• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.201-209
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• 2009

In this paper, we prove the stability of the functional equation $$\sum_{i=0}^3_3C_i(-1)^{3-i}f(ix+y)=0$$ in the sense of Th.M.Rassias on the punctured domain. Also, we investigate the superstability of the functional equation.

• Journal of the Korean Society of Costume
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• v.15
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• pp.21-45
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• 1990

The purpose of this thesis is to study the method of the reasonable pattern design. The studying method is based on the original principle of the trousers' cutting and I have a hypothesis about the trousers pattern which should be proved. When I selected the practical method, I made use of the international measuring rule, graph paper and tracing paper, in order to prove the new pattern design. The reasonable pattern design should be the one of the suitable original principles to be suited in the design through any measurement. Therefore, I have discussed the above mentioned design. I find out the conclusion to prove the hypothesis of pattern design with the experimental measure after showing the above mentiond design. The characteristics is as follows. First : To be convinient when walking, because of little degree as folding of the front part of trousers with the under-angle. Second : To be suitable in proportion to the length of trousers and the under-angle. Third ; When folding the center line of the Sapok (a name of one of the trousers parts), the length of the Sapoks is same and harmonized with the Sapoks because of the same angle of both Sapoks in any case of the measurement. Fourth : No correction of the lines when dressing, for the same points of the large Sapok and the small one. Fifth : To be easiness of the pattern design through the concrete measurement. I could find out a little extent errors of pattern showings, an easiness of dressing, scientification of formation in Korean trousers and standard of the practical measurement in the program to be presented as the result of studying.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.309-319
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• 1997

We introduce $R^i$-sets and give various relations between $R^i$-sets and prove that the hyperspace of a metric continuum containing any one of the $R^i$-set also contains $R^i$ and hence is not contractible.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.401-408
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• 2009

Let {$Y_i,-{\infty}<i<{\infty}$} be a doubly infinite sequence of identically distributed and ${\rho}^*$-mixing random variables and {$a_i,-{\infty}<i<{\infty}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence of $\{\sum\limits_{k=1}^n\;\sum\limits_{n=-\infty}^\infty\;a_{i+k}Y_i/n^{1/t};\;n{\geq}1\}$ under suitable conditions.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.499-501
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• 1994

Let ${X_n}$ be conditionally i.i.d. given $g \subset \sigma(X_n, n \geq 1)$. We will prove that $g$ is degenerate if and only if ${X_n, n \geq 1}$ are i.i.d. random variable(r.v.s). As a corollary the Hewitt-Savage zero-one law is obtained using the fact that interchageable process is conditionally i.i.d. given the $\sigma$-algebra of permutable events.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.667-680
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• 2014

In this paper, $\mathcal{I}$-scattered spaces are introduced, and their characterizations and properties are given. We prove that (X, ${\tau}$) is scattered if and only if (X, ${\tau}$, $\mathcal{I}$) is $\mathcal{I}$-scattered for any ideal $\mathcal{I}$ on X.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.455-467
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• 2014

In this paper, we consider the additive set-valued functional equation $nf(\sum_{i=1}^{n}x_i)=\sum_{i=1}^{n}f(x_i){\oplus}\sum_{1{\leq}i&lt;j{\leq}n}f(x_i+x_j)$ where $n{\geq}2$ is an integer, and prove the Hyers-Ulam stability of the functional equation.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.399-422
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• 1998

A useful method of proving the finite decidability of an equationally definable class V of algebras (i.e., variety) is to prove the decidability of the class of finite directly indecomposable members of V. The validity of this method relies on the well-known result of Feferman-Vaught: if a class K of first-order structures is decidable, then so is the class {$\prod$$_{i}$＜n/ $A_{i}$│ $A_{i}$ $\in$ X (i < n), n $\in$ $\omega$}. In this paper we show that the converse of this does not necessarily hold.d.d.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.653-666
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• 2007

Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)

• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.109-117
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• 2021

In this paper, as an application of a multivalued generalization of the Németh fixed point theorem, we will prove a new existence theorem of Nash equilibrium for a generalized game 𝓖 = (X_i; A_i, P_i)_i∈I with geodesic convex values in Hadamard manifolds.