• 대한수학회지
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• 제36권4호
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• pp.787-811
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• 1999

Let M be the maximal ideal space of the Banach algebra $H^{\infty}$ of bounded analytic functions on the open unit disc $\triangle$. For a positive singular measure ${\mu}\;on\;{\partial\triangle},\;let\;{L_{+}}^1(\mu)$ be the set of measures v with $0\;{\leq}\;{\nu}\;{\ll}\;{\mu}\;and\;{{\psi}_{\nu}}$ the associated singular inner functions. Let $R(\mu)\;and\;R_0(\mu)$ be the union sets of $\{$\mid$\psiv$\mid$\;<\;1\}\;and\;\{$\mid${\psi}_{\nu}$\mid$\;<\;0\}\;in\;M\;{\setminus}\;{\triangle},\;{\nu}\;\in\;{L_{+}}^1(\mu)$, respectively. It is proved that if $S(\mu)\;=\;{\partial\triangle}$, where $S(\mu)$ is the closed support set of $\mu$, then $R(\mu)\;=\;R0(\mu)\;=\;M{\setminus}({\triangle}\;{\cup}\;M(L^{\infty}(\partial\triangle)))$ is generated by $H^{\infty}\;and\;\overline{\psi_{\nu}},\;{\nu}\;{\in}\;{L_1}^{+}(\mu)$. It is proved that %d{\theta}(S(\mu))\;=\;0$ if and only if there exists as Blaschke product b with zeros $\{Zn\}_n$ such that $R(\mu)\;{\subset}\;{$\mid$b$\mid$\;<\;1}\;and\;S(\mu)$ coincides with the set of cluster points of $\{Zn\}_n$. While, we proved that $\mu$ is a sum of finitely many point measure such that $R(\mu)\;{\subset}\;\{$\mid${\psi}_{\lambda}$\mid$\;<\;1}\;and\;S(\lambda)\;=\;S(\mu)$. Also it is studied conditions on \mu for which $R(\mu)\;=\;R0(\mu)$.

• 대한수학회지
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• 제51권6호
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• pp.1305-1319
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• 2014

A submodule N of a right R-module M is called coneat if for every simple right R-module S, any homomorphism $N{\rightarrow}S$ can be extended to a homomorphism $M{\rightarrow}S$. M is called coneat-flat if the kernel of any epimorphism $Y{\rightarrow}M{\rightarrow}0$ is coneat in Y. It is proven that (1) coneat submodules of any right R-module are coclosed if and only if R is right K-ring; (2) every right R-module is coneat-flat if and only if R is right V -ring; (3) coneat submodules of right injective modules are exactly the modules which have no maximal submodules if and only if R is right small ring. If R is commutative, then a module M is coneat-flat if and only if $M^+$ is m-injective. Every maximal left ideal of R is finitely generated if and only if every absolutely pure left R-module is m-injective. A commutative ring R is perfect if and only if every coneat-flat module is projective. We also study the rings over which coneat-flat and flat modules coincide.

• 상하수도학회지
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• 제19권6호
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• pp.720-727
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• 2005

This study was performed to advance nitrogen removal efficiency by employing an single biofilter packed with granular sulfur, which consists of nitrification occurring at upper part and denitrification at lower part of the reactor. Continuos nitrification/denitrification was carried out with different alkalinity sources, which were $NaHCO_3$ and $CaCO_3$(limestone). In the downflow nitrification/denitrification biofilter packed with granular sulfur, first, terms for nitrogen removal was decided. As results, nitrification and denitrification rate with NaHCO3 at 0.85 kg $NH_4^+-N/m^3{\cdot}d$ were accomplished $0.80kg\;N/m_3{\cdot}d$, $0.43kg\;N/m^3{\cdot}d$, respectively. In the sulfur/limestone packed downflow nitrification/denitrification biofilter, sulfur and limestone were mixed packed, preliminary test showed sulfur/limestone mixing ratio was 3:1 and that was ideal. In the result, nitrification and denitrification rate at $0.7kg\;NH_4^+-N/m^3{\cdot}d$ were accomplished$0.65kg\;N/m^3{\cdot}d$, $0.34kg\;N/m^3{\cdot}d$, respectively. In general, employing granular sulfur can be implemented for only denitrification, but this system can accomplish nitrification as well as denitrification in a single reactor even though low carbon concentration was present in influent limiting to nutrient removal process. This biofilter system of limestone and granular sulfur packed together can successfully apply for nutrient removal effectively.

• 한국자기학회지
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• 제5권5호
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• pp.366-371
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• 1995

High performance magnetic materials are characterized by the combination of outstanding magnetic properties and optimized microstructures, e.g., nanocrystalline composites of multilayers and small particle systems. The characteristic parameters of the hysteresis loops of these materials vary over more than a factor of $10^{6}$ with optimum values for the coercive field of several Tesla and permeabilities of $10^{6}$. Within the framework of the computational micromagnetism (nanomagnetism) using the finite element method the upper and lower bounds of the coercive field of different types of grain ensembles and multilayers have been determined. For the case of nanocrystalline composites the role of grain size, exchange and dipolar coupling between grains and the degree of grain alignment will be discusses in detail. It is shown that the largest coercivities are obtained for exchange decoupled grains, whereas remanence enhancing requires exchange coupled grains below 20 nm. For composite permanent magnets based on $Nd_{2}Fe_{14}B$ with an amount of ~ 50% soft $\alpha$-Fe-phase coercivities of ${\mu}_{0}H_{c}=0.75\;T$, a remanence of 1.5 T and an energy product of $400\;kJ/m^{3}$ is expected. In nanocrystalline systems the temperature dependence of the coercivity is well described by the relation ${\mu}_{0}H_{c}=(2\;K_{1}/M_{s}){\alpha}-N_{eff}{\mu}_{0}M_{s}$, where the microstructural parameters $\alpha$ and $N_{eff}$ take care of the short-range perturbations of the anisotropy and $N_{eff}$ is related to the long-range dipolar interactions. $N_{eff}$ is found to follow a logarithmic grain size size dependence ${\mu}_{0}H_{c}=(2\;K_{1}/M_{s}){\alpha}-N_{eff}(\beta1nD){\mu}_{0}M_{s}$. Several trends how to achieve the ideal situation $\alpha$->1 and $N_{eff}$->1->0 will be discussed.

• 산업경영시스템학회지
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• 제26권4호
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• pp.31-41
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• 2003

This paper deals with a cell formation problem for a set of m-machines and n-processing parts. Generally, a cell formation problem is known as NP-completeness. Hence the cell formation problem with multiple objectives is more difficult than single objective problem. The paper considers multiple objectives; minimize number of intercell movements, minimize intracell workload variation and minimize intercell workload variation. We propose a multiple objective genetic algorithms(MOGA) resolving the mentioned three objectives. The MOGA procedure adopted Pareto optimal solution for selection method for next generation and the concept of Euclidean distance from the ideal and negative ideal solution for fitness test of a individual. As we consider several weights, decision maker will be reflected his consideration by adjusting high weights for important objective. A numerical example is given for a comparative analysis with the results of other research.

• Korean Journal of Mathematics
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• 제26권2호
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• pp.175-189
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• 2018

In this paper, at first we generalize the notion of algebra over a field. A ${\Gamma}$-algebra is an algebraic structure consisting of a vector space V, a groupoid ${\Gamma}$ together with a map from $V{\times}{\Gamma}{\times}V$ to V. Then, on every associative ${\Gamma}$-algebra V and for every ${\alpha}{{\in}}{\Gamma}$ we construct an ${\alpha}$-Lie algebra. Also, we discuss some properties about ${\Gamma}$-Lie algebras when V and ${\Gamma}$ are the sets of $m{\times}n$ and $n{\times}m$ matrices over a field F respectively. Finally, we define the notions of ${\alpha}$-derivation, ${\alpha}$-representation, ${\alpha}$-nilpotency and prove Engel theorem in this case.

• Kyungpook Mathematical Journal
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• 제64권2호
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• pp.303-309
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• 2024

An imaginary bicyclic biquadratic number field K is a field of the form ${\mathbb{Q}}({\sqrt{-m}},{\sqrt{-n}})$ where m and n are squarefree positive integers. The ideal class number h_K of K is the order of the abelian group I_K/P_K, where I_K and P_K are the groups of fractional and principal fractional ideals in the ring of integers 𝒪_K of K, respectively. This provides a measure on how far is 𝒪_K from being a PID. We determine all imaginary bicyclic biquadratic number fields with class number 5. We show there are exactly 243 such fields.

• 대한화학회지
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• 제48권3호
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• pp.236-242
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• 2004

25$^{\circ}C$의 순수 물 및 n-부탄올 수용액에서 Dodecylpyridinium chloride(DPC)와 Cetyldimethylethylammonium bromide(CDEAB)의 혼합계면활성제가 나타내는 임계마이셀농도(CMC)와 반대이온결합상수(B)값을 DPC의 겉보기몰분율(${\alpha}_1$)에 따른 변화를 전도도법으로 측정하였다. 이와같이 측정한 CMC값에 비이상적 혼합마이셀화모델을 적용함으로써 여러 가지 열역학적 함수값(($X_i,\;{\gamma}_i,\;C_i,\;a^M_i,\;{\beta},\;and\;{\Delta}H_{mix})$들을 계산하고 분석하였다. 그리고 DPC/CDEAB 혼합계면활성제의 마이셀화에 미치는 n-부탄올의 효과를 조사하기 위하여 n-부탄올의 농도에 따른 열역학 함수값(CMC, B 및 ${\Delta}G_o\;^m$)의 변화를 측정하고 분석하였다.

• 대한수의학회지
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• 제32권4호
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• pp.543-553
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• 1992

Properties of unitary ATP-sensitive $K^+$ channels were studied using planar lipid bilayer technique. Vesicles were prepared from bullfrog (Rana catesbeiana) skeletal muscle. ATP-sensitive $K^+$ (K (ATP)) channels were identified by their unitary conductance and sensitivity to ATP. In the symmetrical solution containing 200mM KCI, 10mM Hepes, 1mM EGTA and pH 7.2, single K (ATP) channels showed a linear current-voltage relations with slight inward rectification. Slope conductance at reversal potential was $60.1{\pm}0.43$ pS(n=3)). Micromolar ATP reversibly inhibited the channel activity when applied to the cytoplasmic side. In the range of -50~＋50 mV, the channel activity was not voltage-dependent, but the channel gating within a burst was more frequent at negative voltage range. Varying the concentrations of external/internal KCl(mM) to 40/200, 200/200, 200/100 and 200/40 shifted reversal potentials to $-30.8{\pm}2.9$(n=3), $-1.1{\pm}2.7$(n=3), 10.5 and 30.6(mV), respecrivety. These reversal potentials were close to the expected values by the Nernst equation, indicating nearly ideal selectivity for $K^+$ over $Cl^-$. Under bi-ionic conditions of 200mM external test ions and 200mM internal $K^+$, the reversal potentials for each test ion/K pair were measured. The measured reversal potentials were used for the calculation of the releative permeability of alkali cations to $K^+$ ions using the Goldman-Hodgkin-Katz equation. The permeability sequence of 5 cations relative to $K^+$ was $K^+$(1), $Rb^+$(0.49), $Cs^+$(0.27), $Na^+$(0.027) and $Li^+$(0.021). This sequence was recognized as Eisenman's selectivity sequence IV. In addition, modelling the permeation of $K^+$ ion through ATP-sensitive $K^+$ channel revealed that a 3-barrier 2-site multiple occupancy model can reasonably predict the observed current-voltage relations.

• 대한수학회논문집
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• 제18권1호
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• pp.59-63
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• 2003

Let A be a $C^*$-algebra and $K_{A}$ its Pedersen's ideal. A is called a PCS-algebra if the multiplier $\Gamma(K_{A})\;of\;K_{A}$ is the multiplier M(A) of A. J. Mack [5]characterized PCS-algebras by weak compactness on the spectrum of A. We give a new simple proof of this Mack's result using the concept of semicontinuity and N. C. Phillips' description of $\Gamma(K_{A})$.