• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.6
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• pp.799-805
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• 2012

We introduce the notions of ordinary smooth, quasi-ordinary smooth and weak ordinary smooth structure, showing that various properties of an ordinary smooth topological space can be expressed in terms of these structures. In particular, the definitions and results of [2, 4, 5] may be expressed in terms of the ordinary smooth and quasi-ordinary smooth structures. Furthermore, we present the basic concepts relating to the weak ordinary smooth structure of an ordinary smooth topological space and the fundamental properties of the objects in these structures.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.929-942
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• 2023

In this paper, we discuss topological ergodic shadowing property and topological pseudo-orbital specification property of iterated function systems(IFS) on uniform spaces. We show that an IFS on a sequentially compact uniform space with topological ergodic shadowing property has topological shadowing property. We define the notion of topological pseudo-orbital specification property and investigate its relation to topological ergodic shadowing property. We find that a topologically mixing IFS on a compact and sequentially compact uniform space with topological shadowing property has topological pseudo-orbital specification property and thus has topological ergodic shadowing property.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.755-762
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• 1999

Let X be a p-compace groyp, Y -> X bd a p-compact-subgroup of X and G -> X be a p-compact toral subgroup of X with $(X/Y)^{hG} \neq 0$. In this paper we show that the homotopy fixed point set of the homotopy fibre $(X/Y)^{hG}$ is $F_p$-finite.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.717-723
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• 1997

The compact transformation group has been developed with lots of properties. Many properties which are satisfied on G-space for compact group G do not hold for noncompact case. To recover some theory on spaces with noncompact group action we give some restriction on G-spaces. Hence we introduced Cartan G-spaces and proper G-spaces for our goal and we prove some properties on these G-spaces with noncompact G.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.445-453
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• 1996

A closed subspace J of a Banach space X is called an M-ideal in X if the annihilator $J^\perp$ of J is an L-summand of $X^*$. That is, there exists a closed subspace J' of $X^*$ such that $X^* = J^\perp \oplus J'$ and $\left\$\mid$ p + q \right\$\mid$ = \left\$\mid$ p \right\$\mid$ + \left\$\mid$ q \right\$\mid$$ wherever $p \in J^\perp and q \in J'$.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.91-97
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• 1998

In this paper we study the Weyl spectrum of weight $\alpha, \omega_\alpha(T)$, of an operator T acting on an infinite dimensional Hilbert space. Main results are as follows. Firstly, we show that the Weyll spectrum of weight $\alpha$ of a polynomially $\alpha$-compact operator is finite, and that similarity preserves polynomial $\alpha$-compactness and the $\alpha$-Weyl's theorem both. Secondly, we give a sufficient condition for an operator to be the sum of an unitary and a $\alpha$-compact operators.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.899-910
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• 2012

Let $\mathcal{H}$ be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on $\mathcal{H}$ to satisfy that $f(T)$ obeys generalized Weyl's theorem for each function $f$ analytic on some neighborhood of ${\sigma}(T)$. Also we investigate the stability of generalized Weyl's theorem under (small) compact perturbations.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.71-84
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• 2017

We discuss the qualitative uncertainty principle for Gabor transform on certain classes of the locally compact groups, like abelian groups, ${\mathbb{R}}^n{\times}K$, K ⋉ ${\mathbb{R}}^n$ where K is compact group. We shall also prove a weaker version of qualitative uncertainty principle for Gabor transform in case of compact groups.

• Journal of The Korean Astronomical Society
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• v.29 no.spc1
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• pp.235-236
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• 1996

Using a phenomenological model for the accretion onto the magnetic white dwarf, we calclliated some optical line profiles from the magnetosphere of such systems. Line profiles of these systems seem to be produced in the magnetosphere of the compact star due to the reemission of X-ray produced near the stellar surface. Some results of our new calculation and the analysis of these results will be presented. Our results show that the model used here can reproduce the observed optical line profiles and open the possiblity to determine the parameters of individual systems.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.41-51
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• 2017

In this note, we deal with some characterizations of relative compactness on the $L_p$ metric space of fuzzy sets. And then, we point out that a characterization of relative compact subsets of fuzzy numbers with sendograph metric can be improved.