• Communications of the Korean Mathematical Society
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• v.30 no.1
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• pp.23-34
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• 2015

We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets.

• International Journal of Control, Automation, and Systems
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• v.6 no.3
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• pp.306-319
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• 2008

Reaching fault tolerance in technological systems requires to detect malfunctions. This paper presents a diagnostic method that is robust with respect to unknown-but-bounded uncertainties of the dynamical model and the measurements. By using models of the faultless and the faulty behaviours, a state-set observer computes polyhedral sets from which the consistency of the models with the interval measurements is determined. The diagnostic result is proven to be complete, i.e., the set of faults obtained by the diagnostic algorithm includes the actual fault. The algorithm is illustrated by an application example.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.3
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• pp.723-736
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• 2014

Glass Fiber Reinforced Plastic (GFRP) structures are primarily manufactured using hand lay-up or vacuum infusion techniques, which are cost-effective for the construction of marine vessels. This paper aims to investigate the mechanical properties and failure mechanisms of the hybrid GFRP composites, formed by applying the hand lay-up processed exterior and the vacuum infusion processed interior layups, providing benefits for structural performance and ease of manufacturing. The hybrid GFRP composites contain one, two, and three vacuum infusion processed layer sets with consistent sets of hand lay-up processed layers. Mechanical properties assessed in this study include tensile, compressive and in-plane shear properties. Hybrid composites with three sets of vacuum infusion layers showed the highest tensile mechanical properties while those with two sets had the highest mechanical properties in compression. The batch homogeneity, for the GFRP fabrication processes, is evaluated using the experimentally obtained mechanical properties.

• Journal of the Korean Mathematical Society
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• v.11 no.1
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• pp.49-51
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• 1974

• Journal of the Korean Mathematical Society
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• v.11 no.1
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• pp.7-17
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• 1974

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.363-379
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• 2014

In this paper, introducing various separation axioms on a bi-GTS, it has been observed that such separation axioms actually unify the well-known separation axioms on topological spaces. Several characterizations of such separation properties of a bi-GTS are established in terms of ${\gamma}_{{\mu}_i,{\mu}_j}$-closure operator, generalized cluster sets of functions and graph of functions.

• Kyungpook Mathematical Journal
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• v.18 no.1
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• pp.61-69
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• 1978

• International Journal of Control, Automation, and Systems
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• v.3 no.3
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• pp.502-507
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• 2005

The dual-mode strategy has been adopted in many constrained MPC (Model Predictive Control) methods. The size of stabilizable regions of states of MPC methods depends on the size of underlying feasible and positively invariant sets and the number of control moves. The results, however, may perhaps be conservative because the definition of positive invariance does not allow temporal departure of states from the set. In this paper, a concept of periodic invariance is introduced in which states are allowed to leave a set temporarily but return into the set in finite time steps. The periodic invariance can be defined with respect to sets of different state feedback gains. These facts make it possible for the periodically invariant sets to be considerably larger than ordinary invariant sets. The periodic invariance can be defined for systems with polyhedral model uncertainties. We derive a MPC method based on these periodically invariant sets. Some numerical examples are given to show that the use of periodic invariance yields considerably larger stabilizable sets than the case of using ordinary invariance.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.91-95
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• 1988

The nature of a H-set in a Hausdorff space is not well understood. In this note it is shown that if X is a countable union of nowhere dense compact sets, then X is not H-embeddable in any Hausdorff space. An example is given to show that there exists a non-Urysohn, non-H-closed space X such that each H-set of X is compact.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.309-319
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• 1997

We introduce $R^i$-sets and give various relations between $R^i$-sets and prove that the hyperspace of a metric continuum containing any one of the $R^i$-set also contains $R^i$ and hence is not contractible.