• Korean Journal of Mathematics
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• v.27 no.4
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• pp.879-898
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• 2019

In this paper we prove some interesting inclusions concerning the numerical range of some operators and the numerical range of theirs ranges with a convex function. Further, we prove some inequalities for the numerical radius. These inclusions and inequalities are based on some classical convexity inequalities for non-negative real numbers and some operator inequalities.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1029-1044
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• 2023

The purpose of this paper is to introduce the concept of joint essential numerical spectrum 𝜎_en(·) of q-tuple of operators on a Banach space and to study its properties. This notion generalize the notion of the joint essential numerical range.

• Atmosphere
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• v.34 no.1
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• pp.23-34
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• 2024

The Korea Meteorological Administration has improved medium-range weather forecasts by implementing post-processing methods to minimize numerical model errors. In this study, we employ a statistical correction technique known as the minimum continuous ranked probability score (CRPS) to refine medium-range forecast guidance. This technique quantifies the similarity between the predicted values and the observed cumulative distribution function of the Unified Model Ensemble Prediction System for Global (UM EPSG). We evaluated the performance of the medium-range forecast guidance for surface air temperature and relative humidity, noting significant enhancements in seasonal bias and root mean squared error compared to observations. Notably, compared to the existing the medium-range forecast guidance, temperature forecasts exhibit 17.5% improvement in summer and 21.5% improvement in winter. Humidity forecasts also show 12% improvement in summer and 23% improvement in winter. The results indicate that utilizing the minimum CRPS for medium-range forecast guidance provide more reliable and improved performance than UM EPSG.

• Bulletin of the Korean Mathematical Society
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• v.21 no.1
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• pp.27-30
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• 1984

The concepts of the numerical range of an operator on a Hillbert space and on a Banach space were introduced by Toeplitz in 1918 and Bauer in 1962 respectively. Bauer's paper was concerned only with finite dimensional Banach spaces, but the concept of numerical range that he introduced is available without restriction of the dimension [1, 2]. In this paper, we define a C-algebra spatial numerical range of an operator on C-algebra valued inner product modules introduced by Paschke [4], and give analogous results on these modules as those on Banach spaces.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.125-131
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• 2021

In the paper, we investigate the representation of the numerical range W(An) for the 2 × 2 complex matrix A, in terms of the numerical range W(A) of the matrix A, and the elements of A or the eigenvalue of A.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.169-176
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• 2015

A sequence of composition operators on Hardy space is considered. We prove that, by numerical range properties, it is SOT-convergence but not converge.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.03b
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• pp.183-190
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• 2000

Effective range of Hydraulic Hammer Compaction was studied by numerical analysis instead of empirical method. Numerical analyses were carried out with commercial FEM code, ABAQUS, and verified by comparing the numerical results with field tests of Hydraulic Hammer Compaction. Most of material properties were evaluated by data from laboratory and in-situ tests. Vertical effective range was estimated by distribution curve of plastic strain energy dissipated through soil layers under dynamic load and these results were in good agreement with field tests. Based on verification, the effects of governing properties of Hydraulic Hammer Compaction such as number of hit can be determined by numerical analyses. In addition, vertical effective range can also be determined by Menard's empirical equation using the external work at converging time of plastic strain energy in numerical analysis. This implies that the minimum energy of Hydraulic Hammer Compaction for improvement can be determined by Menard's equation.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.537-542
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• 2000

When A is a subalgebra of a $C^*$-algebra, the spatial numerical range of element of A can be described in terms of positive linear functionals on the $C^*$-algebra.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1963-1971
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• 2015

Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras. Denote by W(a) the numerical range of an element $a{\in}\mathcal{A}$. We show that the condition W(ax) = W(bx), ${\forall}x{\in}\mathcal{A}$ implies that a = b. Using this, among other results, it is proved that if ${\phi}$ : $\mathcal{A}{\rightarrow}\mathcal{B}$ is a surjective map such that $W({\phi}(a){\phi}(b){\phi}(c))=W(abc)$ for all a, b and $c{\in}\mathcal{A}$, then ${\phi}(1){\in}Z(B)$ and the map ${\psi}={\phi}(1)^2{\phi}$ is multiplicative.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• v.4 no.2
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• pp.103-110
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• 2000

In order to understand the wintertime intermittent characteristics of the trans-boundary air pollutant transport observed in East Asia, a numerical simulation of the long-range transport of pollutants was applied using an atmospheric transport model(STEM-II). The numerical simulation was carried out for the entire month of January 1997 and specific atmospheric aerosol (including sulfate, nitrate, and other ion compounds0 observation data were compared from four observation sites(Cheju Island, Kanghwa Island, Dazaifu, and Fukue Island). The observation data revealed that concentration peaks were intermittently observed at 3 to 4-day intervals plus the four observation sites exhibited a very similar spatial variation. The horizontal and spatial scale of the heavily polluted air masses was analyzed based on numerical results. The mechanism of the intermittent transport of air pollutants was clearly explained by a comparison of the observed data with the numerical output. It was found that the wind pattern variations associated with the synoptic scale pressure system changes play an extremely important role in the transport of pollutants in this region.