• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.59-64
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• 2011

In this paper, we show that every $C^1$-robustly positively expansive map is expanding.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.481-506
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• 2022

This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties of these dynamical systems. We show that h-shadowing, limit shadowing and s-limit shadowing properties are conjugacy invariant. Also, we investigate the relationships between these notions of shadowing for time varying maps and examine the role that expansivity plays in shadowing properties of such dynamical systems. Specially, we prove some results linking s-limit shadowing property to limit shadowing property, and h-shadowing property to s-limit shadowing and limit shadowing properties. Moreover, under the assumption of expansivity, we show that the shadowing property implies the h-shadowing, s-limit shadowing and limit shadowing properties. Finally, it is proved that the uniformly contracting and uniformly expanding time varying maps exhibit the shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.569-581
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• 2020

In this paper, we introduce the new general concept of usual expansiveness which is called "positively weak measure expansiveness" and study the basic properties of positively weak measure expansive C¹-differentiable maps on a compact smooth manifold M. And we prove that the following theorems. (1) Let 𝓟𝓦𝓔 be the set of all positively weak measure expansive differentiable maps of M. Denote by int(𝓟𝓦𝓔) is a C¹-interior of 𝓟𝓦𝓔. f ∈ int(𝓟𝓦𝓔) if and only if f is expanding. (2) For C¹-generic f ∈ C¹ (M), f is positively weak measure-expansive if and only if f is expanding.

• Journal of information and communication convergence engineering
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• v.17 no.4
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• pp.227-233
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• 2019

In long-haul optical communication system consisting of standard single-mode fiber spans and fiber amplifiers, such as the erbium-doped fiber amplifier, performance is deteriorated by signal distortion due to chromatic dispersion and nonlinearity of the fiber. A combination of dispersion management and optical phase conjugation is an effective technique to compensate for the distortion. In an optical link configured by this combination, a dispersion map mainly affects the compensation of the distorted optical signals. This paper proposes new dispersion maps configured by the decaying or expanding distribution of residual dispersion per span (RDPS) in a dispersion-managed link combined with a midway optical phase conjugator. The effect of the proposed dispersion maps on the compensation for distorted 24 channel × 40 Gbps wavelength-division multiplexed signals was assessed through numerical simulation. It was confirmed that all the proposed dispersion maps are most appropriate for the compensation and, furthermore, for the flexibility of link configuration than conventional links.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.883-914
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• 2001

We present a survey of research results obtained for infra-nilmanifolds, their fundamental groups and some of their generalizations. This is presented from two different approaches and covers achievements obtained during the past four decades and showing a remarkable amount of mathematical interdisciplinarity. We go more in depth concerning the existence and construction of polynomial structures for these manifolds and groups, a direction where significant progress was made in the past few years. The bounded-degree polynomial structures developed by the authors triggered a number of challenging open problems. Also, their study already has lead to some interesting results concerning e.g. Anosov diffeomorphisms and expanding maps.

• Proceedings of the KSRS Conference
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• 1998.09a
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• pp.331-341
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• 1998

With high resolution capability, satellite images are expanding their roles from earth resource monitorings to map production. Until now, maps are produced from airborne photos, but as large as at 1:2,400 scale, low cost satellite ortho images will replace the airborne photos. However, there has been no standard for map productions with satellite images. In this paper, we study the process of map productions with the satellite images of SPOT, IRS-lC, KOMPSAT, the positional accuracy of map features extracted from the satellite images, and the relationship between the image resolution and the map scale.

• 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.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.96-101
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• 2007

A new metallic sandwich panel with a quasi-Kagome truss core subjected to bending load has been analyzed. First, equations of the failure loads corresponding to the eight failure modes are presented. Then, non-dimensional forms of the equations are derived as functions of three geometric variables, one material parameter (yield strain), one load index and one weight index. Failure maps are presented for a given weight index. By using the dimensionless forms of equations as the design constraints, two kinds of optimization are performed. One is based on the weight, that is, the objective function, namely, the dimensionless load is to be maximized for a given weight. Another is based on the load, that is, the dimensionless weight is to be minimized for a given load. The results of the two optimization processes are found to agree each other. The optimized geometric variables are derived as a function of given weights or failure loads. The performance of the quasi-Kagome truss as the core of a sandwich panel is evaluated by comparison with those of honeycomb cored and octet truss cored panels

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.9
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• pp.943-950
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• 2007

A new metallic sandwich panel with a quasi-Kagome truss core subjected to bending load has been analyzed. First, equations of the failure loads corresponding to the eight failure modes are presented. Then, non-dimensional forms of the equations are derived as functions of three geometric variables, one material parameter (yield strain), one load index and one weight index. Failure maps are presented for a given weight index. By using the dimensionless forms of equations as the design constraints, two kinds of optimization are performed. One is based on the weight, that is, the objective function, namely, the dimensionless load is to be maximized for a given weight. Another is based on the load, that is, the dimensionless weight is to be minimized for a given load. The results of the two optimization processes are found to agree each other. The optimized geometric variables are derived as a function of given weights or failure loads. The performance of the quasi-Kagome truss as the core of a sandwich panel is evaluated by comparison with those of honeycomb cored and octet truss cored panels.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2005.10a
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• pp.26-31
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• 2005

In national prospective, the needs to develop water resources has been increased due to water shortage from diverse use of water resources in agricultural areas. Existing agricultural water demand, which has mainly been limited to the use of farming, are now expanding to diverse water uses such as supporting daily lives, diluting environmental pollution as well as industrial use for agricultural complex currently under construction in agricultural region. In this situation, for the sake of effective procurement of water resources and supply method, it is definitely required to enhance the effectiveness of budget investment and project proceedings through integrated re-development which links projects to strengthen existing dams, reservoirs and hydraulic facilities. The major scopes of this research includes developing different types of system such as selecting potential sites to re-construct reservoirs including generating base maps and thematic maps, data collection regarding water demands and reservoir status; analyzing reservoir data; estimating developable capacity and index calculation; and forecasting inundated areas. In addition, this study provides other products such as developing output generation system which can support wide use of data built and analyzed; database generation for better data management; data analysis including selection, extraction, indexation, and calculation of base items through standardization; data security system prohibiting exterior proliferation and malicious manufacturing of data.