• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.47-54
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• 2007

In [6] some computation of spectral measures induced by normal operators $T^{*n}T^n$ was introduced. In this note we improve some computations by using spectral measures, which are related t o extremal vectors. Also, we discuss the extremal value properties and apply our spectral measure equations to moment sequences which are induced by weighted shifts.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.561-572
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• 2018

In this paper we consider the concept of statistical causality in continuous time between flows of information, represented by filtrations. Then we relate the given concept of causality to the equivalent change of measure that plays an important role in mathematical finance. We give necessary and sufficient conditions, in terms of statistical causality, for extremality of measure in the set of martingale measures. Also, we have considered the extremality of measure which involves the stopping time and the stopped processes, and obtained similar results. Finally, we show that the concept of unique equivalent martingale measure is strongly connected to the given concept of causality and apply this result to the continuous market model.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1123-1139
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• 2014

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < ${\alpha}$ < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.811-825
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• 2022

Given a compact subset P ⊂ (ℝ⁺)^d and a compact set K in ℂ^d. We concern with the Bernstein-Markov properties of the triple (P, K, 𝜇) where 𝜇 is a finite positive Borel measure with compact support K. Our approach uses (global) P-extremal functions which is inspired by the classical case (when P = Σ the unit simplex) in [7].

• Journal of the Korea Society for Simulation
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• v.27 no.2
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• pp.1-10
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• 2018

This paper presents an autonomous detection and aiming point computation of a battle tank by using RGB images. Maximally stable extremal regions algorithm was implemented to find features of the tank, which are matched with images extracted from streaming video to figure out the region of interest where the tank is present. The median filter was applied to remove noises in the region of interest and decrease camouflage effects of the tank. For the tank segmentation, k-mean clustering was used to autonomously distinguish the tank from its background. Also, both erosion and dilation algorithms of morphology techniques were applied to extract the tank shape without noises and generate the binary image with 1 for the tank and 0 for the background. After that, Sobel's edge detection was used to measure the outline of the tank by which the aiming point at the center of the tank was calculated. For performance measurement, accuracy, precision, recall, and F-measure were analyzed by confusion matrix, resulting in 91.6%, 90.4%, 85.8%, and 88.1%, respectively.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.419-431
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• 2021

In this paper we discuss the classical problem of finding conditions on the entire coefficients A(z) and B(z) guaranteeing that all nontrivial solutions of f" + A(z)f' + B(z)f = 0 are of infinite order. We assume A(z) is an entire function of completely regular growth and B(z) satisfies three different conditions, then we obtain three results respectively. The three conditions are (1) B(z) has a dynamical property with a multiply connected Fatou component, (2) B(z) satisfies T(r, B) ~ log M(r, B) outside a set of finite logarithmic measure, (3) B(z) is extremal for Denjoy's conjecture.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.2
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• pp.561-574
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• 2018

In this study, regional variations and factors associated with prevalence of metabolic syndrome were grasped using GWR (geographically weighted regression) and methodologies for the efficient management of metabolic syndrome were then set up to resolve health inequalities. Based on the National Health Screening Statistical Yearbook published by the National Health Insurance Service (NHIS), community health survey (KCDC) and other governmental institutions, indicators of social structural and mediation factors related to the regional prevalence of metabolic syndrome were collected. First, the existence of indicators to measure variations in metabolic syndrome were confirmed with the collected data by calculating the EQ (extremal quotient) and CV (coefficient of variations). The GWR, which is able to take spatial variations into consideration, was then adopted to analyze the factors of regional variations in metabolic syndrome. The GWR analysis revealed that severity and management of the main causes need to be prioritized in accordance with the prevalence of metabolic syndrome. Consequently, the order of priority in management of regional prevalence of metabolic syndrome was established, and plans that can increase the effectiveness of management of metabolic syndrome were confirmed to be feasible.