• Korean Journal of Mathematics
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• v.7 no.1
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• pp.123-130
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• 1999

We characterize the compactness, weak precompactness and weak compactness in $L^P({\mu},X)$ and in more general space $P^c({\mu},X)$. Moreover, we present this characterization in terms of extremal structure in X.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.91-98
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.233-240
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• 2006

In this paper we introduce the concepts of several types of $weak^*$ quasi-smooth ${\alpha}$-compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and investigate some of their properties.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.223-234
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• 2005

We introduce the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and obtain some of their structural properties. We also introduce the concepts of several types of quasi-smooth ${\alpha}$- compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set and investigate some of their properties.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1081-1107
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• 2021

In this paper, we introduce the notion of toric special weak Fano manifolds, which have only special primitive crepant contractions. We study their structure, and in particular completely classify smooth toric special weak Fano 4-folds. As a result, we can confirm that almost every smooth toric special weak Fano 4-fold is a weakened Fano manifold, that is, a weak Fano manifold which can be deformed to a Fano manifold.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.445-453
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• 2005

We say that a module M is weak lifting if M is supplemented and every supplement submodule of M is a direct summand. The module M is called lifting, if it is weak lifting and amply supplemented. This paper investigates the structure of weak lifting modules and lifting modules having small radical over commutative noetherian rings.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1389-1421
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• 2018

In this paper, we introduce the notion of C-Gorenstein weak injective modules with respect to a semidualizing bimodule $_SC_R$, where R and S are arbitrary associative rings. We show that an iteration of the procedure used to define $G_C$-weak injective modules yields exactly the $G_C$-weak injective modules, and then give the Foxby equivalence in this setting analogous to that of C-Gorenstein injective modules over commutative Noetherian rings. Finally, some applications are given, including weak co-Auslander-Buchweitz context, model structure and dual pair induced by $G_C$-weak injective modules.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.209-218
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• 2007

In this paper we investigate the ${\ell}^p$ space structure of the Banach envelope of $WeakL_1$. In particular, the Banach envelope of $WeakL_1$ contains a complemented Banach sublattice that is isometrically isomorphic to the nonseparable Banach lattice ${\ell}^p$, ($1{\leq}p<\infty$) as well as the separable case.

• Structural Engineering and Mechanics
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• v.62 no.2
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• pp.151-162
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• 2017

Two $Chang-{\alpha}$ dissipative family methods and two $KR-{\alpha}$ family methods were developed for time integration recently. Although the four family methods are in the category of the dissipative structure-dependent integration methods, their performances may be drastically different due to the detrimental property of weak instability or overshoot for the two $KR-{\alpha}$ family methods. This weak instability or overshoot will result in an adverse overshooting behavior or even numerical instability. In general, the four family methods can possess very similar numerical properties, such as unconditional stability, second-order accuracy, explicit formulation and controllable numerical damping. However, the two $KR-{\alpha}$ family methods are found to possess a weak instability property or overshoot in the high frequency responses to any nonzero initial conditions and thus this property will hinder them from practical applications. Whereas, the two $Chang-{\alpha}$ dissipative family methods have no such an adverse property. As a result, the performances of the two $Chang-{\alpha}$ dissipative family methods are much better than for the two $KR-{\alpha}$ family methods. Analytical assessments of all the four family methods are conducted in this work and numerical examples are used to confirm the analytical predictions.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.1
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• pp.42.1-42.1
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• 2014

A gravitational weak-lensing map provides a weighted "picture" of the projected surface mass density and is to be an important tool for identifying "mass-selected" clusters of galaxies. However, weak-lensing maps have a limitation due to the projection of large-sclae structure along the line-of-sight. Geller et al. (2010) and Kurtz et al. (2012) compared massive clusters identified in a dense redshift survey with significant weak-lensing map convergence peaks. Both assessments of the efficiency of weak-lensing map for cluster identification did not draw a general conclusion, because the sample is so small. Thus, we additionally perform deep imaging observations of fields in a dense galaxy redshift survey that contain galaxy clusters at z~0.2-0.5, using CFHT Megacam. Our study will provide an important opportunity to examine the efficiency and completeness of a weak-lensing selection, and further to improve the method of cluster identification in future weak-lensing surveys.