• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.927-938
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• 2011

Let G be an abelian monoid with identity e. Let R be a G-graded commutative ring, and M a graded R-module. In this paper we first introduce the concept of graded primal submodules of M an give some basic results concerning this class of submodules. Then we characterize the graded primal ideals of the idealization R(+)M.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.463-480
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• 2013

We in this note introduce a concept, so called nil generalized power serieswise Armendariz ring, that is a generalization of both S-Armendariz rings and nil power serieswise Armendariz rings. We first observe the basic properties of nil generalized power serieswise Armendariz rings, constructing typical examples. We next study the relationship between the nilpotent property of R and that of the generalized power series ring [[$R^{S,{\leq}}$]] whenever R is nil generalized power serieswise Armendariz.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1513-1528
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• 2018

The aim of this paper is to introduce the concept of generalized cone metric spaces over Banach algebras as a generalization of generalized metric spaces and present several fixed point results of a class of contractive mappings in generalized cone metric spaces over Banach algebras. Moreover, in order to support our main results, one example is given at the end of this paper.

• Korean Management Science Review
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• v.26 no.1
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• pp.161-169
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• 2009

A traffic analysis on the Internet has an advantage for obtaining the characteristics of transferred packets. There were many studies to understand the characteristics of the Internet traffic with mathematical statistical approach. The approach of this study is different from previous studies. We first introduced a virtual network concept to present the Internet as a simplified mathematical model. It also represents each traffic flowing on the Internet as a parallel Gaussian channel on the virtual network. We suggest the optimal capacity of each parallel Gaussian channel using some related studies on the Gaussian channel model.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.155-165
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• 2009

We investigate the growth of solutions of complex linear differential equations in the unit disc. We obtain properties of solutions of differential equations with entire coefficients. We use the concept of the hyper order to estimate the growth of solutions.

• Journal of Korean Society for Quality Management
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• v.15 no.1
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• pp.2-12
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• 1987

Warranty cost usually involves complex factors paticularly when the product concerned consists of a great deal of parts. In spite of that it can be assessed by means of rather simple mathematical expression, it is possible to realistically appraise the sensitivity to any type of quality policy. This paper thus presents the mathematical concept related to the warranty cost and the general relationship showing that quality policy can be established in connection with the economic quality level.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.443-451
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• 2016

In this paper, we introduce the concept of a symmetric bi-f-multiplier in incline algebras and give some properties of incline algebras. Also, we characterize Ker(D) and $Fix_a(D)$ by symmetric bi-f-multipliers in incline algebras.

• East Asian mathematical journal
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• v.31 no.3
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• pp.357-362
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• 2015

For a ring R of imaginary quadratic integers, using a concept of a unitary number system in place of the Motzkin's universal side divisor, we show that the following statements are equivalent: (1) R is Euclidean. (2) R has a unitary number system. (3) R is norm-Euclidean. Through an application of the above theorem we see that R admits binary or ternary number systems if and only if R is Euclidean.

• East Asian mathematical journal
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• v.26 no.1
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• pp.49-58
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• 2010

In this paper, we consider and study a new class of generalized vector quasi-variational type inequalities and obtain some existence theorems for both under compact and noncompact assumptions in topological vector spaces without using monotonicity. For the noncompact case, we use the concept of escaping sequences.

• East Asian mathematical journal
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• v.23 no.2
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• pp.159-174
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• 2007

In this paper, the concepts of pairwise fuzzy $G_{\delta}$-connected spaces and pairwise fuzzy $G_{\delta}$-extremally disconnected spaces are introduced. The concept of pairwise fuzzy $G_{\delta}$-basically disconnected spaces is defined. Characterizations of the above spaces are given besides giving several examples. Interrelations among the spaces introduced are discussed and some relevant counter examples are given.