• pp.65-71
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• 2003

Terbinafine is a synthetic allylamine that is available in an oral formulation and is used at a dosage of 250mg/day. It is used as an active antifungal agent and inhibits the fungal enzyme squalene epoxidase, which leads to the accumulation of the sterol squalene, which is toxic to the organism. The purpose of the present study was to evaluate the bioequivalence of two terbinafine tablets, Lamisil (Novartis Korea Ltd.) and Terbinex (C-TRI Ltd.), according to the guidelines of Korea Food and Drug Administration (KFDA). Eighteen normal male volunteers, 26.00$\pm$2.57 year in age and 70.51$\pm$9.36 kg in body weight, were divided into two groups and a randomized 2${\times}$2 cross-over study was employed. After one tablet containing 125 mg of terbinafine was orally administered, blood was taken at predetermined time intervals and the concentrations of terbinafine in plasma were determined using HPLC with UV detector. Pharmacokinetic parameters such as AUC, $C_{max}$ and $T_{max}$ were calculated and ANOVA test was utilized for the statistical analysis of the parameters. The results showed that the differences in AUC, $C_{max}$ and $T_{max}$ between two tablets were －4.191％, 5.223％ and －25.720％, respectively when calculated against the Lamisil, tablet. The powers (1-$\beta$) for AUC, $C_{max}$ and $T_{max}$ were 81％, 87％ and below 60％, respectively. Minimum detectable differences(.il) at alpha=O.1 and 1-/3=0.8 were less than 20％ (e.g., 19.72％ and 17.77％ for AUC and $C_{max}$, respectively). But minimum detectable differences($\Delta$) at alpha=0.1 and 1-$\beta$=0.8 for $T_{max}$ were more than 20％ (e.g., 26.25％). The 90％ confidence intervals were within $\pm$20％ (e.g., －17.440∼9.06 and －6.713∼17.160 for AUC and $C_{max}$ respectively). But 90％ confidence intervals for $T_{max}$ were not within $\pm$20％ (e.g., －43.346∼8.083). Another ANOVA test was conducted for logarithmically transformed AUC and $C_{max}$. These results showed that there are no significant differences in AUC and $C_{max}$ between the two formulations: The differences between the formulations in these log transformed parameters were all for less than 20％ (e.g., －4.19％ and 5.22％ for AUC and $C_{max}$, respectively). The 90％ confidence intervals for the log transformed data were not the acceptance range of log 0.8 to log 1.25 in AUC but the acceptance range of log 0.8 to log 1.25 in $C_{max}$ (e.g., log 1.13∼log 1.50 and log 0.94-log 1.22 for AUC and $C_{max}$ respectively). The major parameters, AUC and $C_{max}$ met the criteria of KFDA for bioequivalence although $T_{max}$ did not meet the criteria of KFDA (1998 year) for bioequivalence, indicating that Onfran tablet is bioequivalent to Zofran tablet. But in another ANOVA test AUC did not meet the criteria of KFDA (2002) for bioequivalence but $C_{max}$ met the criteria of KFDA (2002 year) for bioequivalence.or bioequivalence.equivalence.equivalence.equivalence.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.217-227
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• 2016

Let X be a nonempty set, and let $\mathfrak{F}=\{Y_i:i{\in}I\}$ be a family of nonempty subsets of X with the properties that $X={\bigcup}_{i{\in}I}Y_i$, and $Y_i{\cap}Y_j={\emptyset}$ for all $i,j{\in}I$ with $i{\neq}j$. Let ${\emptyset}{\neq}J{\subseteq}I$, and let $T^{(J)}_{\mathfrak{F}}(X)=\{{\alpha}{\in}T(X):{\forall}i{\in}I{\exists}_j{\in}J,Y_i{\alpha}{\subseteq}Y_j\}$. Then $T^{(J)}_{\mathfrak{F}}(X)$ is a subsemigroup of the semigroup $T(X,Y^{(J)})$ of functions on X having ranges contained in $Y^{(J)}$, where $Y^{(J)}:={\bigcup}_{i{\in}J}Y_i$. For each ${\alpha}{\in}T^{(J)}_{\mathfrak{F}}(X)$, let ${\chi}^{({\alpha})}:I{\rightarrow}J$ be defined by $i{\chi}^{({\alpha})}=j{\Leftrightarrow}Y_i{\alpha}{\subseteq}Y_j$. Next, we define two congruence relations ${\chi}$ and $\widetilde{\chi}$ on $T^{(J)}_{\mathfrak{F}}(X)$ as follows: $({\alpha},{\beta}){\in}{\chi}{\Leftrightarrow}{\chi}^{({\alpha})}={\chi}^{({\beta})}$ and $({\alpha},{\beta}){\in}\widetilde{\chi}{\Leftrightarrow}{\chi}^{({\alpha})}{\mid}_J={\chi}^{({\alpha})}{\mid}_J$. We begin this paper by studying the regularity of the quotient semigroups $T^{(J)}_{\mathfrak{F}}(X)/{\chi}$ and $T^{(J)}_{\mathfrak{F}}(X)/{\widetilde{\chi}}$, and the semigroup $T^{(J)}_{\mathfrak{F}}(X)$. For each ${\alpha}{\in}T_{\mathfrak{F}}(X):=T^{(I)}_{\mathfrak{F}}(X)$, we see that the equivalence class [${\alpha}$] of ${\alpha}$ under ${\chi}$ is a subsemigroup of $T_{\mathfrak{F}}(X)$ if and only if ${\chi}^{({\alpha})}$ is an idempotent element in the full transformation semigroup T(I). Let $I_{\mathfrak{F}}(X)$, $S_{\mathfrak{F}}(X)$ and $B_{\mathfrak{F}}(X)$ be the sets of functions in $T_{\mathfrak{F}}(X)$ such that ${\chi}^{({\alpha})}$ is injective, surjective and bijective respectively. We end this paper by investigating the regularity of the subsemigroups [${\alpha}$], $I_{\mathfrak{F}}(X)$, $S_{\mathfrak{F}}(X)$ and $B_{\mathfrak{F}}(X)$ of $T_{\mathfrak{F}}(X)$.