• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.49-59
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• 2021

Recently, Andrews introduced partition functions ����(n) and ${\bar{\mathcal{EO}}}$(n) where the function ����(n) denotes the number of partitions of n in which every even part is less than each odd part and the function ${\bar{\mathcal{EO}}}$(n) denotes the number of partitions enumerated by ����(n) in which only the largest even part appears an odd number of times. In this paper we obtain some congruences modulo 2, 4, 10 and 20 for the partition function ${\bar{\mathcal{EO}}}$(n). We give a simple proof of the first Ramanujan-type congruences ${\bar{\mathcal{EO}}}$ (10n + 8) ≡ 0 (mod 5) given by Andrews.

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.7
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• pp.318-326
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• 2008

In this paper, we will analyze embedding among Folded Hypercube, Even Network and Odd Network to further improve the network cost of Hypercube. We will show Folded Hypercube $FQ_n$ can be embedded into Even Network $E_{n-1}$ with dilation 2, congestion 1 and Even Network $E_d$ can be embedded into Folded Hypercube $FQ_{2d-3}$ with dilation 1. Also, we will prove Folded Hypercube $FQ_n$ can be embedded into Odd Network $O_{n-1}$ with dilation 2, congestion 1 and Odd Network $O_d$ can be embedded into Folded Hypercube $FQ_{2d-3}$ with dilation 2, congestion 1. Finally, we will show Even Network $E_d$ can be embedded into Odd Network $O_d$ with dilation 2, congestion 1 and Odd Network $O_d$ can be embedded into Folded Hypercube $E_{d-1}$ with dilation 2, congestion 1.

• Journal of The Korean Astronomical Society
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• v.36 no.3
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• pp.81-87
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• 2003

It is suggested that a flying-by star in a hot accretion disk may cool the hot accretion disk by the Comptonization of the stellar emission. Such a stellar cooling can be observed in the radio frequency regime since synchrotron luminosity depends strongly on the electron temperature of the accretion flow. If a bright star orbiting around the supermassive black hole cools the hot disk, one should expect a quasi-periodic modulation in radio, or even possible an anti-correlation of luminosities in radio and X-rays. Recently, the unprecedentedly accurate infrared imaging of the Sagittarius A$\ast$ for about ten years enables us to resolve stars around it and thus determine orbital parameters of the currently closest star S2. We explore the possibility of using such kind of observation to distinguish two quite different physical models for the central engine of the Sagittarius A$\ast$, that is, a hot accretion disk model and a jet model. We have attempted to estimate the observables using the observed parameters of the star S2. The relative difference in the electron temperature is a few parts of a thousand at the epoch when the star S2 is near at the pericenter. The relative radio luminosity difference with and without the stellar cooling is also small of order $10^{-4}$, particularly even when the star S2 is near at the pericenter. On the basis of our findings we tentatively conclude that even the currently closest pass of the star S2 is insufficiently close enough to meaningfully constrain the nature of the Sagittarius A$\ast$ and distinguish two competing models. This implies that even though Bower et al. (2002)have found no periodic radio flux variations in their data set from 1981 to 1998, which is naturally expected from the presence of a hot disk, a hot disk model cannot be conclusively ruled out. This is simply because the energy bands they have studied are too high to observe the effect of the star S2 even if it indeed interacts with the hot disk. In other words, even if there is a hot accretion disk the star like S2 has imprints in the frequency range at v $\le$ 100 MHz.

• Archives of Pharmacal Research
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• v.21 no.6
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• pp.621-628
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• 1998

The "evolution" of a thing, a custom, an organ is thus by no means its progressus toward a goal, even less a logical progressus by the shortest route and with the least expendit ure of force, but a succession of more or less profound, mutually independent processes of subduing, plus the resistances they encounter, the attempts at transformation for the purpose of defense and reaction, and the results of successful counteractions. The form is fluid, but the "meaning" is even more so (Friedrich W. Nietzsche).

• Clinical and Experimental Pediatrics
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• v.62 no.10
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• pp.367-373
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• 2019

Bronchopulmonary dysplasia (BPD) is a chronic lung disease of preterm infants with multiple factors affected from prenatal to postnatal periods. Despite significant advances in neonatal care over almost 50 years, BPD rates have not decreased; in fact, they may have even increased. Since more preterm infants, even at periviable gestational age, survive today, different stages of lung development affect the pathogenesis of BPD. Hence, the definition of BPD has changed from "old" to "new." In this review, we discuss the various definitions of BPD, risk factors from the prenatal to postnatal periods, management strategies by phase, and future directions for research.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.821-833
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• 2017

We get a result that shows the existence of infinitely many solutions for a class of the elliptic systems involving subcritical Sobolev exponents nonlinear terms with even functionals on the bounded domain with smooth boundary. We get this result by variational method and critical point theory induced from invariant subspaces and invariant functional.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.475-487
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• 2003

A generalized even-dimensional Riemannian manifold defined by the ME-connection which is both Einstein and of the form (3.3) is called an even-dimensional ME-manifold and we denote it by $MEX_{2n}$. The purpose of this paper is to study a necessary and sufficient condition that there is an ME-connection, to derive the useful properties of some tensors, and to investigate a representation of the ME-vector in $MEX_{2n}$.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 1998.10b
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• pp.1-9
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• 1998

In the decision of a collision avoidance action for navigators and intellignet ships, it is necessary to evaluate the degree of surrounding risks effectively. We propose the new risk evaluation technique in two dimensions using Even Risk Contour on the basis of the concept of contour line. In this paper, we introduce the algorithms ofERC and Approach Velocity(AV) and show their application for avoiding traffic collision at sea.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1357-1365
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• 2013

We find a lower bound on the number of real/inert imagi-nary/ramified imaginary quadratic extensions of the function field $\mathbb{F}_q(t)$ whose ideal class groups have an element of a fixed order, where $q$ is a power of 2.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.341-357
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• 2018

We examine various dualities over the fields of even orders, giving new dualities for additive codes. We relate the MacWilliams relations and the duals of ${\mathbb{F}}_{2^{2s}}$ codes for these various dualities. We study self-dual codes with respect to these dualities and prove that any subgroup of order $2^s$ of the additive group is a self-dual code with respect to some duality.