• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.581-600
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• 2017

A classical result of A. Cohn states that, if we express a prime p in base 10 as $$p=a_n10^n+a_{n-1}10^{n-1}+{\cdots}+a_110+a_0$$, then the polynomial $f(x)=a_nx^n+a_{n-1}x^{n-1}+{\cdots}+a_1x+a_0$ is irreducible in ${\mathbb{Z}}[x]$. This problem was subsequently generalized to any base b by Brillhart, Filaseta, and Odlyzko. We establish this result of A. Cohn in $O_K[x]$, K an imaginary quadratic field such that its ring of integers, $O_K$, is a Euclidean domain. For a Gaussian integer ${\beta}$ with ${\mid}{\beta}{\mid}$ > $1+{\sqrt{2}}/2$, we give another representation for any Gaussian integer using a complete residue system modulo ${\beta}$, and then establish an irreducibility criterion in ${\mathbb{Z}}[i][x]$ by applying this result.

• Journal of electromagnetic engineering and science
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• v.14 no.4
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• pp.360-366
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• 2014

A single-feed composite cavity-backed four-arm curl antenna is presented for use in global positioning systems (GPS). Its primary radiating element is fed by a vacant-quarter printed ring, which helps the antenna directly match to a $50-{\Omega}$ coaxial line and produce a good circular polarization (CP). The cavity-backed reflector is employed to improve the CP radiation characteristics in terms of 3-dB axial ratio (AR) beamwidth and minimum AR value. The optimized design with an overall size of $90{\times}90{\times}25mm^3$ ($0.4725{\lambda}_o{\times}0.4725{\lambda}_o{\times}0.13{\lambda}_o$ at 1,575 MHz) results in a ${\mid}S_{11}{\mid}<-10dB$ bandwidth of 8.66% (1,514-1,651 MHz) and a 3-dB AR bandwidth of 2.23% (1,555-1,590 MHz). The antenna radiates a widebeam right-hand circular polarization and operates with a measured radiation efficiency greater than 90% within its impedance matching bandwidth.

• Journal of the Korea Furniture Society
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• v.23 no.4
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• pp.449-459
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• 2012

The article aims to making a comparison between traditional Korean and Western furniture metal handles to give the detail information of the handle terms by analyzing the related literature including internet and interviews. In terms of that, the Korean and Western metal handles are compared in the types, components, materials, methods, and terms affecting the development made by the craftsmen before the Industrial Revolution about the mid or late 18th century. As a result, first, ring and drop pull handles were mostly and wooden knobs were a little used to open the furniture doors and drawers. The Korean drop pulls, Deulswae, came out after the ring pulls, Gori, while the Western drops called loop or bail handles as well, came out before the ring pulls. Second, the components were composed by ring, Gori, loop or bail, Deulswae, Post, Baemok, washer, Baemokbatchim, and backplate, Deulswaebatchim. Most of the Western handles were fastened by the bolt and nut, while the post of two strips, Baemok, fastened the Korean metal handles. Third, the metal handles were created of brass and iron mostly, gilded gold and silver. Forth, the method were largely used by casting, engraving, forging, plating, and hammering in the Korean handles, and by casting, molding, engraving, and stamped in the Western handles. Finally, the terms such as "knobs, pulls, drops, ring and drop pulls, loop or bail handles, posts, washers, backplate, casting, molding, engraving, forging, plating, and stamped" were clarified by the two comparison in Korean and English.

• Journal of Chest Surgery
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• v.43 no.5
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• pp.475-481
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• 2010

Background: We evaluated mid-term results of mitral annuloplasty using a flexible band and a completely rigid ring for mitral valve repair in patients with degenerative mitral regurgitation (MR). Material and Method: From January 2004 to September 2008, 71 patients (M:F=36:35, $55{\pm}13$ years) underwent mitral valve repair with mitral annuloplasty for degenerative MR. Ring annuloplasty was done using a Cosgrove-Edwards flexible band (Group I, n=43) or a Carpentier-Edwards classic ring (Group II, n=28). There were no differences in preoperative characteristics of the participants. Average duration of follow-up was 36 months (range: 2~69 mos). Result: There was no in-hospital mortality. Postoperative morbidity, which included atrial fibrillation (n=7) and low cardiac output syndrome (n=5) in groups I and II were similar. There was one late death in group II. The proportion exhibiting freedom from recurrent mitral regurgitation ($\geq$moderate) at 4 years in Groups I and II were, respectively, 94.5 and 91.8%, (p=0.695). Left ventricular ejection fraction decreased in the early postoperative period ($7{\pm}2$ days) and recovered by last follow-up ($25{\pm}16$ mos; p=0.002). The pattern was similar in groups I and II (p=0.905). Re-operation was performed in 3 patients (1 in Group I and 2 in Group II, p=0.316). Four-year event-free survival (free of adverse valve-related events) was 95.2% for Group I and 92.6% for Group II; this difference was not significant, p=0.646). Conclusion: The type of technique used in mitral annuloplasty to repair the mitral valve repair after degenerative MR did not affect mid-term clinical and functional results.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.233-260
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• 2017

Let R be a factorial domain. In this work we investigate the connections between the arithmetic of Int(R) (i.e., the ring of integer-valued polynomials over R) and its monadic submonoids (i.e., monoids of the form {$g{\in}Int(R){\mid}g{\mid}_{Int(R)}f^k$ for some $k{\in}{\mathbb{N}}_0$} for some nonzero $f{\in}Int(R)$). Since every monadic submonoid of Int(R) is a Krull monoid it is possible to describe the arithmetic of these monoids in terms of their divisor-class group. We give an explicit description of these divisor-class groups in several situations and provide a few techniques that can be used to determine them. As an application we show that there are strong connections between Int(R) and its monadic submonoids. If $R={\mathbb{Z}}$ or more generally if R has sufficiently many "nice" atoms, then we prove that the infinitude of the elasticity and the tame degree of Int(R) can be explained by using the structure of monadic submonoids of Int(R).

• East Asian mathematical journal
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• v.33 no.3
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• pp.257-263
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• 2017

Let n be any positive integer and ${\mathbb{Z}}_n=\{0,1,{\cdots},n-1\}$ be the ring of integers modulo n. Let $X_n$ be the set of all nonzero, nonunits of ${\mathbb{Z}}_n$, and $G_n$ be the group of all units of ${\mathbb{Z}}_n$. In this paper, by investigating the regular action on $X_n$ by $G_n$, the following are proved : (1) The number of orbits under the regular action (resp. the number of annihilators in $X_n$) is equal to the number of all divisors (${\neq}1$, n) of n; (2) For any positive integer n, ${\sum}_{g{\in}G_n}\;g{\equiv}0$ (mod n); (3) For any orbit o(x) ($x{\in}X_n$) with ${\mid}o(x){\mid}{\geq}2$, ${\sum}_{y{\in}o(x)}\;y{\equiv}0$ (mod n).

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.371-379
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• 2012

Let D be an integral domain, $\bar{D}$ be the integral closure of D, * be a star operation of finite character on D, $*_w$ be the so-called $*_w$-operation on D induced by *, X be an indeterminate over D, $N_*=\{f{\in}D[X]{\mid}c(f)^*=D\}$, and $Kr(D,*)=\{0\}{\cup}\{\frac{f}{g}{\mid}0{\neq}f,\;g{\in}D[X]$ and there is an $0{\neq}h{\in}D[X]$ such that $(c(f)c(h))^*{\subseteq}(c(g)c(h))^*$}. In this paper, we show that D is a *-quasi-Pr$\ddot{u}$fer domain if and only if $\bar{D}[X]_{N_*}=Kr(D,*_w)$. As a corollary, we recover Fontana-Jara-Santos's result that D is a Pr$\ddot{u}$fer *-multiplication domain if and only if $D[X]_{N_*} = Kr(D,*_w)$.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.39-44
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• 1996

Throughout this paper $Z^p, Q_p$ and C_p$ will denote the ring of p-adic rational integers, the field of p-adic rational numbers and the completion of the algebraic closure of $Q_p$, respectively. Let $v_p$ be the normalized exponential valuation of $C_p$ with $$\mid$p$\mid$_p = p^{-v_p (p)} = p^{-1}$. We set $p^* = p$ for any prime p > 2 $p^* = 4 for p = 2$.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.191-207
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• 2000

Let R be a ommutative ring with unity and F a finite free R-module. For a nonnegative integer r, there exists a natural filtration of$S_r(S_2F)$ such that its associated graded module is isomorphic to $\Sigma_{{\lambda}{\epsilon}{\tau}_r}\;L_{\lambda}F$, where ${\Gamma}_{\gamma}$ set of partitions such that $$\mid${\lambda}$\mid$-2r,{{\widetilde}{\lambda}}-{{\widetilde}{\lambda}}_1},...,{{\widetilde}{\lambda}}_k},\;each\;{{\widetilde}{\lambda}}_t}$,is even. We call such filtrations plethysm formulas. We extend the above plethysm formula to the version of chain complexes. By plethysm formula we mean the composition of universally free functors. $Let{\emptyset}:G->F$ be a morphism of finite free R-modules. We construct the natural decomposition of $S_{r}(S_2{\emptyset})$,up to filtrations, whose associated graded complex is isomorphic to ${\Sigma}_{{\lambda}{\varepsilon}{\tau}}_r}\;L_{\lambda}{\emptyset}$.

• The Korean Journal of Quaternary Research
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• v.17 no.2
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• pp.63-69
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• 2003

Three tree-ring monsoon rainfall reconstructions from China and Korea have been used in this paper to investigate the variation of the East Asian summer monsoon over the past 160 years. Statistically, there is no linear correlation on a year-by-year basis between Chinese and Korean monsoon rainfall, but region-wide synchronous variation on decadal-scale was observed. Strong monsoon intervals (more rainfall) were 1860-1890, 1910-1925,1940-1960, and weak monsoon periods (dry or even drought) were 1890-1910, 1925-1940, 1960- present. Reconstructions also display that the East Asian summer monsoon suddenly changed from strong into weak around mid-1920, and the East Asian summer monsoon keeps going weak after 1960.