• Communications of the Korean Mathematical Society
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• v.36 no.1
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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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• v.13 no.1_2
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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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• v.34 no.5
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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 $f{\neq}0$.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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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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• v.27 no.6
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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.

• Journal of Korean Society of Environmental Engineers
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• v.22 no.10
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• pp.1851-1859
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• 2000

Crude oil-degrading bacteria were isolated from the sites contaminated by oil products. The isolates were identified as Acinetobacter sp. A132, Pseudomonas putida A422, Pseudomonas aeruginosa F721, F722, and Xanthomonas maltophilia B823. The results of investigation on the degradability of crude oil indicated that the strain A132 had the highest rate of $6.04g/L{\cdot}day$. Also, the strain A132 and F722 almost degraded each of n-alkane compounds between $nC_{10}$ and $nC_{32}$. The strain A422 degraded benzene and xylene but not n-alkane. The strain B823 grew somewhat in crude oil but did not entirely degrade other substrates used in this study. The results of the GC/FID analysis on the degradability of the mixed n-alkane compounds showed that the strain F722 could degrade 100% of the compounds with $nC_7{\sim}nC_{10}$ and more than 80% of those with $nC_{11}{\sim}nC_{24}$.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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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.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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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}.

• Honam Mathematical Journal
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• v.24 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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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.