• Communications of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1105-1115
• /
• 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.

• Journal for History of Mathematics
• /
• v.22 no.2
• /
• pp.53-68
• /
• 2009

From ancient Greek times, the infinite concepts had debated, and then they had been influenced by Hebrew's tradition Kabbalab. Next, those infinite thoughts had been developed by Roman Catholic theologists in the medieval ages. After Renaissance movement, the mathematical infinite thoughts had been described by the vanishing point in Renaissance paintings. In the end of 1800s, the infinite thoughts had been concreted by Cantor such as Set Theory. At that time, the set theoretical trend had been appeared by pointillism of Seurat and Signac. After 20 century, mathematician $M\ddot{o}bius$ invented <$M\ddot{o}bius$ band> which dimension was more 3-dimensional space. While mathematicians were pursuing about infinite dimensional space, artists invented new paradigm, surrealism. That was not real world's images. So, it is called by surrealism. In contemporary arts, a lot of artists has made their works by mathematical material such as Mo?bius band, non-Euclidean space, hypercube, and so on.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.747-752
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.9 no.4
• /
• pp.945-950
• /
• 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 $\partial B^m$.

• Honam Mathematical Journal
• /
• v.37 no.4
• /
• pp.423-429
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.31 no.1
• /
• pp.177-184
• /
• 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.

• Journal of English Language & Literature
• /
• v.64 no.2
• /
• pp.299-305
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.1
• /
• pp.57-61
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.3
• /
• pp.491-499
• /
• 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
• /
• v.18 no.1
• /
• pp.29-35
• /
• 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 $k{\leq}p{\leq}k+1$.