• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1125-1140
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• 2018

Let A be a normed space, ${\mathcal{B}}(A)$ the algebra of all bounded operators on A, and V a family of strongly upper semicontinuous functions from a Hausdorff completely regular space X into ${\mathcal{B}}(A)$. In this paper, we investigate some properties of the weighted spaces CV (X, A) of all A-valued continuous functions f on X such that the mapping $x{\mapsto}v(x)(f(x))$ is bounded on X, for every $v{\in}V$, endowed with the topology generated by the seminorms ${\parallel}f{\parallel}v={\sup}\{{\parallel}v(x)(f(x)){\parallel},\;x{\in}X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.242-246
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• 2010

It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.34-40
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• 2007

Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equations with nonlocal initial condition. Park et al. (2006) found the sufficient condition of this system. Recently, Kwun et al. (2006) proved the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal initial conditions and forcing term with memory in $E_N$. In this paper, we study the controllability for this system by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.215-223
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• 2013

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

• Journal of Microbiology and Biotechnology
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• v.19 no.1
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• pp.93-98
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• 2009

The thermophilic aerobic digestion (TAD) process is recognized as an effective method for rapid waste activated sludge (WAS) degradation and the deactivation of pathogenic microorganisms. Yet, high energy costs due to heating and aeration have limited the commercialization of economical TAD processes. Previous research on autothermal thermophilic aerobic digestion (ATAD) has already reduced the heating cost. However, only a few studies have focused on reducing the aeration cost. Therefore, this study applied a two-step aeration control strategy to a fill-and-draw mode semicontinuous TAD process. The NADH-dependent fluorescence was monitored throughout the TAD experiment, and the aeration rate shifted according to the fluorescence intensity. As a result, the simple two-step aeration control operation achieved a 20.3% reduction in the total aeration, while maintaining an effective and stable operation. It is also expected that more savings can be achieved with a further reduction of the lower aeration rate or multisegmentation of the aeration rate.

• Proceedings of the Korea Technical Association of the Pulp and Paper Industry Conference
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• 2003.04a
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• pp.180-187
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• 2003

The lignin-degrading fungus Trichophyton sp. LKY-7 was immobilized in ca-alginate beads for laccase production and PCP remediation. The immobilized Trichopphyton sp. LKY-7 enabled the repeated use of this fungus for laccase production and produced high amount of laccase throughout 5 cycles incubation. As a laccase inducer oak wood meal(Quercus variabilis) seemed to be effective laccase inducer for Trichophyton sp. LKY-7, and the optimum addition amount was 1%(W/W) in glucose-peptone medium. Biotransformation of pentachlorophenol by immobilized Trichophyton sp. LKY-7 reached an efficency of up to 90% without toxic inhibition. Immobilized Trichophyton sp. LKY-7 might thus be applicable for semicontinuous laccase production and bioremediation to serve inoculum for reactor system.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.263-271
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• 2012

We introduce the concept of fuzzy $r$-minimal ${\beta}$-open set on a fuzzy minimal space and basic some properties. We also introduce the concept of fuzzy $r-M$ ${\beta}$-continuous mapping which is a generalization of fuzzy $r-M$ continuous mapping and fuzzy $r-M$ semicontinuous mapping, and investigate characterization for the continuity.

• Journal of the Korean Applied Science and Technology
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• v.9 no.1
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• pp.31-40
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• 1992

This study is on the biodegradability of the activated sludge, which used to biodegrade Linear Alkylbenzene Sulfonate(LAS), synthetic detergents and sufactants. The activated sludge in waste water treatment plant is used to the test of biodegradation of anionic surfactants and nonionic surfactants, but it have the periodic change of the biological propety to the lapse of the time. For the puropse of controlling and adjusting of the activated sludge in biodegradation test, we collected microorganisms from the sewage plant and the soil, and then, made the activated sludge in semicontinuous aeration chamber. From determined biodegradation data, and the degree of biodegradability to the LAS, we confirmd the standardized synthetic activated sludge which have more stable biodegradability than the sewage activated sludge. In continuous biodegradation test, LAS(dodecene-1) was biodegraded more than 99%, In 7days by the standardized activated sludge.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.858-863
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• 2010

In this paper, we study the asymptotic behavior of solutions for the delay semilinear fuzzy integrodifferential systems on $E^1_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E^1_N$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.1
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• pp.15-20
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• 2006

In this paper we study the exact controllability for the nonlinear fuzzy control system with nonlocal initial condition in $E_N^n$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in $R^n$. $E_N^n$ be the set of all fuzzy numbers in $R^n$ with edges having bases parallel to axis $X_1,X_2,\;,X_n$.