• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1329-1352
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• 2020

In this paper we consider a class of nonlinear evolution equations on infinite dimensional Banach spaces driven by vector measures. We prove existence and uniqueness of solutions and continuous dependence of solutions on the control measures. Using these results we prove existence of optimal controls for Bolza problems. Based on this result we present necessary conditions of optimality.

• Journal of Korean Institute of Industrial Engineers
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• v.4 no.2
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• pp.107-118
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• 1978

The paper illustrates a possible application of control theory to an economic growth system. Simultaneous nonlinear system of differential equations has been modeled which is different from the traditional formulation, based on the theory of economic growth for a two-sector (dual) economy. Necessary and sufficient conditions for the existence of the optimal control are derived directly from the Hamiltonian, and the optimal controls are also obtained by solving simultaneous equations. Obtaining the trajectories of the optimal control and state variables, however, should rely on the numerical procedures. Empirical application has been conducted for the case of the Korean economy as an illustration.

• The Journal of Society for e-Business Studies
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• v.22 no.2
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• pp.99-121
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• 2017

Standard makers in both private and public sectors have been increasingly mandating security standards upon organizations to protect organizational digital assets. A major issue in security standardization is that standards often cannot regulate all possible security efforts by the standard maker because some efforts are unverifiable by nature. This paper studies from an analytical perspective how a standard maker should design the standard using a verifiable security control in the presence of another related unverifiable one. We compare it with two benchmark standards; $na{\ddot{i}}ve$-standard which refers to the standard maker who ignores the existence of the unverifiable control, and complete-information standard which refers to the maker sets standards on both controls. Optimal standard and benchmark standard depend critically on how the two controls are configured. Under parallel configuration, the existence of the unverifiable control induces the policy maker to set a higher standard (the complete-information standard is optimal); under serial configuration, a lower standard is applied (neither benchmark works). Under best-shot configuration and if the verifiable control is more cost-efficient, the existence of the unverifiable control has no impact on the optimal standard (the $na{\ddot{i}}ve$ standard is optimal).

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.757-769
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• 2008

This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

• Korean journal of food and cookery science
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• v.24 no.3
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• pp.358-366
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• 2008

The antioxidant properties of red ginseng extracts prepared under different extraction conditions were evaluated by a variety of antioxidant assays, including $DPPH^{\cdot}$ radical scavenging, $ABTS^{+\cdot}$ radical scavenging, superoxide anion scavenging, nitrite scavenging and reducing power activities. The contents of total phenolic compounds and flavonoids were also determined. The various antioxidant activities were compared to positive controls such as Trolox, tannic acid and ascorbic acid. The antioxidant activities of all of the extracts were shown to be the highest in the ethanol extract. The antioxidant activities of the red ginseng powder were the lowest among the samples. The amounts of total phenolic compounds and flavonoids were at a maximum in the ethanol extract. Correlation analysis demonstrated the existence of a linear relationship between free radical scavenging activities and the phenolic compounds contents of extracts. The antioxidant activity of yogurt was increased as the result of the addition of red ginseng extract. The quality characteristics of the yogurt to which red ginseng extract was added were similar to those of yogurt without red ginseng extract. The overall sensory score and color of yogurt made from 0.5% red ginseng was the best of the tested yogurts. In accordance with the antioxidant activity and quality characteristics, the optimal concentration of red ginseng extract was approximately 0.5%.