• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.25-28
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• 2002

In this Paper, we find the controllability conditions of nonlinear fuzzy differential equations with nonlocal initial condition in by using the concept of fuzzy number of dimension 2 whose values are normal convex upper semicontinuous and compactly supported surface in $R^{2}$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.288-292
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• 2006

Many authors have studied several concepts of fuzzy systems. Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. Recently, Park, Park and Kwun (2006) find the sufficient condition of nonlocal controllability for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. In this paper, we study the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in $E_{N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_{N}$.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.550-556
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• 2007

In this paper, we introduce the concepts of fuzzy (r, s)-semi-preopen sets and fuzzy (r, s)-semi-precontinuous mappings on intuitionistic fuzzy topological spaces in ${\check{S}}ostak's$ sense. The relations among fuzzy (r, s)-semicontinuous, fuzzy (r, s)-precontinuous, and fuzzy (r, s)-semi-precontinuous mappings we discussed. The concepts of fuzzy (r, s)-semi-preinterior, fuzzy (r, s)-semi-preclosure, fuzzy (r, s)-semi-preneighborhood, and fuzzy (r, s)-quasi-semi-preneighborhood are given. Using these concepts, the characterization for the fuzzy (r, s)-semi-precontinuous mapping is obtained. Also, we introduce the notions of fuzzy (r, s)-semi-preopen and fuzzy (r, s)-semi-preclosed mappings on intuitionistic fuzzy topological spaces in ${\check{S}}ostak's$ sense, and then we investigate some of their characteristic properties.

• Biotechnology and Bioprocess Engineering:BBE
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• v.7 no.6
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• pp.347-351
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• 2002

Benzoate produced from the degradative pathways of various aromatic chemicals is generally recognized as a pollutant compound. However, various bacterial strains isolated as benzoate degraders have exhibited certain limits to their functions, including a loss of viability and degradability when cultivated in a broth medium for a longer time. Accordingly, immobilization techniques have been utilized to overcome such problems, and the current study examined the use of alginate and polyurethane for immobilizing Klebsiella oxytoca C302 to extend its viability and degradability of benzoate. The organism was well encapsulated by both matrices and the immobilized cells showed a high stability as regards their viability and degradability of 2 mM benzoate in a MM2 broth medium during cultivation for longer than 60 h in a semicontinuous batch system.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.11a
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• pp.275-278
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• 2006

In this paper. we study the controllability for the impulsive semilinear fuzzy integrodifferential equations with nonlocal condition in $E_{N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_{N}$.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.5
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• pp.621-625
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• 2005

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

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.749-780
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• 2021

In this paper, we give the notion of M(., .)-𝜂-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. As an application, we introduce and investigate a new system of variational-like inclusions in Banach spaces. By means of M(., .)-𝜂-proximal mapping method, we give the existence of solution for the system of variational inclusions. Further, propose an iterative algorithm for finding the approximate solution of this class of variational inclusions. Furthermore, we discuss the convergence and stability analysis of the iterative algorithm. The results presented in this paper may be further expolited to solve some more important classes of problems in this direction.

• Biotechnology and Bioprocess Engineering:BBE
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• v.11 no.4
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• pp.306-312
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• 2006

Two culture modes, continuous and semi-continuous, of the decolorization fungus, Geotrichum candidum Dec 1, were compared to obtain a high treatment efficiency of molasses decolorization and a large productivity of peroxidase (DyP) to simultaneously decolorize dyes and molasses. The continuous culture of G. candidum Dec 1 using a 5-I jar-fermentor showed high DyP activity at a low dilution ratio of $0.005h^{-1}$, and decolorization ratio of molasses of 80% was obtained concomitantly. Therefore, a semi-continuous culture was performed by repeated refill and draw. In this mode, approximately 1.5 liters of the culture broth was replaced per cycle when the decolorization ratio of molasses was near 80%. The molasses medium (1.0 liter per day) was treated and the peroxidase productiveity in the drawn culture broth was 26.6U/day, whereas the peroxidase productiveity was 17.9U/day in the continuous culture with a dilution rate of $0.005h^{-1}$. The semi-continuous treatment system was an efficient decolorization method for the strain, G. candidum Dec 1.

• Journal of Microbiology and Biotechnology
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• v.20 no.7
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• pp.1086-1091
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• 2010

This study explored the use of gellan gum as an immobilization matrix for the production of cyclosporin A (CyA) by immobilized spores and mycelia of Tolypocladium inflatum MTCC 557. Different carriers, such as gellan gum, sodium alginate, celite beads, and silica, were tested as immobilization carriers, along with the role of the carrier concentration, biomass weight, number of spore-inoculated beads, and repeated utilization of the immobilized fungus. The maximum CyA production was 274 mg/l when using gellan gum [1% (w/v)], and a mycelial weight of 7.5% (w/v) supported the maximum production of CyA. Additionally, the addition of a combination of $_L$-valine (6 g/l) and $_L$-leucine (5 g/l) after 48 h of fermentation produced 1,338 mg/l of CyA when using gellan gum. The immobilized mycelia beads were found to remain stable for four repetitive cycles, indicating their potential for semicontinuous CyA production.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.175-178
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• 2005

In the present paper, we observe a relation between fuzzy norms and induced crisp norms on a linear space. We first prove that if $\rho_1,\;\rho_2$ are equivalent fuzzy norms on a linear space, then for every $\varepsilon\in(0.1)$, the induced crisp norms $P_\varepsilon^1,\;and\;P_\varepsilon^2$, respectively are equivalent. Since the converse does not hold, we prove it under some strict conditions. And consider the following theorem proved in [8]: Let $\rho$ be a lower semicontinuous fuzzy norm on a normed linear space X, and have the bounded support. Then $\rho$ is equivalent to the fuzzy norm $\chi_B$ where B is the closed unit ball of X. The lower semi-continuity of $\rho$ is an essential condition which guarantees the continuity of $P_\varepsilon$, where 0 < e < 1. As the last result, we prove that : if $\rho$ is a fuzzy norm on a finite dimensional vector space, then $\rho$ is equivalent to $\chi_B$ if and only if the support of $\rho$ is bounded.