• 대한수학회논문집
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• 제36권1호
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• pp.1-10
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• 2021

Let R and S be two commutative rings, J be an ideal of S and f : R → S be a ring homomorphism. The amalgamation of R and S along J with respect to f, denoted by R ⋈f J, is the special subring of R × S defined by R ⋈f J = {(a, f(a) + j) | a ∈ R, j ∈ J}. In this paper, we study some basic properties of a special kind of R ⋈f J-modules, called the amalgamation of M and N along J with respect to ��, and defined by M ⋈�� JN := {(m, ��(m) + n) | m ∈ M and n ∈ JN}, where �� : M → N is an R-module homomorphism. The new results generalize some known results on the amalgamation of rings and the duplication of a module along an ideal.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } for n $\geq$ 1. We say $X_{j}$ is an upper record value of { $X_{n}$ , n$\geq$1} if $Y_{j}$ > $Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, n$\geq$1, where u(n) = min{j｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• East Asian mathematical journal
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• 제34권5호
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• pp.703-713
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• 2018

Let $N{\geq}3$, $2^*=2N/(N-2)$ and $p{\in}(2,2^*)$. Our purpose in this paper is to consider multiple existence of solutions of problem $$-{\Delta}u-{\frac{\mu}{{\mid}x{\mid}^2}}+{\alpha}u={\mid}u{\mid}^{p-2}u+{\lambda}f\;u{\in}H^1({\mathbb{R}}^n)$$, where a, ${\lambda}$ > 0, ${\mu}{\in}(0,(N-2)^2/4)f{\in}H^{-1}({\mathbb{R}}^N)$, $f{\geq}0$ and $f{\neq}0$.

• 대한수학회지
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• 제57권6호
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• pp.1535-1549
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• 2020

This paper deals with the inverse of tails of Hurwitz zeta function. More precisely, for any positive integer s ≥ 2 and 0 ≤ a < 1, we give an algorithm for finding a simple form of f_s,a(n) such that $$\lim_{n{\rightarrow}{\infty}}\{\({\sum\limits_{k=n}^{\infty}}{\frac{1}{(k+a)^s}}\)^{-1}-f_{s,a}(n)\}=0$$. We show that f_s,a(n) is a polynomial in n-a of order s-1. All coefficients of f_s,a(n) are represented in terms of Bernoulli numbers.

• Journal of Nutrition and Health
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• 제27권6호
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• pp.574-582
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• 1994

The effects of age and dietary fatty acid composition on prostagladin production was investigated in Sprague-Dawley strain male rats. Animals weighing 88.6$\pm$2.2g were fed 10% dietary fat(W/W, 20% of total energy). The P/S ratios of dietary lipid were three levels(0.5, 1, 2) and there were three different levels of n-6/n-3 fatty acid ratio(2, 4, 8) in each P/S ratio. The experimental period were 1 month and 12 months, respectively. The results of this study were as follows. As the age of rats increased, the plasma thromboxane B2 production increased, but aorta 6-keto prostaglandin F1$\alpha$ decreased. When a higher amount of n-3 fatty acid was fed in each P/S ratio, the relative percentage of linolenic acid and EPA in platelet increased.

• 대한환경공학회지
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• 제22권10호
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• pp.1851-1859
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• 2000

원유를 분해하는 미생물을 석유화합물로 오염된 토양으로부터 분리하였고, 이들은 Acinetobacter sp. A132, Pseudomonas putida A422, Pseudomonas aeruginosa F721, F722, 그리고 Xanthomonas maltophilia B823으로 동정되었다. 이들 미생물의 유류 분해율을 조사한 결과, strain A132가 $6.04g/L{\cdot}day$로 가장 놓은 분해율을 나타내었다. 탄소수가 10개에서 32개 사이의 n-alkane 화합물을 기질로 사용하여 각각의 화합물에 대한 분해능력을 조사한 결과, strain A132와 F722는 대부분의 기질에 대하여 분해능력을 보였다. Strain A422는 n-alkane 화합물에 대한 분해능력은 높지 않았으나, benzene과 xylene을 분해하는 능력을 가지고 있었다. Strain B823은 원유에서는 조금 생장하였으나, 본 연구에서 사용한 다른 기질들에 대해서는 전혀 분해능력을 보이지 않았다. 한편, n-alkane 혼합화합물에 대한 분해율을 GC/FID로 분석한 결과, strain F722는 $nC_7{\sim}nC_{10}$에서 100%, $nC_{11}{\sim}nC_{24}$에서는 80% 이상 의 높은 분해율을 나타내었다.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.27-40
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• 2002

For two integers m, n with m $\leq$ n, an [m,n]-factor F in a graph G is a spanning subgraph of G with m $\leq$ d$\_$F/(v) $\leq$ n for all v ∈ V(F). In 1996, H. Enomoto et al. proved that every 3-connected Planar graph G with d$\_$G/(v) $\geq$ 4 for all v ∈ V(G) contains a [2,3]-factor. In this paper. we extend their result to all 3-connected locally finite infinite planar graphs containing no unbounded faces.

• 대한수학회보
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• 제26권2호
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• pp.119-126
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• 1989

Throughout this paper, X will always denote a Banach space over the complex numbers C, and L(X) will denote the Banach algebra of all continuous linear operators on X. Operator will always mean continuous linear operator. An n-tuple of operators T$_{1}$,..,T$_{n}$ on X will be denoted by over ^ T=(T$_{1}$,..,T$_{n}$ ). Let L$^{n}$ (X) be the set of all n-tuples of operators on X. X' will denote the dual space of X, S(X) its unit sphere and .PI.(X) the subset of X*X' defined by .PI.(X)={(x,f).mem.X*X': ∥x∥=∥f∥=f(x)=1}.

• 호남수학학술지
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• 제24권1호
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• pp.75-86
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• 2002

A Nielsen number $\bar{N}(f:X-A)$ is a homotopy invariant lower bound for the number of fixed points on X-A where X is a compact connected polyhedron and A is a connected subpolyhedron of X. This number is extended to Nielsen type numbers $\bar{NP_{n}}(f:X-A)$ of least period n and $\bar{N{\phi}_{n}}(f:X-A)$ of the nth iterate on X-A where the subpolyhedron A of a compact connected polyhedron X is no longer path connected.

• 대한수학회논문집
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• 제38권2호
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• pp.643-648
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• 2023

Let X be a simply connected rationally elliptic space such that H²(X; ℚ) ≠ 0. In this paper, we show that if H²ⁿ(X^[2n-2]; ℚ) = 0 or if π_2n(X²ⁿ) ⊗ ℚ = 0 for all n, then X is an F₀-space.