• 한국세라믹학회지
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• 제25권1호
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• pp.1-6
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• 1988

The IR edge absorption of the important pure components of ZrF4-based glasses, including two previously uncharacterized components(ZrF4 and AlF3), has been measured. Values of the glass IR edge absorption coefficients have been calculated from these results, assuming additivity, and are compared with experimental glass absorption coefficients. The calculated ${\alpha}$ values are about a factor of two lower than the experimental values for ZrF4-based glasses, and the ZrF4 makes the largest contribution to the calculated ${\alpha}$ value.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권1호
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• pp.49-58
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• 2019

In this paper, I prove the stability problem for a quadratic-cubic functional equation $$f(x+ky)-k^2f(x+y)-k^2f(x-y)+f(x-ky)+f(kx)-{\frac{k^3-3k^2+4}{2}}f(x)+{\frac{k^3-k^2}{2}}f(-x)=0$$ in modular spaces by applying the direct method.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권2호
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• pp.157-162
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• 1995

Let I be the interval, $S^1$ the circle and let X be a compact metric space. And let $C^{circ}(X,\;X)$ denote the set of continuous maps from X into itself. For any f$f\in\;C\circ(X,\;X),\;let\;P(f),\;R(f),\;\Gamma(f),\;\Lambda(f)\;and\;\Omega(f)$ denote the collection of the periodic points, recurrent points, ${\gamma}-limit{\;}points,{\;}{\omega}-limit$ points and nonwandering points, respectively.(omitted)

• 상하수도학회지
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• 제13권4호
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• pp.27-34
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• 1999

An experimental study on improvement of the paper-mill wastewater treatment using the pure oxygen activated sludge process was conducted. The effects of hydraulic retention time(HRT) and BOD loading on organic removal efficiency were investigated. The BOD removal efficiencies were above 90% under all examined HRTs except for HRT of 3 hours. The increase of HRT from 3 hours to 6 hours, and to 12 hours significantly improved BOD and COD removal efficiencies, respectively. However, additional increase of HRT did not affect organic removal efficiency. F/M ratio change at fixed HRT did not affect organic removal efficiency. However, F/M ratio investigated in this study(0.11~1.98kgBOD/kgMLVSS/day) was 5 times greater in maximum than that of conventional activated sludge process, which implies that pure oxygen activated sludge process can treat wastewater with high organic strength. Under the same HRT, the volumetric BOD loading change cause no effect on organic removal efficiency also.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권1호
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• pp.9-14
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• 2001

In some problems of abstract approximation theory the approximating set depends on some parameter p. In this paper, we make a set M(f) depends on the element f, $\phi$ and then best approximations are sought from a subset M(f) of M.

• 대한수학회보
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• 제56권2호
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• pp.439-450
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• 2019

Let R be a ring with unity. Given modules $M_R$ and $_RN$, $M_R$ is said to be absolutely $_RN$-pure if $M{\otimes}N{\rightarrow}L{\otimes}N$ is a monomorphism for every extension $L_R$ of $M_R$. For a module $M_R$, the subpurity domain of $M_R$ is defined to be the collection of all modules $_RN$ such that $M_R$ is absolutely $_RN$-pure. Clearly $M_R$ is absolutely $_RF$-pure for every flat module $_RF$, and that $M_R$ is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, $M_R$ is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. $R_R$ is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is $Pr{\ddot{u}}fer$ if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권4호
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• pp.383-396
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• 2012

In this paper, we investigate a fuzzy version of stability for the functional equation $$f(x+2y)-3f(x+y)+3f(x)-f(x-y)-3f(y)+3f(-y)=0$$ in the sense of M. Mirmostafaee and M. S. Moslehian.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권1호
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• pp.23-35
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• 2007

We investigate the modified Hyers-Ulam-Rassias stability for the following mixed type functional equation, i.e, cubic or quadratic type functional equation : 9f(x+y)-9f(x-y)+f(6y)=3f(x+3y)-3f(x-3y)+9f(2y).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.389-401
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• 2015

We will show the general solution of the functional equation f(x + ay) + f(x − ay) + 2(a² − 1)f(x) = a²f(x + y) + a²f(x − y) + 2a²(a² − 1)f(y) and investigate the stability of quartic Lie *-derivations associated with the given functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권2호
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• pp.167-178
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• 2009

In this paper, we obtain the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation f(x+y, z)-f(x, z)-f(y, z)=0, $$2f\;x,\;{\frac{y+z}{2}}-f(x,\;y)-f(x,\;z)=0$$ in the spirit of P. $G{\breve{a}}vruta$.