• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.447-469
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• 2018

Types (over parameters) in the theory of atomless random variable structures correspond precisely to (conditional) distributions in probability theory. Moreover, the logic (resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) convergence of distributions. In this paper, we study metrics between types. We show that type spaces under $d^{\ast}-metric$ are isometric to Wasserstein spaces. Using optimal transport theory, two formulas for the metrics between types are given. Then, we give a new proof of an integral formula for the Wasserstein distance, and generalize some results in optimal transport theory.

• Bulletin of the Korean Space Science Society
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• 2011.04a
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• pp.28.4-29
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• 2011

Solar Proton Events (SPEs, ${\geq}\;10\;cm^{-1}s^{-1}sr^{-1}$ with >10 MeV) are very important for space weather forecasting. It is well known that they are associated with solar flares and/or CME-driven shocks. Especially, the CME-driven shocks have been observed as solar and interplanetary type II bursts. In this study, we estimated the occurrence probability of SPEs depending on three groups: (1) metric, (2) decameter-hectometric (D-H), and (3) meter-to-kilometric (m-to-km) type II bursts. For this work, we used SPEs and all available type II burst data in 1996-2004. The primary findings of this study are as follows. First, the majority (77%) of the m-to-km type II bursts are associated with SPEs and its probability is noticeably higher than D-H type II bursts probability strongly depend on longitude: eastern (0%), center(45%), and western (33%) for X-class associated metric type II bursts, eastern (15%), center (55%), and western (50%) for X-class associated D-H type II bursts, eastern (17%), center (77%), and western (64%) for X-class associated m-to-km type II bursts. Third, for m-to-km type II bursts, the SPE probability increases with CME speed: 400km/s${\leq}$V <1000km/s (36%), 1000km/s ${\leq}$V<1500km/s (40%), 1500km/s${\leq}$V (66%). Finally, we expect that these results will be used for setting up more reasonable solar proton event forecasting models.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.951-965
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• 2019

Let $f:X{\rightarrow}X$ be a continuous map on a compact metric space (X, d) and for an arbitrary $x{\in}X$, $${\mathcal{SC}}_d(x,f):=\{y{\mid}x{\text{ can be strong }}d-{\text{chain to }}y\}$$. We give an example to show that ${\mathcal{SC}}_d(x,f)$ is dependent on the metric d on X but it is a closed and f-invariant set. We prove that if ${\mathcal{SC}}_d(x,f){\supseteq}{\Omega}(f)$ or f has the asymptotic-average shadowing property, then ${\mathcal{SC}}_d(x,f)=X$. Also, we show that if f has the shadowing property, then ${\lim}\;{\sup}_{n{\in}{\mathbb{N}}}\{f^n\}={\mathcal{SC}}_d(f)$ where ${\mathcal{SC}}_d(f)=\{(x,y){\mid}y{\in}{\mathcal{SC}}_d(x,f)\}$. For each $n{\in}{\mathbb{N}}$, we give an example in which ${\mathcal{SCR}}_d(f^n){\neq}{\mathcal{SCR}}_d(f)$. In spite of it, we prove that if $f^{-1}:(X,d){\rightarrow}(X,d)$ is an equicontinuous map, then ${\mathcal{SCR}}_d(f^n)={\mathcal{SCR}}_d(f)$ for all $n{\in}{\mathbb{N}}$.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.473-482
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• 2015

Let Qf be the maximal derivative of f with respect to the Bergman metric $b_B$. In this paper, we will find conditions such that $(1-{\parallel}z{\parallel})^s(Qf)^p(z)$ is bounded on B. We will also find conditions such that Bergman projection type operator $P_r$ is bounded operator from $L^p(B,d{\mu}_r)$ to the holomorphic Besov p-space Bs $B^s_p(B)$ with weight s.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.391-399
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• 2003

Let (X,S,$\mu$) be a measure space and M be the vector space of all real valued S-measurable functions defined on (X,S,$\mu$). For $E\;{\in}\;S$ with $\mu(E)\;<\;{\infty}$, $d_E$ is a pseudometric on M. With the notion of D = {$d_E$\mid$E\;{\in}\;S,\mu(E)\;<\;{\infty}$}, in this paper we investigate some topological structure T of M. Indeed, we shall show that it is possible to define a complete invariant metric on M which is compatible with the topology T on M.

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.269-276
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• 2013

We find an explicit $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on the 4-d hyperbolic space $\mathbb{H}^4$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the hyperbolic metric on $\mathbb{H}^4$, the scalar curvatures of $g_t$ are strictly decreasing in t in an open ball and $g_t$ is isometric to the hyperbolic metric in the complement of the ball.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.341-350
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• 1995

Let (M,g) be a compact manifold of dimension n with metric tensor g. Let $\Delta^p = d\delta + \deltad$ be the Laplace-Beltrami operator acting on the space of smooth p-forms.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.507-518
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• 2020

In this article, we establish some fixed point results in G-metric spaces using the modified JS-G-contractions and we provide some suitable examples to support the results. Also, we give an application to solve an integral equation.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.8
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• pp.491-494
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• 2000

A scheme is proposed for measuring similarities between the binary pulse signals in the pulse-code modulation using the Integra-Normalizer. The Integra-Normalizer provides a better interpretation of the relationship between the pulse signals by removing redundant codes, which maps all possible observed signals to one of the codes to be received with relative similarities between each pair of compared signals. The proposed method provides better error tolerance than L2 metric, such as Hamming distance, since the distances between pulse signals are measured not useful for the time-delay detection in the pulse-code modulation.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.391-394
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• 2005

In this paper, we present an approach that is able to reconstruct 3 dimensional metric models from un-calibrated images acquired by a freely moved camera system. If nothing is known of the calibration of either camera, nor the arrangement of one camera which respect to the other, then the projective reconstruction will have projective distortion which expressed by an arbitrary projective transformation. The distortion on the reconstruction is removed from projection to metric through self-calibration. The self-calibration requires no information about the camera matrices, or information about the scene geometry. Self-calibration is the process of determining internal camera parameters directly from multiply un-calibrated images. Self-calibration avoids the onerous task of calibrating cameras which needs to use special calibration objects. The root of the method is setting a uniquely fixed conic(absolute quadric) in 3D space. And it can make possible to figure out some way from the images. Once absolute quadric is identified, the metric geometry can be computed. We compared reconstruction image from calibrated images with the result by self-calibration method.