• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.156-162
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• 1998

The main objective of this paper is to study the boundedness of solutions of the differential equation $L_{n} {\chi}＋F(t,{\chi}) = f(t), n {\geq} 2 $(*) Necessary and sufficient conditions for boundedness of all solutions of (*) will be obtainded. The asymptotic behavior of solutions of (*) will also be studied.

• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.61-72
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• 2016

In this paper, a boundary version of the Schwarz lemma for the holom- rophic function satisfying f(a) = b, |a| < 1, b ∈ ℂ and ℜf(z) > α, 0 ≤ α < |b| for |z| < 1 is invetigated. Also, we estimate a modulus of the angular derivative of f(z) function at the boundary point c with ℜf(c) = a. The sharpness of these inequalities is also proved.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.459-467
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• 2013

In this paper, Matlis injective modules are introduced and studied. It is shown that every R-module has a (special) Matlis injective preenvelope over any ring R and every right R-module has a Matlis injective envelope when R is a right Noetherian ring. Moreover, it is shown that every right R-module has an ${\mathcal{F}}^{{\perp}1}$-envelope when R is a right Noetherian ring and $\mathcal{F}$ is a class of injective right R-modules.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.9-18
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• 2007

In this paper we establish the existence theorem of the operator-valued function space integral $K_{\lambda}(F)$ for $\lambda\in\mathbb{C}_{+,\lambda_0}^\sim$ where F is of the form (1.1). Our result is a generalization for Johnson and Skoug result in [8].

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.9-16
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• 1995

D. Dubois and H. Prade introduced the notions of fuzzy numbers and defined its basic operations [3]. R. Goetschel, W. Voxman, A. Kaufmann, M. Gupta and G. Zhang [4,5,6,9] have done much work about fuzzy numbers. Let $\mathbb{R}$ the set of all real numbers and $F^{*}(\mathbb{R})$ all fuzzy subsets defined on $\mathbb{R}$. G. Zhang [8] defined the fuzzy number $\tilde{a}\;\in\;F^{*}(\mathbb{R})$ as follows : (omitted)

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.27-33
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• 1997

Let (M = B$\times$f F, g) be an ($n \geq3$ )-dimensional differential manifold with Riemannian metric g. We solve the following elliptic nonlinear partial differential equation (equation omitted). where $\Delta_{g}$ is the Laplacian in the $\Delta$g-metric and ($h(\chi)$) is the scalar curvature of g and ($H(\chi)$) is a function on M.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.115-119
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• 1997

We show that if $f_{i}$:$X_{i}$ longrightarrow Y is strongly continuous(resp. weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly $\theta$-continuous, $\theta$-continuous, g-continuous, V-map), then F : $X_1 \bigoplus X_2$longrightarrow Y is strongly continuous(resp.weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly $\theta$-continuous, $\theta$-continuous, g-continuous, V-map).

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.57-63
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• 2005

Let ∑(p)(p ∈ N) be the class of functions f(z) = z/sup -p/ + α/sub 1-p/ z/sup 1-p/ + α/sub 2-p/z/sup 2-p/ + ... analytic in 0 < ｜z｜ < 1 and let M(p, λ, μ)(0 < λ≤ 2 and 2λ(λ - 1) ≤ μ ≤ λ²) denote the class of functions f(z) ∈ ∑(p) which satisfy (equation omitted). The object of the present paper is to derive some properties of functions in the class M(p, λ, μ).

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.45-54
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• 1998

We study the space-times that have a unique terminal indecomposable past set or a unique terminal indecomposable future set and examine their causal boundary, and we investigate some conditions for the warped product space-times of the form (a, b) ${\times}_fF$ to have a unique terminal indecomposable past set or a unique terminal indecomposable future set.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.95-101
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• 1996

In this paper, we extend Ganelius' lemma in Anderson [1]. In the Ganelius' original version several of the ${\alpha}$$\sub$k/ are equal to 1, but in our extension theorem we have the ${\alpha}$$\sub$k/ distinct and all unequal to 1. Then our theorem can be used to introduce an indefinite quadrature formula for ∫$\sub$-1/$\^$1/ f($\chi$)d$\chi$, f $\in$ H$\^$p/, with p ＞ 1. We will also correct an error in the proof of Ganelius' theorem provided in Ganelius [2].(omitted)