• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.115-126
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• 1998

We study the optimal control problem of system governed by retarded functional differential $$ x'(t) = A_0 x(t) + A_1 x(t - h) + \\ulcorner\ulcorner\ulcorner_{-h}^{0} a(s)A_2 x(t + s)ds + B_0 u(t) $$ in Hilbert space H. After the fundamental facts of retarded system and the description of condition so called a weak backward uniqueness property are established, the technically important maximal principle and the bang-bang principle are given. its corresponding linear system.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1019-1036
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• 2016

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.213-230
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• 2002

We deal with the approximate controllability for semilinear systems with time delay in a Hilbert space. First, we show the existence and uniqueness of solutions of the given systems with the mere general Lipschitz continuity of nonlinear operator f from $R\;\times\;V$ to H. Thereafter, it is shown that the equivalence between the reachable set of the semilinear system and that of its corresponding linear system. Finally, we make a practical application of the conditions to the system with only discrete delay.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.479-497
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• 2018

This paper deals with an optimal control on semilinear stochastic functional differential equations with Poisson jumps in a Hilbert space. The existence of an optimal control is derived by the solution of proposed system which satisfies weakly sequentially compactness. Also the stochastic maximum principle for the optimal control is established by using spike variation technique of optimal control with a convex control domain in Hilbert space. Finally, an application of retarded type stochastic Burgers equation is given to illustrate the theory.

• Journal of the Korean Ceramic Society
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• v.21 no.2
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• pp.143-148
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• 1984

In this study we mainly dealt with the effects of organic retarder(calcium lignosulfate) on the early hydration process of clinker minerals. From a consideration of the hydration process of tricalcium silicate $(C_3S)$ tricalcium silicate $(C_3S)$-tricalcium aluminate $(C_3A)$ tricalcium silicate $(C_3S)$-tetracalcium aluminof-errite $(C_4AF)$ systems with calcium lignosulfate the following results were obtained. 1. when 0.25wt% of CLS was added to $C_3S$ the hydration process was progressed normally but adding of 0.5wt% its hydration was greatly retarded. 2. The hydration of $C_3S$-$C_3A$ system was progressed normally up to 0.5wt% but by adding gypsum its hydration was retarded slightly. 3. The hydration of $C_3S$-$C_4AF$ system was greatly retarded even with 0.25wt% of CLS but by adding gypsum its hydration process was recovered normally.

• 한국정보교육학회:학술대회논문집
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• 2010.08a
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• pp.143-149
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• 2010

Although importance of music education for the mentally retarded children is realized, it is hard to improve study effects for those children with the existing music education methods due to cognitive disorders of the children. In the paper, we propose a system to improve music cognition ability of the mentally retarded children. The system is designed based on the existing MMCP theory. Our system has the following characteristics. First, the system can improve cognitive, physical, social and emotional development as well as development of music cognition ability. Second, the individualized music education is possible for the children. Third, more active and interactive education is possible.

• Korean Chemical Engineering Research
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• v.52 no.1
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• pp.68-74
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• 2014

In the spiral wound module of the pressure-retarded osmosis (PRO) system for the salinity gradient power generation, effects of the inlet pressure differences between feed-channel and draw-channel were studied. Fluxes of water and solute through membrane and power were estimated. The water flux through membrane decreased along the x-direction and increased along the y-direction with the increase of inlet pressure differences between two channels. On the other hand, the solute flux through membrane showed the opposite trend. The concentration of flow in the feed-channel increased a lot along the y-direction and that in the draw-channel decreased along the x-direction. In our system, for the inlet pressure differences of 1~11 atm, the flow rate in the feed-channel decreased about 8~13% and that in the draw-channel increased by the same amount. The power density increased and then decreased with the increasing inlet pressure difference.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.81-97
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• 1999

This paper deals with the time optimal control problem for the retarded semilinear system by using the construction of fundamental solution in case where the principal operators are unbounded operators.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.317-332
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• 1999

In this paper we deal with the optimal control problem for the semilinear functional differential equations with unbounded delays. We will also establish the regularity for solutions of the given system. By using the penalty function method we derive the optimal conditions for optimality of an admissible state-control pairs.

• East Asian mathematical journal
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• v.19 no.1
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• pp.133-150
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• 2003

This paper will show that the relation (1.1) $$L^1({\Omega}){\subset}C_0(\bar{\Omega}){\subset}H_{p,q}$$ if 1/p'-1/n(1-2/q')<0 where p'=p/(p-1) and q'=q/(q-1) where $H_{p.q}=(W^{1,p}_0,W^{-1,p})_{1/q,q}$. We also intend to investigate the control problems for the retarded systems with $L^1(\Omega)$-valued controller in $H_{p,q}$.