• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.77-84
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• 2021

Let f : [0, 1] → [0, 1] be a multimodal map with positive topological entropy. The dynamics of the renormalization operator for multimodal maps have been investigated by Daniel Smania. It is proved that the measure of maximal entropy for a specific category of Cr interval maps is unique.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.377-384
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• 2015

It is well known that the entropy map is upper semi-continuous for expansive homeomorphisms on a compact metric space. Recently, Morales [3] introduced the notion of measure expansiveness which is general than that of expansiveness. In this paper, we prove that the entropy map is upper semi-continuous for measure expansive homeomorphisms.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1561-1597
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• 2019

In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets. NAIFSs differ from the usual (autonomous) iterated function systems, they are given [32] by a sequence of collections of continuous maps on a compact topological space, where maps are allowed to vary between iterations. Several basic properties of topological pressure and topological entropy of NAIFSs are provided. Especially, we generalize the classical Bowen's result to NAIFSs ensures that the topological entropy is concentrated on the set of nonwandering points. Then, we define the notion of specification property, under which, the NAIFSs have positive topological entropy and all points are entropy points. In particular, each NAIFS with the specification property is topologically chaotic. Additionally, the ${\ast}$-expansive property for NAIFSs is introduced. We will prove that the topological pressure of any continuous potential can be computed as a limit at a definite size scale whenever the NAIFS satisfies the ${\ast}$-expansive property. Finally, we study the NAIFSs induced by expanding maps. We prove that these NAIFSs having the specification and ${\ast}$-expansive properties.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.373-382
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• 2006

In this paper, we prove that the topological entropy of a sequence of equi-continuous monotone maps $f_{1,\infty}={f_i}\;\infty\limits_{i=1}$on circles is $h(f_{1,\infty})={\frac{lim\;sup}{n{\rightarrow}\infty}}\;\frac 1 n \;log\;{\prod}\limits_{i=1}^n|deg\;f_i|$. As applications, we give the estimation of the entropies for some skew products on annular and torus. We also show that a diffeomorphism f on a smooth 2-dimensional closed manifold and its extension on the unit tangent bundle have the same entropy.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.21-29
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• 2017

We review a partial trace alternatively defined by the composition of positive linear maps, and see how the partial trace acts on the matrix geometric means. We also study the quantum Tsallis relative entropy under partial trace related with the fidelity.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1157-1175
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• 2018

For a switched system with constraint on switching sequences, which is also called a subshift action, on a metric space not necessarily compact, two kinds of topological entropies, average topological entropy and maximal topological entropy, are introduced. Then we give some properties of those topological entropies and estimate the bounds of them for some special systems, such as subshift actions generated by finite smooth maps on p-dimensional Riemannian manifold and by a family of surjective endomorphisms on a compact metrizable group. In particular, for linear switched systems on ${\mathbb{R}}^p$, we obtain a better upper bound, by joint spectral radius, which is sharper than that by Wang et al. in [42,43].

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.165-185
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• 2012

In this paper, the topological entropy and measure-theoretic entropy for nonautonomous dynamical systems are studied. Some properties of these entropies are given and the relation between them is discussed. Moreover, the bounds of them for several particular nonautonomous systems, such as affine transformations on metrizable groups (especially on the torus) and smooth maps on Riemannian manifolds, are obtained.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.2
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• pp.131-139
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• 2008

This paper presents a new saliency map which is constructed by providing dynamic weights on individual features in an input image to search ROI(Region Of Interest) or FOA(Focus Of Attention). To construct a saliency map on there is no a priori information, three feature-maps are constructed first which emphasize orientation, color, and intensity of individual pixels, respectively. From feature-maps, conspicuity maps are generated by using the It's algorithm and their information quantities are measured in terms of entropy. Final saliency map is constructed by summing the conspicuity maps weighted with their individual entropies. The prominency of the proposed algorithm has been proved by showing that the ROIs detected by the proposed algorithm in ten different images are similar with those selected by one-hundred person's naked eyes.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.152-152
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• 2021

The importance of groundwater has long been recognized, but the ground water potential to become contaminated as a result of human activities has only been recognized in recently. Before 1980 it was thought that soils served as filters, preventing harmful substances deposited at the surface from migrating into groundwater. Today it is known that soils have a finite capacity to protect groundwater. It can be contaminated from divers sources. Therefore, Assessment of aquifer vulnerability to pollution is essential for the protection and management of groundwater and land use planning. In this study, we used DRASTIC and AVI for groundwater vulnerability to contamination assessment. the different methods were applied to the southern coastal sedimentary basin of Benin and DRASTIC method was modified in two different steps. First, we modified DRASTIC by adding land use parameter to include the actual pollution sources (DRASTIC_LcLu) and second, classic DRASTIC weights was modified using Shannon's entropy (Entropy weight DRASTIC). The reliability of the applied approaches was verified using nitrate (NO3^-) concentration and by comparing the overall vulnerability maps to the previous researches in the study area and in the world. The results from validation showed that the addition of landcover/land use parameter to the classic DRASTIC helps to improve the method for better definition of the vulnerable areas in the basin and also, the weight modification using entropy improved better the method because Entropy weight DRASTIC_LcLu showed the highest correlation with nitrate concentration in the study basin. In summary the weight modification using entropy approach reduced the uncertainty of the human subjectivity in assigning weights and ratings in the standard DRASTIC.

• Journal of Digital Convergence
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• v.10 no.3
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• pp.173-178
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• 2012

In this paper, a new saliency map generation method is discussed which extracts objects effectively using extracted Salient Region. Feature map is constructed first using four features of edge, hue of HSV color model, focus and entropy and then conspicuity map is generated from Center Surround Differences using the feature map. Final saliency map is constructed by the combination of conspicuity maps. Saliency map generated using this procedure is compared to the conventional technique and confirmed that new technique has better results.