• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.757-767
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• 2013

We investigate the general solution of the following functional equation and the generalized Hyers-Ulam-Rassias stability problem in quasi ${\beta}$-normed spaces and then the stability by using alternative fixed point method for the following quintic function $f:X{\rightarrow}Y$ such that f(3x+y)+f(3x-y)+5[f(x+y)+f(x-y)]=4[f(2x+y)+f(2x-y)]+2f(3x)-246f(x), for all $x,y{\in}X$.

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.61-69
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• 1991

By $C^{(1)}$[0, 1] we denote the Banach algebra of complex valued continuously differentiable functions on [0, 1] with norm given by $${\parallel}f{\parallel}=\sup_{x{\in}[0,1]}({\mid}f(x){\mid}+{\mid}f^{\prime}(x){\mid})\text{ for }f{\in}C^{(1)}$$. By A we denote the sub algebra of $C^{(1)}$ defined by $$A=\{f{\in}C^{(1)}:f(0)=f(1)\text{ and }f^{\prime}(0)=f^{\prime}(1)\}$$. By an isometry of A we mean a norm-preserving linear map of A onto itself. The purpose of this article is to describe the isometries of A. More precisely, we show tht any isometry of A is induced by a point map of the interval [0, 1] onto itself.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.293-300
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• 2020

In this article, we define a (an amply) F_δ-supplemented module in category of R-Mod. The general properties of F_δ-supplemented modules are briefly discussed. Then, concentrating on the F_δ-small submodule, we find the necessary and sufficient condition for F_δ- supplemented modules. Also, we introduce ascending chain condition for F_δ-small submodules of any module and establish a basic theorem for amply F_δ-supplemented modules by using π-projectivity.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.433-438
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• 2007

Let $\mathbb{A}=\mathbb{F}_q[T]$ and $k=\mathbb{F}_q(T)$. Assume q is odd, and fix a prime divisor ${\ell}$ of q - 1. Let P be a monic irreducible polynomial in A whose degree d is divisible by ${\ell}$. In this paper we define a subgroup $\tilde{C}_F$ of $\mathcal{O}^*_F$ which is generated by $\mathbb{F}^*_q$ and $\{{\eta}^{{\tau}^i}:0{\leq}i{\leq}{\ell}-1\}$ in $F=k(\sqrt[{\ell}]{P})$ and calculate the unit-index $[\mathcal{O}^*_F:\tilde{C}_F]={\ell}^{\ell-2}h(\mathcal{O}_F)$. This is a generalization of [3, Theorem 16.15].

• Journal of the Korean Mathematical Society
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• v.52 no.4
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• pp.685-697
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• 2015

For a field K, a square-free monomial ideal I of K[$x_1$, . . ., $x_n$] is called an f-ideal, if both its facet complex and Stanley-Reisner complex have the same f-vector. Furthermore, for an f-ideal I, if all monomials in the minimal generating set G(I) have the same degree d, then I is called an $(n, d)^{th}$ f-ideal. In this paper, we prove the existence of $(n, d)^{th}$ f-ideal for $d{\geq}2$ and $n{\geq}d+2$, and we also give some algorithms to construct $(n, d)^{th}$ f-ideals.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.11
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• pp.2145-2147
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• 2015

In this letter, we investigate the performance analysis of massive MIMO systems using MRT and ZF precodings according to the number of DoF. We analyze the ergodic received SINRs with MRT and ZF precodings as closed-forms over the number of DoF normalized by the number of antennas. In simulation results, we verify the analyzed results and observe that MRT precoding is better than ZF precoding in terms of the ergodic received SINR with a small number of DoF.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.435-441
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• 2016

Let G be a graph, and let g, f be two nonnegative integer-valued functions defined on V (G) with g(x) ≤ f(x) for each x ∈ V (G). A graph G is called a fractional (g, f, n)-critical graph if after deleting any n vertices of G the remaining graph of G admits a fractional (g, f)-factor. In this paper, we obtain a binding number condition for a graph to be a fractional (g, f, n)-critical graph, which is an extension of Zhou and Shen's previous result (S. Zhou, Q. Shen, On fractional (f, n)-critical graphs, Inform. Process. Lett. 109(2009)811-815). Furthermore, it is shown that the lower bound on the binding number condition is sharp.

• Korean Journal of Animal Reproduction
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• v.12 no.2
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• pp.77-83
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• 1988

This study was done with mouse embryo to assess effects of freezing media containing sucrose, freezing metods(1-F, 0.3$^{\circ}C$/min;2-F, 3-5$^{\circ}C$/min;3-F, 15$^{\circ}C$min;4-F, LN2 vapour) and cell freezers on the embryo survival determined using the FDA test. The results are summarized as follows. 1. The FDA score obtained with 1, 2, 3 and 4-F was 3.8, 3.6, 3.2 and 3.2, respectively. There was a significant difference(P<0.05) between 1-F, 3-F and 2-F, 4-F. 2. The score at the morular stage(3.8) higher(P<0.005) than the blastocyst stage of embryos(3.2). 3. No difference (P>0.05) was found between the score obtained with a automatic embryo freezer(4.0) and a liquid nitrogen container(3.7).

• Korean Journal Plant Pathology
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• v.11 no.4
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• pp.330-337
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• 1995

Forty-six isolates of Fusarium oxysporum collected from infected tomato plants and soils in greenhouses in Sedo, Chungnam and Angang, Kyeongbuk and 8 isolates of F. oxysporum f. sp. lycopersici from Japan and USA were used to determine vegetative compatibility groups (VCGs). Vegetative comaptibility was assessed on the basis of heterokaryon formation among nitrate nonutilizing mutants. All Korean isolates of F. oxysporum f. sp. lycopersici used in this study belonged to the same type of VCG (003) regardless of their geographic origin, cultivar and race, but they were incompatible with the foreign isolates of VCG 0030, 0031, 0032 and 0033. Based on the results, the Korean isolates of F. oxysporum f. sp. lycopersici were classified as a new VCG 003.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1095-1113
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• 2020

In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations $f^nf^{(k)}+Q_{d_*}(z,f)=R(z)e^{{\alpha}(z)}$ and fⁿf^(k) + Q_d(z, f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z), where $Q_{d_*}(z,f)$ and Q_d(z, f) are differential polynomials in f with small functions as coefficients, of degree d_* (≤ n - 1) and d (≤ n - 2) respectively, R, p₁, p₂ are non-vanishing small functions of f, and α, α₁, α₂ are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.