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

• Kyungpook Mathematical Journal
• /
• v.51 no.1
• /
• pp.69-76
• /
• 2011

In this paper, we introduce a partitioning ideal of a ternary semiring which is useful to develop the quotient structure of ternary semiring. Indeed we prove : 1) The quotient ternary semiring S/$I_{(Q)}$ is essentially independent of choice of Q. 2) If f : S ${\rightarrow}$ S' is a maximal ternary semiring homomorphism, then S/ker $f_{(Q)}$ ${\cong}$ S'. 3) Every partitioning ideal is subtractive. 4) Let I be a Q-ideal of a ternary semiring S. Then A is a subtractive ideal of S with I ${\subseteq}$ A if and only if A/$I_{(Q{\cap}A)}$ = {q + I : q ${\in}$ Q ${\cap}$ A} is a subtractive idea of S/$I_{(Q)}$.

• The Korean Journal of Ecology
• /
• v.20 no.2
• /
• pp.145-151
• /
• 1997

A census of the forest vegetation of Mt. Kaya National Park was taken with respect to the medthods of ordination and classification. Eight groups were classified by cluster analysis : Quercus mongolica, Q. mongolica-Sasa borealis, Q. serrata, Q. variabilis, Carpinus laxiflora, Cornus controversa, Fraxinus mandshurica and Pinus densiflora. Among them, the Q. mongolica group and Q. mongolica-S. borealis group, the F. mandshurica group and C. controversa group showed similar floristic compositions to each other. The interrelationship between the floristic compositon of the vegetation and soil environment was analyzed by PCA, the Q. mongolica group and the Q. mongolica-S. borealis group were distributed in areas of high CEC and total nitrogen content, while the Q. serrata. Q. variabilis. C. laxiflora and Pinus densiflora groups formed their communities in the more moderate areas of pH, soil moisture and soil organic matter. F. mandshurica and C. controversa groups were distributed in the areas of high soil moisture, soil organic matter, pH and available phosphate.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.525-530
• /
• 2015

Let D be an integrally closed domain with quotient field K, X be an indeterminate over D, $f=a_0+a_1X+{\cdots}+a_nX^n{\in}D[X]$ be irreducible in K[X], and $Q_f=fK[X]{\cap}D[X]$. In this paper, we show that $Q_f$ is a maximal ideal of D[X] if and only if $(\frac{a_1}{a_0},{\cdots},\frac{a_n}{a_0}){\subseteq}P$ for all nonzero prime ideals P of D; in this case, $Q_f=\frac{1}{a_0}fD[X]$. As a corollary, we have that if D is a Krull domain, then D has infinitely many height-one prime ideals if and only if each maximal ideal of D[X] has height ${\geq}2$.

• Communications of the Korean Mathematical Society
• /
• v.27 no.1
• /
• pp.107-116
• /
• 2012

Here, by using the symbolical method introduced by Burchnall and Chaundy, we aim at constructing certain expansion formulas for the generalized hypergeometric function $_pF_q$. In addition, using our expansion formulas for $_pF_q$, we present formulas of an analytic continuation of the Clausen hypergeometric function $_3F_2$, which are much simpler than an earlier known result. We also give some integral representations for $_3F_2$.

• Korean Journal of Mathematics
• /
• v.29 no.2
• /
• pp.361-370
• /
• 2021

Let 𝕂 be a complete ultrametric algebraically closed field and 𝓐 (𝕂) be the 𝕂-algebra of entire function on 𝕂. For any p-adic entire functions f ∈ 𝓐 (𝕂) and r > 0, we denote by |f|(r) the number sup {|f (x)| : |x| = r} where |·|(r) is a multiplicative norm on 𝓐 (𝕂). In this paper we study some growth properties of composite p-adic entire functions on the basis of their relative (p, q)-𝜑 order where p, q are any two positive integers and 𝜑 (r) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function of r.

• Proceedings of the KOR-KST Conference
• /
• 1999.10a
• /
• pp.211-216
• /
• 1999

• Journal for History of Mathematics
• /
• v.13 no.2
• /
• pp.151-160
• /
• 2000

In this paper we prove that for all irreducible complex characters of a finite group, there exist F-representations and a finite degree field extension F ⊇ Q, where Q is the rational number field.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.10 no.6
• /
• pp.105-113
• /
• 2006

This paper presents the results of an experimental investigation carried out to evaluate the mechanical properties of concrete mixtures in which fine(S) and coarse(G) aggregate was fully replaced with fly ash(FA). And flowability reduction problem in a large amount of fly ash concrete settled addition water($W_f$) in concrete mixture. In the test, water-cement ratio($W_c/C$) was 0.35, 0.45, and water-fly ash ratio($W_f/FA$) was 0.35, 0.45. The fly ash replacement is two different method of P and Q. The P method is mix property that the fly ash and addition water($W_f$) weight is equal to the aggregate weight [ $FA+W_f$ = G (or S)]. The Q method is mix property that fly ash is equal to aggregate weight, and added addition water($W_f$) [$FA+W_f$ > G (or S)]. Test were performed for properties of fresh concrete and compressive strength were determined at 3, 7, 28 and 91 days. The result, compressive strength was improvement that $W_c/C=0.35$, $W_f/FA=0.35$ and fine aggregate replacement in P method series than others. The flowability at Q method was improvement result than P method, but compressive strength was not. Test results indicate significant improvement in the strength properties and flowability of plain concrete by the inclusion of fly ash as fully replacement of fine and coarse aggregate, and can be effectively the fly ash replacement method.

• The Mathematical Education
• /
• v.21 no.3
• /
• pp.7-11
• /
• 1983

A measurable function f defined on a measurable subset A of the real line R is called pth power summable on A if │f│$^{p}$ is integrable on A and the set of all pth power summable functions on A is denoted by L$^{p}$ (A). For each member f in L$^{p}$ (A), we define ∥f∥$_{p}$ =(equation omitted) For real numbers p and q where (equation omitted) and (equation omitted), we discuss the Holder's inequality ∥fg∥$_1$<∥f∥$_{p}$ ∥g∥$_{q}$ , f$\in$L$^{p}$ (A), g$\in$L$^{q}$ (A) and the Minkowski inequality ∥＋g∥$_{p}$ <∥f∥$_{p}$ ＋∥g∥$_{p}$ , f,g$\in$L$^{p}$ (A). In this paper also discuss that L$_{p}$ (A) becomes a metric space with the metric $\rho$ : L$^{p}$ (A) $\times$L$^{p}$ (A) longrightarrow R where $\rho$(f,g)=∥f-g∥$_{p}$ , f,g$\in$L$^{p}$ (A). Then, in this paper prove the Riesz-Fischer theorem, i.e., the space L$^{p}$ (A) is complete and that the space L$^{p}$ (A) is separable.