• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.19-34
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• 2011

A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.81.1-81.1
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• 2011

The new coherent scatter ionospheric radar has been operating at Gyerong city ($36.18^{\circ}N$, $127.14^{\circ}E$, dip lat $26.7^{\circ}N$), South Korea. This VHF radar is consisted of 24 Yagi antennas having 5 elements and observes the E- and F-region field-aligned irregularities (FAIs) in a single frequency of 40.8 MHz with a peak power of 24 kW. We present the first results of the E- and F-region FAIs over Korea by using the new VHF coherent scatter ionospheric radar. The morphological and echo characteristics are studied in terms of their echo strength, Doppler velocity and also by spectral width values. From the continuous observations from December 2009, we found ionospheric E- and F-region FAIs appeared frequently. The most interesting and striking observations for E region are occurrence of daytime E-region irregularities and strong Quasi-Periodic (QP) echoes at nighttime. And for F region, strong post-sunset and pre-sunrise FAIs appeared frequently. The VHF radar observations over Korea are discussed in the light of current understanding of mid-latitude E- and F-region FAIs.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.697-711
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• 2017

Let X, Y be real normed vector spaces. We exhibit all the solutions $f:X{\rightarrow}Y$ of the functional equation f(rx + sy) + rsf(x - y) = rf(x) + sf(y) for all $x,y{\in}X$, where r, s are nonzero real numbers satisfying r + s = 1. In particular, if Y is a Banach space, we investigate the Hyers-Ulam stability problem of the equation. We also investigate the Hyers-Ulam stability problem on a restricted domain of the following form ${\Omega}{\cap}\{(x,y){\in}X^2:{\parallel}x{\parallel}+{\parallel}y{\parallel}{\geq}d\}$, where ${\Omega}$ is a rotation of $H{\times}H{\subset}X^2$ and $H^c$ is of the first category. As a consequence, we obtain a measure zero Hyers-Ulam stability of the above equation when $f:\mathbb{R}{\rightarrow}Y$.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.23-34
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• 1988

A version of Ascoli's Theorem (equating compact and equicontinuous sets) is presented in the context of convergence spaces. This theorem and another, (involving equicontinuity) are applied to characterize compact subsets of quasi-multipliers of a $C^*$-algebra B, and to characterize the compact subsets of the state space of B. The classical Ascoli Theorem states that, for pointwise pre-compact families F of continuous functions from a locally compact space Y to a complete Hausdorff uniform space Z, equicontinuity of F is equivalent to relative compactness in the compact-open topology([4] 7.17). Though this is one of the most important theorems of modern analysis, there are some applications of the ideas inherent in this theorem which arc not readily accessible by direct appeal to the theorem. When one passes to so-called "non-commutative analysis", analysis of non-commutative $C^*$-algebras, the analogue of Y may not be relatively compact, while the conclusion of Ascoli's Theorem still holds. Consequently it seems plausible to establish a more general Ascoli Theorem which will directly apply to these examples.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.127.1-127.1
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• 2012

The 40.8-MHz VHF coherent scatter ionospheric radar, located in South Korea (Gyeryong, $36.18^{\circ}N$, $127.14^{\circ}E$), has been operating since December 2009 to investigate ionosphere E- and F-region field-aligned irregularities (FAIs) of mid-latitude. During the observation, we found E- and F-region FAIs appeared frequently: continuous echoes during the post-sunrise period and Quasi-Periodic (QP) echoes at nighttime for E region ; strong post-sunset and pre-sunrise FAIs for F region. The characteristics of E- and F-region FAIs are presented in terms of seasonal and local time variations of occurrence during December 2009 to August 2012. In addition, to investigate the correlation with geomagnetic activity to FAIs occurrence, we compared K-index variations to local time occurrence. It is worth to note our occurrence result since long term observation over several years in the mid-latitude has not yet been carried out.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.163-169
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• 2011

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. In this note, we aim at an extension of (GS) due to Kazmi and Khan [7] into a multi-valued circumstance. We consider a fairly general problem called the multi-valued quasi-generalized system (in short, MQGS). Based on the existence of 1-person game by Ding, Kim and Tan [5], we give a generalization of (GS) in the name of (MQGS) within the framework of Hausdorff topological vector spaces. As an application, we derive an existence result of the generalized vector quasi-variational inequality problem. This result leads to a multi-valued vector quasi-variational inequality extension of the strong vector variational inequality (SVVI) due to Fang and Huang [6] in a general Hausdorff topological vector space.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.917-933
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• 2021

In this paper, we investigate the behavior and sensitivity analysis of a solution set for a parametric generalized multi-valued nonlinear quasi-variational inclusion problem in a real Hilbert space. For this study, we utilize the technique of resolvent operator and the property of a fixed-point set of a multi-valued contractive mapping. We also examine Lipschitz continuity of the solution set with respect to the parameter under some appropriate conditions.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.233-246
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• 2008

In this paper, we obtain the general solution of the following cubic type functional equation and establish the stability of this equation (0.1) $kf({{\sum}\limits^{n-1}_{j=1}}x_j+kx_n)+kf({{\sum}\limits^{n-1}_{j=1}}x_j-kx_n)+2{{\sum}\limits^{n-1}_{j=1}}f(kx_j)+(k^3-1)(n-1)[f(x_1)+f(-x_1)]=2kf({\sum\limits^{n-1}_{j=1}}x_j)=K^3{\sum\limits^{n-1}_{j=1}[f(x_j+x_n)+f(x_j-x_n)]$ for any integers k and n with k ${\geq}$ 2 and n ${\geq}$ 3.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.47.1-47.1
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• 2019

We report the design and vibration analysis for the optomechanical structures of Linear Astigmatism Free - Three Mirror System (LAF-TMS). LAF-TMS is the linear astigmatism free off-axis wide-field telescope with D = 150 mm, F/3.3, and FOV = 5.51° × 4.13°. The whole structure consists of four optomechanical modules. It can accurately mount mirrors and also can survive from vibration environments. The Mass Acceleration Curve (MAC) is adapted to the quasi-static analysis. Modal, harmonic, and random vibration analysis have been performed under the qualification level of the launch system. We evaluate the final results in terms of von Mises stress and Margin of Safety (MoS).

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.151-159
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• 1997

Observing that for any dense weakly Lindelof subspace of a space Y, X is $Z^{#}$ -embedded in Y, we show that for any weakly Lindelof space X, the minimal Cloz-cover ($E_{cc}$(X), $z_{X}$) of X is given by $E_{cc}$(X) = {(\alpha, \chi$) : $\alpha$ is a G(X)-ultrafilter on X with $\chi\in\cap\alpha$}, $z_{X}$=(($\alpha, \chi$))=$\chi$, $z_{X}$ is $Z^{#}$ -irreducible and $E_{cc}$(X) is a dense subspace of $E_{cc}$($\beta$X).