• Korean Journal of Mathematics
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• v.17 no.4
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• pp.349-359
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• 2009

As students have been familiar to Internet or media which has big visual effects rather than letters, they preferred the class in computer lab to theoretical class. The class in computer lab showed all the students good reactions in concern and interest. Statistics achievements of high level students in 2008 became better than that in 2007 but those of low level students became worse than that in 2007. I analyze the reason why the achievements of low level students have become worse. The purpose of this study is to supplement of the trouble of the class in computer lab and find out a better teaching and develop mathematics education's satisfaction and qualification.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.85-91
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• 1995

For a locally compact Hausdorff space, we denote by $C_0(X)$ the Banach space of all continuous complex valued functions defined on X which vanish at infinity, equipped with the usual sup norm. In case X is compact, we write C(X) instead of $C_0(X)$. A well-known Banach-Stone theorem states that the existence of an isometry between the function spaces $C_0(X)$ and $C_0(Y)$ implies X and Y are homemorphic. D. Amir [1] and M. Cambern [2] independently generalized this theorem by proving that if $C_0(X)$ and $C_0(Y)$ are isomorphic under an isomorphism T satisfying $\left\$\mid$ T \right\$\mid$ \left\$\mid$ T^1 \right\$\mid$ < 2$, then X and Y must also be homeomorphic.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.715-726
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• 2010

We continue the study of fully idempotent rings initiated by Courter. It is shown that a (semi)prime ring, but not fully idempotent, can be always constructed from any (semi)prime ring. It is shown that the full idempotence is both Morita invariant and a hereditary radical property, obtaining $hs(Mat_n(R))\;=\;Mat_n(hs(R))$ for any ring R where hs(-) means the sum of all fully idempotent ideals. A non-semiprimitive fully idempotent ring with identity is constructed from the Smoktunowicz's simple nil ring. It is proved that the full idempotence is preserved by the classical quotient rings. More properties of fully idempotent rings are examined and necessary examples are found or constructed in the process.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.379-396
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• 2004

In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space E$_2$$^4$. Also, we obtain the complete classification theorems for the flat rotation surfaces with finite type Gauss map, pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. In fact, we characterize the flat rotation surfaces of finite type immersion with the Gauss map and the mean curvature vector field, namely the Gauss map of finite type, pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surfaces with respect to the induced metric.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.797-800
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• 2008

Let R be a ring and I be a proper ideal of R. For the case of R being commutative, Anderson proved that (*) there are only finitely many prime ideals minimal over I whenever every prime ideal minimal over I is finitely generated. We in this note extend the class of rings that satisfies the condition (*) to noncommutative rings, so called homomorphically IFP, which is a generalization of commutative rings. As a corollary we obtain that there are only finitely many minimal prime ideals in the polynomial ring over R when every minimal prime ideal of a homomorphically IFP ring R is finitely generated.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.89-100
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• 2010

Let g = (V, E, ${\mu}$) be a weighted directed tree, where V is a vertex set, E is an edge set, and ${\mu}$ is ${\sigma}$-finite measure on V. The tree g induces a composition operator C on the Hilbert space $l^2$(V). Hand-type directed trees are defined and characterized the weak hyponormalities of such C in this note. Also some additional related properties are discussed. In addition, some examples related to directed hand-type trees are provided to separate classes of weak-hyponormal operators.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.349-371
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• 2011

Using the "belongs to" relation and "quasi-coincident with" relation between a fuzzy point and a fuzzy subgroup, Bhakat and Das, in 1992 and 1996, initiated general types of fuzzy subgroups which are a generalization of Rosenfeld's fuzzy subgroups. In this paper, more general notions of "belongs to" and "quasi-coincident with" relation between a fuzzy point and a fuzzy set are provided, and more general formulations of general types of fuzzy (normal) subgroups by Bhakat and Das are discussed. Furthermore, general type of coset is introduced, and related fundamental properties are investigated.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.129-135
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• 2012

The aim of this paper is to establish the well-known and very useful classical Saalsch$\ddot{u}$tz's theorem for the series $_3F_2$(1) by following a different method. In addition to this, two summation formulas closely related to the Saalsch$\ddot{u}$tz's theorem have also been obtained. The results established in this paper are further utilized to show how one can obtain certain known and useful hypergeometric identities for the series $_3F_2$(1) and $_4F_3(1)$ already available in the literature.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.251-274
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• 2020

We study a dynamical system that was originally defined by Romik in 2008 using an old theorem of Berggren concerning Pythagorean triples. Romik's system is closely related to the Farey map on the unit interval which generates an additive continued fraction algorithm. We explore some number theoretical properties of the Romik system. In particular, we prove an analogue of Lagrange's theorem in the case of the Romik system on the unit quarter circle, which states that a point possesses an eventually periodic digit expansion if and only if the point is defined over a real quadratic extension field of rationals.

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.275-283
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• 2015

Let T be a bounded linear operator on a complex Hilbert space H. For a positive integer k, an operator T is said to be a k-quasi-2-isometric operator if T^∗k(T^∗2T² − 2T^∗T + I)T^k = 0, which is a generalization of 2-isometric operator. In this paper, we consider basic structural properties of k-quasi-2-isometric operators. Moreover, we give some examples of k-quasi-2-isometric operators. Finally, we prove that generalized Weyl’s theorem holds for polynomially k-quasi-2-isometric operators.