• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.935-942
• /
• 2018

In this paper, we prove that any stable f-harmonic map from sphere ${\mathbb{S}}^n$ to Riemannian manifold (N, h) is constant, where f is a smooth positive function on ${\mathbb{S}}^n{\times}N$ satisfying one condition with n > 2. We also prove that any stable f-harmonic map ${\varphi}$ from a compact Riemannian manifold (M, g) to ${\mathbb{S}}^n$ (n > 2) is constant where, in this case, f is a smooth positive function on $M{\times}{\mathbb{S}}^n$ satisfying ${\Delta}^{{\mathbb{S}}^n}(f){\circ}{\varphi}{\leq}0$.

• 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.

• Communications of the Korean Mathematical Society
• /
• v.10 no.4
• /
• pp.875-880
• /
• 1995

Let $S_p(\alpha)$ denote the class of the Spirallike functions of order $\alpha, 0 < $\mid$\alpha$\mid$ < \frac{\pi}{2}$ Let $\Pi_N$ denote the subset of $S_p(\alpha)$ consisting of all products $z\Pi^N_{j=1}(1-u_j z)^{-mt_j}$ where $m = 1 + e^{-2i\alpha},$\mid$u_j$\mid$ = 1, t_j > 0$ for $j = 1, \cdots, N$ and $\sum^{N}_{j=1}{t_j = 1}$. In this paper we prove that extreme points of $S_p(\alpha)$ may be found which lie in $\Pi_N$ for some $N \geq 2$. We are let to conjecture that all exreme points of $S_p(\alpha)$ lie in $\Pi_N$ for somer $N \geq 1$ and that every such function is an extreme point.

• Kyungpook Mathematical Journal
• /
• v.54 no.1
• /
• pp.23-30
• /
• 2014

For two positive integers r and s, $\mathcal{G}$(n; r; ${\theta}_s$) denotes to the class of graphs on n vertices containing no r of edge disjoint ${\theta}_s$-graphs and f(n; r; ${\theta}_s$) = max{${\varepsilon}(G)$ : G ${\in}$ $\mathcal{G}$(n; r; ${\theta}_s$)}. In this paper, for integers r, $k{\geq}2$, we determine f(n; r; ${\theta}_{2k+1}$) and characterize the edge maximal members in G(n; r; ${\theta}_{2k+1}$).

• Proceedings of the Korean Society of Applied Pharmacology
• /
• 1993.04a
• /
• pp.163-163
• /
• 1993

대상환자는 모두 23명이였으여, 이중 12명은 fluconazole을, 11명은 nystatin을 투여받았다. 두 군사이에 연령, 남여비, 기저질환, 진균감염의 위험요소는 차이가 없었다. 투약기간은 fluconazole군(F)이 24일, nystatin군(N)이 23일이였다. 중도탈락은 3례로 F중 MRSA ？혈증 1례, N중 오심, 구토 1례외 Stevens-Johnson증후군 1례였다. 평가가능한 20례중, F 11례중 8례와, N 9례중 4례에서 진균감염중의 예방에 성공하였고, F 3례와 N 5례는 실패하였다. 실패한 F 3례는 코의 피부조직에서 aspergillus가 중명된 1례와 경험적으로 amphotericin을 투여한 2례였고, N 5례는 혈액배양에서 Candida tropicalis가 분리된 1례와 경험적 amphotericin을 받은 4례였다. 진균의 colonization은 F중 3균주는 치료중 소실되었으나, 2례는 증가하였다. N은 1균주가 소실된 반면, 3례는 증가하였다. Colonization이 증가한 F 2례는 C. albicans와 Trichosporon beigelli가 대변에서 분리된 경우이고. M 3례는 대변에서 C. albicans가 분리된 1례, 구강에서 aspergillus가 분리된 1례, 혈액배양에서 C. tropicalis가 분해된 1례였다. 부작용은 오심 구토가 F중 1례, N중 2례 였으며, 이중 N의 1례는 증상이 심하여 투약을 중지하였다. 간기능 검사상 SGOT/SGPT의 상승은 F 12중 3례, N 11중 2례에서 관찰되었으나, 두 군사이에 통계학적으로 유의한 차이는 없었다.

• Journal of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.573-582
• /
• 1995

J.Milnor[Mi2] has introduced the notion of directional entropy in his study of Cellular Automata. Cellular Automaton map can be considered as a continuous map from a space $K^Z^n$ to itself which commute with the translation of the lattice $Z^n$. Since the space $K^Z^n$ is compact, map S is uniformly continuous. Hence S is a block map(a finite code)[He]. (S is said to have a finite memory.) In the case of n = 1, we have a shift map, T on $K^Z$, and a block map S and they together generate a $Z^2$ action.

• Animal Systematics, Evolution and Diversity
• /
• v.16 no.2
• /
• pp.177-182
• /
• 2000

Sponges of the genus Sarcotragus are very poorly known in the world. Two new species of Sarcotragus, S. maraensis n. sp. and S. gapaensis n. sp., are described from Korea.

• Animal Systematics, Evolution and Diversity
• /
• v.24 no.2
• /
• pp.215-218
• /
• 2008

Two new marine sponges in genus Suberites, S. hataedoensis n. sp and S. waedoensis n. sp have been collected from Hataedo Island and Waedo Island, Korea during 2005-2006. S. hataedoensis n. sp. is similar to S. durissimus in the spicule composition and texture. However, they differ in growth form, skeleton and surface. S. waedoensis n. sp. is similar to S. japonicus in spicule composition and skeleton. However, they differ in growth form, surface and texture.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.6
• /
• pp.1643-1653
• /
• 2019

This paper shows that if $1<p<{\infty}$, ${\alpha}{\geq}-n-2$, ${\alpha}>-1-{\frac{p}{2}}$ and f is holomorphic on the unit ball ${\mathbb{B}}_n$, then $${\int_{{\mathbb{B}}_n}}{\mid}Rf(z){\mid}^p(1-{\mid}z{\mid}^2)^{p+{\alpha}}dv_{\alpha}(z)<{\infty}$$ if and only if $${\int_{{\mathbb{B}}_n}}{\int_{{\mathbb{B}}_n}}{\frac{{\mid}f(z)-F({\omega}){\mid}^p}{{\mid}1-(z,{\omega}){\mid}^{n+1+s+t-{\alpha}}}}(1-{\mid}{\omega}{\mid}^2)^s(1-{\mid}z{\mid}^2)^tdv(z)dv({\omega})<{\infty}$$ where s, t > -1 with $min(s,t)>{\alpha}$.

• Journal of the Institute of Convergence Signal Processing
• /
• v.13 no.4
• /
• pp.194-200
• /
• 2012

In this paper we analyze the code sequence generating algorism defined on $GF(2^n)$ proposed by S.Bostas and V.Kumar[7] and derive the implementation functions of code sequence generator using Boolean functions which can map the vector space $F_2^n$ of all binary vectors of length n, to the finite field with two elements $F_2$. We find the code sequence generating boolean functions based on two kinds of the primitive polynomials of degree, n=5 and n=7 from trace function. We then design and implement the code sequence generators using these functions, and produce two code sequence groups. The two groups have the period 31 and 127 and the magnitudes of out of phase(${\tau}{\neq}0$) autocorrelation and crosscorrelation functions {-9, -1, 7} and {-17, -1, 15}, satisfying the period $L=2^n-1$ and the correlation functions $R_{ij}({\tau})=\{-2^{(n+1)/2}-1,-1,2^{(n+l)/2}-1\}$ respectively. Through these results, we confirm that the code sequence generators using boolean functions are designed and implemented correctly.