• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.573-582
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• 2009

This paper is indented to explain a dynamics on homotopies on the compact metric space, by the envelopes of homotopies. It generalizes the notion of not only the envelopes of maps in discrete geometry ([3]), but the envelopes of flows in continuous geometry ([5]). Certain distinctions among the homotopy geometry, the ow geometry and the discrete geometry will be illustrated. In particular, it is shown that any ${\omega}$-limit set, as well as any attractor, for an envelope of homotopies is an empty set (provided the homotopies that we treat are not trivial), whereas it is nonempty in general in discrete case.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.107-113
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• 1996

For continuous maps f of the circle to itself, we show that (1) the set of ${\omega}$-limit points is contained in the set of nonwandering points of $f^n$ for all $n{\geq}1$. (2) if the set of turning points of f is finite, then the set of accumulation points of non wandering set is contained in the set of non wandering points of $f^n$ for all $n{\geq}1$.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.5
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• pp.1086-1090
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• 2001

In this paper, a method deciding the permissible gains of the P and PT controllers for a retarded process under stable condition is proposed. For analysis, the controlled process is assumed to be first-order system with time delay. At first, the adjustable parameter sets causing stability limit are obtained based on the frequency domain condition which makes the roots of the characteristic equation locate on the imaginary axis. And the cut-in frequency ${\omega}_p$ to bring the parameter set to P control from PI control is derived is derived in terms of L and $T_m$ then ${\omega}_p$ is used to compute the maximum gain with stable condition. The results indicate that the permissible controller gains can be described by a unique if parameters L and $T_m$ are know.

• Coupled systems mechanics
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• v.6 no.3
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• pp.369-376
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• 2017

Intermolecular interaction energies and conformer geometries of the hydrogen bonded acrylamide dimers have been studied by using the second-order Møller-Plesset (MP2) perturbation theory and the density functional theory (DFT) with 17 density functionals. Dunning's correlation consistent basis sets (up to aug-cc-pVTZ) have been used to study the basis set effects. The DFT calculated interaction energies are compared to the reference energy data calculated by the MP2 method and the coupled cluster method at the complete basis set (CCSD(T)/CBS) limit in order to determine the relative performance of the studied density functionals. Overall, dispersion-energy-corrected density functionals outperform uncorrected ones. The ${\omega}B97XD$ density functional is particularly effective in terms of both accuracy and computational cost in estimating the reference energy values using small basis sets and is highly recommended for similar calculations for larger systems.