• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.65-76
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• 2004

An entire function $f\;{\in}\;H(\mathbb{C})$ is called universal with respect to translations if for any $g\;{\in}\;H(\mathbb{C}),\;R\;>\;0,\;and\;{\epsilon}\;>\;0$, there is $n\;{\in}\;{\mathbb{N}}$ such that $$\mid$f(z\;+\;n)\;-\;g(z)$\mid$\;<\;{\epsilon}$ whenever $$\mid$z$\mid$\;{\leq}\;R$. Similarly, it is universal with respect to differentiation if for any g, R, and $\epsilon$, there is n such that $$\mid$f^{(n)}(z)\;-\;g(z)$\mid$\;<\;{\epsilon}\;for\;$\mid$z$\mid$\;{\leq}\;R$. In this note, we review G. MacLane's proof of the existence of universal functions with respect to differentiation, and we give a simplified proof of G. D. Birkhoff's theorem showing the existence of universal functions with respect to translation. We also discuss Godefroy and Shapiro's extension of these results to convolution operators as well as some new, related results and problems.

• Journal of Microbiology and Biotechnology
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• v.7 no.6
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• pp.438-440
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• 1997

A continuous fermentation system employing immobilized cells of Zymomonas mobilis and Saccharomyces cerevisiae was studied for the mass production of ethanol. Ethanol production by cells immobilized with Ca-alginate was better than those by cells immobilized with K-carrageenan. Maximum ethanol production employing a continuous system by cells immobilized with Ca-alginate was 77.5 $g.l^{-1}h^{-1}$ at a dilution rate of 1.85 $h^{-1}$ with 82% conversion rate for Z. mobilis while that was 40.2 $g.l^{-1}h^{-1}$ at a dilution rate of 0.92 $h^{-1}$ with 85% conversion rate for S. cerevisiae. These results suggest that Ca-alginate is a better cell immobilization matrix than K-carrageenan and that immobilized cells of Z. mobilis are more efficient than S. cerevisiae for ethanol production.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1511-1522
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• 2022

Let H be a subgroup of $\mathbb{Z}^*_n$ (the multiplicative group of integers modulo n) and h₁, h₂, …, h_l distinct representatives of the cosets of H in $\mathbb{Z}^*_n$. We now define a polynomial J_n,H(x) to be $$J_{n,H}(x)=\prod^l_{j=1} \left( x-\sum_{h{\in}H} {\zeta}^{h_jh}_n\right)$$, where ${\zeta}_n=e^{\frac{2{\pi}i}{n}}$ is the nth primitive root of unity. Polynomials of such form generalize the nth cyclotomic polynomial $\Phi_n(x)={\prod}_{k{\in}\mathbb{Z}^*_n}(x-{\zeta}^k_n)$ as J_n,{1}(x) = Φ_n(x). While the nth cyclotomic polynomial Φ_n(x) is irreducible over ℚ, J_n,H(x) is not necessarily irreducible. In this paper, we determine the subgroups H for which J_n,H(x) is irreducible over ℚ.

• Proceedings of the KIEE Conference
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• 2006.07a
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• pp.145-146
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• 2006

The recent power systems are very complex and to model them completely is impractical for analysis of electromagnetic transient. Therefore areas outside the immediate area of interest must be represented by some form of Frequency Dependent Network Equivalent (FDNE). In this paper a method for developing Frequency Dependent Network Equivalent (FDNE) using Z-domain rational Function Fitting is presented and demonstrated. The FDNE is generated by Linearized Least Squares Fitting(LSF) of the frequency response of a Z-domain formulation. This Three-port FDNE have been applied to the test AC power system. The electromagnetic transient package PSCAD/EMTDC is used to assess the transient response of the Three-port FDNE developed under different condition. The study results have indicated the robustness and accuracy of Three-port FDNE for analisys of electromagnetic transient and harmonic assessment.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.791-804
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• 2006

This paper is concerned with a second-order iterated differential equation of the form $c_0x'(Z)+c_1x'(z)+c_2x(z)=x(az+bx(z))+h(z)$ with the distinctive feature that the argument of the unknown function depends on the state. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.537-545
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• 2005

The aim of this paper is to solve the open problem on product properties of digital covering maps raised from [5]. Namely, let us consider the digital images $X_1 {\subset}Z^{n_{0}}$ with $k_0-adjacency$, $Y_1{\subset}Z^{n_{1}}$ with $k_3-adjacency$, $X_2{\subset}Z^{n_{2}}$ with $k_2-adjacency$ and $Y_2{\subset}Z^{n_{3}}$ with $k_3-adjacency$. Then the reasonable $k_4-adjacency$ of the product image $X_1{\times}X_2$ is determined by the $k_0-$ and $k_2-adjacency$ and the suitable k_5-adjacency$ is assumed on $Y_1{\times}Y_2$ via the $k_1-$ and $k_3-adjacency$ [3] such that each of the projection maps is a digitally continuous map, e.g., $p_1\;:\;X_1{\times}X_2{\rightarrow}X_1$ is a digitally ($k_4,\;k_1$)-continuous map and so on. Let us assume $h_1\;:\;X_1{\rightarrow}Y_1$ to be a digital $(k_0, k_1)$-covering map and $h_2\;:\;X_2{\rightarrow}Y_2$ to be a digital $(k_2,\;k_3)$-covering map. Then we show that the product map $h_1{\times}h_2\;:\;X_1{\times}X_2{\rightarrow}Y_1{\times}Y_2$ need not be a digital $(k_4,k_5)$-covering map.

• Korean Journal of Food Science and Technology
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• v.40 no.5
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• pp.593-598
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• 2008

Differential display RT-PCR was used for screening the differentially expressed specific genes by Rhus verniciflua extract treatment to U937 cell, human leukemic monocyte. As a result, 19 clones differentially expressed were detected. Among the detected clones, one clone was confirmed to be over-expressed by R. verniciflua extract treatment in Northern blot analysis. Nucleotide sequence of the clone showed 100% homology with H2A histone family member Z gene. Therefore, it is concluded that the treatment of R. verniciflua extract to U937 cell specifically induces the expression of H2A.Z gene but its role should be elucidated by future works.

• Progress in Superconductivity
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• v.13 no.3
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• pp.178-183
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• 2012

Two $RuSr_2(EuCe)Cu_2O_z$ samples (as prepared and after $N_2$ treatment) have been investigated by thermogravimetric (TC) analysis, high-resolution x-ray powder diffraction and magnetization measurements. TG measurements which were carried out in $H_2/Ar$ atmosphere showed that the $N_2$ treatment of the as-prepared sample at $650^{\circ}C$ for 2h leads to a decrease in the oxygen content z by about 0.25. This oxygen depletion was accompanied by an increase in the magnetic transition temperature from 54.0 K to 114.9 K. This magnetic behavior is discussed in connection with the results of Rietveld analysis of the x-ray diffraction data which showed that the $N_2$ treatment resulted in both a significant increase in the rotation angle of the $RuO_6$ octahedra and a decrease in c-lattice parameter of the sample.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.569-576
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• 2007

Let $\cal{H}$ be a separable, infinite dimensional, complex Hilbert space. We call "an operator $\cal{T}$ acting on $\cal{H}$ has a star moment sequence supported on a set K" when there exist nonzero vectors u and v in $\cal{H}$ and a positive Borel measure ${\mu}$ such that <$T^{*j}T^ku$, v> = ${^\int\limits_{K}}\;{{\bar{z}}^j}\;{{\bar{z}}^k}\;d\mu$ for all j, $k\;\geq\;0$. We obtain a characterization to find a representing star moment measure and discuss some related properties.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.439-446
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• 2015

In this paper we consider the meromorphic function G(z) with a pole of order 1 at -a and analytic function F(z) with a zero -a of order 2 in $\mathbb{D}=\{z :{\mid}z{\mid}<1\}$, where -1 < a < 1. From these functions we obtain the regular simply-connected minimal surface $S=\{(u(z),\;{\nu}(z),\;H(z)):z{\in}\mathbb{D}\}$ in $E^3$ and the harmonic function $f=u+i{\nu}$ defined on $\mathbb{D}$, and then we investigate properties of the minimal surface S and the harmonic function f.