• 대한수학회지
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• 제25권2호
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• pp.273-287
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• 1988

• 대한수학회논문집
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• 제1권1호
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• pp.81-89
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• 1986

• 대한수학회논문집
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• 제17권3호
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• pp.403-407
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• 2002

In this note We discuss the Uniformity in BCI-algebras using Zhang's congruence relation.

• 충청수학회지
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• 제36권4호
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• pp.245-253
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• 2023

Let G be a semialgebraic group not necessarily compact. In this paper, we prove that the orbit space of every proper semialgebraic G-set has a semialgebraic structure.

• 대한수학회보
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• 제54권4호
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• pp.1123-1139
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• 2017

The aim in this note is to describe some classes of rings in relation to factorization by prime radical, upper nilradical, and Jacobson radical. We introduce the concepts of tpr ring, tunr ring, and tjr ring in the process, respectively. Their ring theoretical structures are investigated in relation to various sorts of factor rings and extensions. We also study the structure of noncommutative tpr (tunr, tjr) rings of minimal order, which can be a base of constructing examples of various ring structures. Various sorts of structures of known examples are studied in relation with the topics of this note.

• 호남수학학술지
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• 제36권3호
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• pp.669-678
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• 2014

We investigate various properties of ${\kappa}$-net convergence structures and define a ${\kappa}$-net-based continuous function on ${\kappa}$-net $\mathcal{L}^+$-convergence structures, and study relationships between continuity and ${\kappa}$-net-based continuity on ${\kappa}$-net $\mathcal{L}^+$-convergence structures. We also provide some characterizations of ${\kappa}$-net-based continuity.

• 충청수학회지
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• 제29권1호
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• pp.177-186
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• 2016

For a map $f:A{\rightarrow}X$, there are concepts of $H^f$-spaces, $T^f$-spaces, which are generalized ones of H-spaces [17,18]. In general, Any H-space is an $H^f$-space, any $H^f$-space is a $T^f$-space. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain some sufficient conditions to having liftings $H^{\bar{f}}$-structures and $T^{\bar{f}}$-structures on $E_k$ of $H^f$-structures and $T^f$-structures on X respectively. We can also obtain some results about $H^f$-spaces and $T^f$-spaces in Postnikov systems for spaces, which are generalizations of Kahn's result about H-spaces.

• 대한수학회논문집
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• 제28권3호
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• pp.589-596
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• 2013

This paper is an attempt to study and introduce the notion of ${\omega}$-dense set in weak structures and the notion of m-dense set in minimal structures. We have also investigate the relationships between ${\omega}$-dense sets, $m$-dense sets, ${\sigma}({\omega})$ sets, ${\pi}({\omega})$ sets, $r({\omega})$ sets, ${\beta}({\omega})$ sets, m-semiopen sets and $m$-preopen sets. Further we give some representations of the above generalized sets in minimal structures as well as in weak structures.

• Steel and Composite Structures
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• 제48권1호
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• pp.73-88
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• 2023

This paper presents a novel implicit level set method for topology optimization of functionally graded (FG) structures with pre-existing discontinuities (pre-cracks) using radial basis functions (RBF). The mathematical formulation of the optimization problem is developed by incorporating RBF-based nodal densities as design variables and minimizing compliance as the objective function. To accurately capture crack-tip behavior, crack-tip enrichment functions are introduced, and an eXtended Finite Element Method (X-FEM) is employed for analyzing the mechanical response of FG structures with strong discontinuities. The enforcement of boundary conditions is achieved using the Hamilton-Jacobi method. The study provides detailed mathematical expressions for topology optimization of systems with defects using FG materials. Numerical examples are presented to demonstrate the efficiency and reliability of the proposed methodology.

• 대한수학회보
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• 제39권1호
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• pp.133-140
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• 2002

On compact complex hyperbolic manifolds of complex dimension two, we show that the dimension of the space of infinitesimal deformations of self-dual conformal structures is smaller than that of the deformation obstruction space and that every self-dual metric with covariantly constant Ricci tensor must be a standard one upto rescalings and diffeomorphisms.