• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.185-195
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• 2005

This article is concerned with the intraclass correlation in survey sampling. From a design-based viewpoint the intraclass correlation is generalized to a finite population with unequal sized clusters. Under simple random cluster sampling the intraclass correlation is given in an explicit form, which is a generalization of the usual one. The range of it is found and the design effect is expressed by means of it. An example is given to compare the intraclass correlation with the homogeneity measure numerically, which shows that two measures are not the same except some limited cases.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.13-30
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• 2002

A generalization of Liouville's theorem on integration in finite terms, by enlarging the class of fields to an extension called Ei-Gamma extension is established. This extension includes the $\varepsilon$L-elementary extension of Singer, Saunders and Caviness and contains the Gamma function.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.333-342
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• 2008

We introduce weak Armendariz ideals which are a generalization of ideals have the weakly insertion of factors property (or simply weakly IFP) and investigate their properties. Moreover, we prove that, if I is a weak Armendariz ideal of R, then I[x] is a weak Armendariz ideal of R[x]. As a consequence, we show that, R is weak Armendariz if and only if R[x] is a weak Armendariz ring. Also we obtain a generalization of [8] and [9].

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.359-373
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• 2017

In this paper, we propose the Stancu type generalization of a kind of modified q-Gamma operators. We estimate the moments of these operators and give the basic convergence theorem. We also obtain the Voronovskaja type theorem. Furthermore, we obtain the local approximation, rate of convergence and weighted approximation for these operators.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.649-652
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• 2007

In this note we provide a generalization of the Schur-Cohn test. If $p_n$ be a polynomial of degree n then $p_n$ is a reduced-stable polynomial whose reduced degree is equal to r if and only if $D_n\;:=\;P_nQ_n^{-1}$ is a contraction such that rank ($I-D_nD_n^*$) = r.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.425-434
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• 2014

In this paper, we introduce a new concept of a countably sequential space which is a generalization of a sequential space and study some properties of a countably sequential space and relations among the space and related spaces.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Honam Mathematical Journal
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• v.37 no.3
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• pp.269-279
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• 2015

Atanassov introduced another fuzzy object, called intu- itionistic fuzzy set as a generalization of the concept of fuzzy subset. The aim of this paper is the elaboration of a representation theory of involutive interval-valued Łukasiewicz-Moisil algebras by using the notion of intuitionistic fuzzy sets.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.439-454
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• 2014

We deal with the boundedness of the n-th derivatives of Bloch-type functions and Toeplitz operators and give a relationship between Bloch-type spaces and ranges of Toeplitz operators. Also we prove that the vanishing property of ${\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}}$ on the boundary of $\mathbb{D}$ implies the compactness of Toeplitz operators and introduce a generalization of Bloch-type spaces.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.529-537
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• 2009

Generalized Menger space introduced by the present authors is a generalization of Menger space as well as a probabilistic generalization of generalized metric space introduced by Branciari [Publ. Math. Debrecen 57 (2000), no. 1-2, 31-37]. In this paper we prove a Kannan type fixed point theorem in generalized Menger spaces. We also support our result by an example.