• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.633-646
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• 2017

Recently, Curto, Lee and Yoon considered the properties (such as, hyponormality, subnormality, and flatness, etc.) for 2-variable weighted shifts and constructed several families of commuting pairs of subnormal operators such that each family can be used to answer a conjecture of Curto, Muhly and Xia negatively. In this paper, we consider the weak and quadratic hyponormality of 2-variable weighted shifts ($W_1,W_2$). In addition, we detect the weak and quadratic hyponormality with some interesting 2-variable weighted shifts.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.261-267
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• 2015

We study backward extensions of 2-variable weighted shifts with finite atomic Berger measure. We provide a necessary and sufficient condition for the subnormality of such extensions. As an application, we give a simple counterexample for the Curto-Muhly-Xia conjecture [10].

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.711-732
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• 2018

In this paper, we give a new approach to solving the 2-variable subnormal completion problem (SCP for short). To this aim, we extend the notion of recursively generated weighted shifts, introduced by R. Curto and L. Fialkow, to 2-variable case. We next provide "concrete" necessary and sufficient conditions for the existence of solutions to the 2-variable SCP with minimal Berger measure. Furthermore, a short alternative proof to the propagation phenomena, for the subnormal weighted shifts in 2-variable, is given.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.943-957
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• 2016

We introduce a 2-variable weighted shift, denoted by $S_2$(a, b, c, d), which arises naturally from analytic function space theory. We investigate when it is subnormal, and compute the Berger measure of it when it is subnormal. And we apply the results to investigate the relationship among 2-variable subnormal, hyponormal and 2-hyponormal weighted shifts.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.439-450
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• 2009

In this note we give a connection between the truncated moment problem and the 2-variable subnormal completion problem.

• Journal of Korean Society for Quality Management
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• v.28 no.2
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• pp.70-88
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• 2000

Short runs where it is neither possible nor practical to obtain sufficient subgroups to estimate accurately the control limit are common in modem business environments. In this study, the standardized control chart, Hillier's exact method, Q chart, EWMA(Exponentially Weighted Moving Average) chart for Q statistics and EWMA chart for mean and absolute deviation among many SPC(Statistical Process Control) techniques for short runs have been reviewed and advantages and disadvantages of these techniques are discussed. The simulation experiments to compare performances of these variable charts for process mean and variations are conducted for combination of subgroup size, scale and timing of shifts of process mean an/or standard deviation. Based upon simulation results, some guidelines for practitioners to choose short run SPC techniques are recommended.

• Earthquakes and Structures
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• v.26 no.2
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• pp.131-147
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• 2024

Damage caused by an earthquake depends on not just the intensity of an earthquake but also the region-specific construction practices. Past earthquakes in Asian countries have highlighted inadequate construction practices, which caused huge life and property losses, indicating the severe need to strengthen existing structures. Strengthening activities shall be proposed as per the proposed weighting factors, first at the higher weighted members to increase the capacity of the building immediately and thereafter, the other members. Through this study on gravity load-designed (GLD) buildings, relative weights are assigned to each storey and exterior and interior columns within a storey based on their contribution to the energy dissipation capacity of the building. The numerical study is conducted on mid-rise archetype GLD buildings, i.e., 4, 6, 8, and 10 stories with variable storey heights, in the high seismic zones. Non-linear static analysis is performed to compute weights based on energy dissipation capacities. The results obtained are verified with the non-linear time history analysis of 4 GLD buildings. It was observed that exterior columns have higher weightage in the energy dissipation capacity of the building than interior columns up to a certain building height. The damage in stories is distributed in a convex to concave parabolic shape from bottom to top as building height increases, and the maxima location of the parabola shifts from bottom to middle stories. Relative weighting factors are assigned as per the damage contribution. And the sequence for strengthening activities is proposed as per the computed weighting factors in descending order for regular RCC buildings. Therefore, proposals made in the study would increase the efficacy of strengthening activities.