• Korean Journal of Mathematics
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• v.4 no.1
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• pp.45-49
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• 1996

Let $F_0$ be the maximal real subfield of $\mathbb{Q}({\zeta}_q+{\zeta}_q^{-1})$ and $F_{\infty}={\cup}_{n{\geq}0}F_n$ be its basic $\mathbb{Z}_p$-extension. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $F_n$. The aim of this paper is to examine the injectivity of the natural $mapA_n{\rightarrow}A_m$ induced by the inclusion $F_n{\rightarrow}F_m$ when $m>n{\geq}0$. By using cyclotomic units of $F_n$ and by applying cohomology theory, one gets the following result: If $p$ does not divide the order of $A_1$, then $A_n{\rightarrow}A_m$ is injective for all $m>n{\geq}0$.

• Journal of the Korean Statistical Society
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• v.8 no.2
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• pp.107-109
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• 1979

Consider a linear model with n observations and k explanatory variables: (1)b $y=X\beta+u, u\simN(0,\sigma^2I_n)$. We assume that the model satisfies the ideal conditions. Consider the general linear constraints on regression coefficient vector: (2) $R\beta=r$, where R and r are known matrices of orders $q\timesk$ and q\times1$ respectively, and the rank of R is $qk+q$.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.563-568
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• 1996

In this paper we study the ramification of prime ideals in the dihedral octic extension N over Q and estimate the possible discriminants of the octic number field N.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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• pp.553-562
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• 2014

In this paper we study of densities of the 4-rank of narrow ideal class groups of real quadratic function fields over the rational function field $\mathbb{F}_q(T)$ when $q{\equiv}3$ mod 4.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.547-553
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• 2010

In this paper we prove that real quadratic function field F over ${\mathbb{F}}_q(T)$ has infinite 2-class field tower if the 4-rank of narrow ideal class group of F is equal to or greater than 4 when $q{\equiv}3$ mod 4.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.1
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• pp.21-32
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• 2002

In this paper, for any prime q, new cyclic difference sets with Singer parameter equation omitted are constructed by using the q-ary sequences (d-homogeneous functions) of period $q_n$-1. When q is a power of 3, new cyclic difference sets with Singer parameter equation omitted are constructed from the ternary sequences of period $q_n$-1 with ideal autocorrealtion found by Helleseth, Kumar and Martinsen.

• Proceedings of the Korean Society of Crop Science Conference
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• 2022.10a
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• pp.280-280
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• 2022

Tiller angle, defined as the angle between the main stem and its side tillers, is one of the main target traits selected inbreeding to achieve the ideal plant type and increase rice yield. Therefore, the discovery and identification of tiller angle-related genes can provide architecture and yield. In the present work, using QTL analysis hence a total of 8 quantitative trait loci (QTLs) were detected based on the phenotype data of tiller angle and tiller crown width in two years. Among them, four QTLs (qTA9, qCW9, qTA9-1, qCW9-1) were overlapped at marker interval RM6235-RM24288 on chromosome 9 with a large effect value regarded as stable major QTL. Twenty tiller angle-related genes were selected from the target region and the relative gene expression levels were checked in five compact type lines, five spreading type lines, and their parental lines. Finally, OsSA URq9 which belongs auxin-responsive SMALL AUXIN UP RNA (SAUR) protein family was selected as a target gene. Overall, this work will help broaden our understanding of the genetic control of tiller angle and tiller crown width, and this study provides both a good theoretical basis and a new genetic resource for the breeding of ideal-type rice.

• Proceedings of the Korean Geotechical Society Conference
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• 1996.04a
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• pp.1-20
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• 1996

• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.501-517
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• 2007

In this paper, we introduce and study a new class containing absolutely summing multilinear mappings and polynomials, which we call multiple weakly summing multilinear mappings and polynomials. We investigate some interesting properties about multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials defined on Banach spaces: In particular, we prove a kind of Dvoretzky-Rogers' Theorem and an ideal property for multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials. We also prove that the Aron-Berner extensions of multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials are also multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing.