• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.883-894
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• 2021

The aim of this work is to introduce for the first time the concept of D-set. This is done by defining a special type of cover called a D-cover. we present some results to study the properties of D-compact spaces and their relations with other topological spaces. Several examples are discussed to illustrate and support our main results. Our results extend and generalized many will known results in the literature.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.255-267
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• 2022

Uniform space is a generalization of metric space. The main purpose of this paper is to extend several results contained in [5, 6] which have for an expansive homeomorphism with the pseudo orbit tracing property(POTP in short) on a compact metric space (X, d) for an expansive homeomorphism with the POTP on a compact uniform space (X, 𝒰). we characterize stable and unstable sets, sink and source and saddle, recurrent points for an expansive homeomorphism which has the POTP on a compact uniform space (X, 𝒰).

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.839-853
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• 2022

We define the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property in terms of the topology of the phase space. Secondly we define these notions in terms of the compatible uniformity of the phase space. When the phase space is a compact Hausdorff space, we establish the equivalence of the corresponding definitions of the topological approach and the uniformity approach. In case the phase space is a compact metric space, the notions of ergodic shadowing property, $\underline{d}$-shadowing property and eventual shadowing property defined in terms of topology and uniformity are equivalent to their respective standard definitions.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.471-481
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• 2024

In this paper, the concept of D-sets will be applied to create D-lindelöf spaces, a new type of topological space covering the property. This is performed by using a D-cover, which is a special type of cover. The primary purpose of this work is to introduce the principles and concepts of D-lindelöf spaces. We look into their properties as well as their relationships with other topological spaces. The basic relationship between D-lindelöf spaces and lindelöf spaces, as well as many other topological spaces, will be given and described, including D-compact, D-countably compact, and D-countably lindelöf spaces. Many novel theories, facts, and illustrative and counter-examples will be investigated. We will use several informative instances to explore certain of the features of the Cartesian product procedure across D-lindelöf spaces as well as additional spaces under more conditions.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.455-462
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• 2011

An analytic self-map ${\phi}$ of the open unit disk $\mathbb{D}$ in the complex plane and an analytic map ${\psi}$ on $\mathbb{D}$ induce the so-called weighted composition operator $C_{{\phi},{\psi}}$: $H(\mathbb{D})\;{\rightarrow}\;H(\mathbb{D})$, $f{\mapsto} \;{\psi}\;(f\;o\;{\phi})$, where H($\mathbb{D}$) denotes the set of all analytic functions on $\mathbb{D}$. We study when such an operator acting between different weighted Bergman spaces is bounded, compact and Schatten class.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.967-970
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• 2018

The aim of this paper is to show that there exists a weakly quasisymmetric homeomorphism $f:(X,d){\rightarrow}(Y,d^{\prime})$ between two locally compact non-complete metric spaces such that $f:(X,d_h){\rightarrow}(Y,d^{\prime}_h)$ is not quasi-isometric, where dh denotes the Gromov hyperbolic metric with respect to the metric d introduced by Ibragimov in 2011. This result shows that the answer to the related question asked by Ibragimov in 2013 is negative.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.259-269
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• 2021

We shall study the following. Let 𝜙 be an expansive flow on a compact TVS-cone metric space (X, d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that lim sup ${\frac{1}{t}}$ log v(t) ≤ h(𝜙), where v(t) denotes the number of closed orbits of 𝜙 with a period 𝜏 ∈ [0, t] and h(𝜙) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space [?].

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.703-708
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• 2005

Let ${\varphi}(z)\;=\;({\varphi}_1(Z),{\cdots},{\varphi}_n(Z))$ be a holomorphic self­map of $\mathbb{D}^n$, where $\mathbb{D}^n$ is the unit polydisk of $\mathbb{C}^n$. The sufficient and necessary conditions for a composition operator to be bounded and compact from the Hardy space $H^2(\mathbb{D}^n)$ into $\alpha$-Bloch space $\beta^{\alpha}(\mathbb{D}^n)$ on the polydisk are given.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.553-562
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• 1995

In a Recent paper [3], D. Chinea, M. Delon and J. C. Marrero proved that a cosymplectic manifold is formal and constructed an example of compact cosymplectic manifold which is not a global product of a Kaehler manifold with the circle. In this paper we study the compact cosymplectic manifolds with critical Riemannian metrics.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.5B no.3
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• pp.262-266
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• 2005

In this paper, in order to enhance thrust of slotless type Permanent Magnet Linear Synchronous Motor, an optimal design is achieved by combining a genetic algorithm with 3D space harmonic method. In the case of multi-objective functions, the ratio of thrust/weight and thrust/volume are increased by $\7.56[%]l\;and\;7.98\[%]$, respectively. Thus, miniaturization and lightweight were realized at the same time.