• 대한수학회논문집
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• 제34권4호
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• pp.1105-1115
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• 2019

For positive integers n and k, let $S_k(n)$ and $S^{\prime}_k(n)$ be the sums of the elements in the finite sets {$x^k:1{\leq}x{\leq}n$, (x, n) = 1} and {$x^k:1{\leq}x{\leq}n/2$, (x, n) = 1}respectively. The formulae for both $S_k(n)$ and $S^{\prime}_k(n)$ are established. The explicit formulae when k = 1, 2, 3 are also given.

• 한국수학사학회지
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• 제22권2호
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• pp.53-68
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• 2009

고대 그리스에서 발현된 수학의 무한 개념은 헤브라이인의 유대교 전통인 카발라의 영향을 받아 중세 기독교 교부 철학자들에 의해 보다 성숙되어져 갔으며, 그 후 기독교의 무한사상이 르네상스 시대에는 화가들에 의해 원근법으로 구체화되었다. 본 논문에서는 그리스 시대부터 발전된 무한 개념의 경로를 살펴보고, 근대와 19세기 이후 무한수학이 발달될 때 당시 미술에서는 무한 개념이 어떻게 표현되었는지 그 시대정신을 고찰한다.

• 대한수학회보
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• 제50권3호
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• pp.747-752
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• 2013

It's known that one could use a fixed loxodromic or parabolic element in $M(\bar{\mathbb{R}}^n)$ as a test map to test the discreteness of a non-elementary M$\ddot{o}$bius group G. In this paper, we discuss the discreteness of G by using a fixed elliptic element.

• 대한수학회논문집
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• 제9권4호
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• pp.945-950
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• 1994

Although the study of the limit points of discrete groups of M$\ddot{o}$bius transformations has been a fertile area for many decades, there are some very natural topological properties of the limit points which appear not to have been previously examined. Let $\Gamma$ be a nonelementary discrete group of hyperbolic isometries acting on the Poincare disc $B^m, m \geq 2$, and let $p \in \partial B^m$ be a limit point of $\Gamma$. By a neighborhood of p, we will always mean an open neighborhood of p in $\partial B^m$.

• 호남수학학술지
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• 제37권4호
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• pp.423-429
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• 2015

Dirichlet series is a Riemann zeta function attached with an arithmetic function. Here, we studied the properties of Dirichlet series and found some identities between arithmetic functions.

• 대한수학회논문집
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• 제31권1호
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• pp.177-184
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• 2016

In this paper, we establish some conjugacy criteria of $M\ddot{o}bius$ groups in infinite dimension by using Clifford matrices. This extends the corresponding known results in finite dimensional setting.

• 영어영문학
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• 제64권2호
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• pp.299-305
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• 2018

Near / Miss, Charles Bernstein's poetry collection, is replete with poems of distinctive styles and pluralistic forms in his idiosyncratic and artistic cosmos. With poetic antics, queerness, sarcasm, irony, and humor, the book showcases the motif of loss, chaos and trauma in postmodern America and the world. The multiplicity and multi-dimensional $M{\ddot{o}}bius$ effect in Near / Miss echo earlier Bernstein's poems, as well as poems by ancient and contemporary poets, with visual artists and musicians, and rabbis and Jewish philosophers. I argue that Near / Miss offers an apotheosis of echopoetics, which has been launched in his previous book Pitch of Poetry. Poems in the book reveal the dark and thick "pitch," namely the queer, the uncanny, the invisible, the disabled, the dispossessed, and the silenced poetic Other and make it explicit. The estrangement and alienation of $clich{\acute{e}}$ through diverse malaprops, mondegreens, non-sequiturs and fragmentations in Near / Miss aim at deconstructing the fixation of language so as to display the poetic Other. The motif of "nothingness" in echopoetics significantly multiplies its meanings. Nothingness mainly refers to the loss of origin, the defiance of tyranny, and the sublimity of the universe and the poetic Other. Melding his personal loss and misfortune, the current political discontent and the postmodern chaos in America and the world, nothingness in echopoetics resonates with American literary tradition and Zen with a healing and transforming power.

• 대한수학회보
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• 제49권1호
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• pp.57-61
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• 2012

It is well known that one could use a fixed loxodromic or parabolic element of a non-elementary group $G{\subset}M(\bar{\mathbb{R}}^n)$ as a test map to test the discreteness of G. In this paper, we show that a test map need not be in G. We also construct an example to show that the similar result using an elliptic element as a test map does not hold.

• 충청수학회지
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• 제25권3호
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• pp.491-499
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• 2012

The hyperbolic metric is invariant under the action of M$\ddot{o}$bius maps and unbounded. For 0 < $r$ < 1, there is an r-lattice in the Bergman metric. Using this r-lattice, we get the measure ${\mu}_r$ and the Toeplitz operator $T^{\alpha}_{\mu}_r$ and we prove that $T^{\alpha}_{\mu}_r$ is bounded and $T^{\alpha}_{\mu}_r$ is compact under some condition.

• Korean Journal of Mathematics
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• 제18권1호
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• pp.29-35
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• 2010

A Fermat-type equation deals with representing a nonzero constant as a sum of kth powers of nonconstant functions. Suppose that $k{\geq}2$. Consider $\sum_{i=1}^{p}\;f_i(z)^k=1$. Let p be the smallest number of functions that give the above identity. We consider the Fermat-type equation for MAobius transformations and obtain $k{\leq}p{\leq}k+1$.