• Bulletin of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.2165-2182
• /
• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.

• Proceedings of the KIEE Conference
• /
• 1996.11a
• /
• pp.224-226
• /
• 1996

The purpose of this study is to research and develop $Li_xNi_{2-x}O_2$ cathode for lithium rechargeable battery. We investigated XRD, cyclic voltammetry, AC impedance response and charge/discharge cycling of $Li_xNi_{2-x}O_2$/Li cells. The cell resistance was decreased much at initial charge process from 100% SOC to 0% SOC. The discharge capacity based on $Li_xNi_{2-x}O_2$ of 1st and 15th cycles was 135mAh/g and 108mAh/g, respectively. The $Li_xNi_{2-x}O_2$/Li cell had a good properties.

• 한국정보디스플레이학회:학술대회논문집
• /
• 2008.10a
• /
• pp.561-564
• /
• 2008

$Ba_{1-x}M_xGa_2S_4:Eu^{2+}$ (M = Ca, Sr) phosphor was prepared for white light emitting diodes application. Photoluminescence (PL) emission and excitation bands were red-shifted with increase of Ca and Sr content due to the crystal field effect. Moreover, the PL intensity under 450 nm was increased by substitution of Ca and Sr.

• Journal of the Korean Ceramic Society
• /
• v.49 no.2
• /
• pp.155-160
• /
• 2012

This paper reported a simple deposition-precipitation method, introducing the metal (Ni, Ag and Sn) and $Na_2S{\cdot}5H_2O$ to preparedispersion metal sulfide nanoparticles on the surface of the Multi-walled carbon nanotube for synthesis of CNT-$M_xS_y$ ($NiS_2$, $Ag_2S$, SnS) composite photocatalysts. The characterization of the prepared CNT-$M_xS_y$ ($NiS_2$, $Ag_2S$, SnS) composites was performed by X-ray diffraction, scanning electron microscopy with energy dispersive X-ray analysis and BET analysis. Furthermore, the MB degradation rate constant for CNT-SnS composite was $5.68{\times}10^{-3}$ under visible light irradiation, which was much higher than the corresponding values for other samples. The detailed formation and photocatalytic mechanism are also provided here.

• Bulletin of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.225-229
• /
• 1991

Our final purpose may be to introduce generalized differential forms on the space Map(S, M) of mappings from a manifold S into a manifold M and discuss the differential geometry of the space Map(S, M) from the point of the generalized forms. Here we take a subspace X of the space Map(S,M) and we introduce the generalized differential forms on X, taking the dual to the chain space with the flat norm. This method of construction allows us to discuss a sufficient condition for a subspace Y of X to admit the generalized differential forms and the natural integration as the dual operation.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.131-150
• /
• 2019

In this paper, we consider the structure of ${\gamma}$-constacyclic codes of length $2p^s$ over the Galois ring $GR(p^a,m)$ for any unit ${\gamma}$ of the form ${\xi}_0+p{\xi}_1+p^2z$, where $z{\in}GR(p^a,m)$ and ${\xi}_0$, ${\xi}_1$ are nonzero elements of the set ${\mathcal{T}}(p,m)$. Here ${\mathcal{T}}(p,m)$ denotes a complete set of representatives of the cosets ${\frac{GR(p^a,m)}{pGR(p^a,m)}}={\mathbb{F}}p^m$ in $GR(p^a,m)$. When ${\gamma}$ is not a square, the rings ${\mathcal{R}}_p(a,m,{\gamma})=\frac{GR(p^a,m)[x]}{{\langle}x^2p^s-{\gamma}{\rangle}}$ is a chain ring with maximal ideal ${\langle}x^2-{\delta}{\rangle}$, where ${\delta}p^s={\xi}_0$, and the number of codewords of ${\gamma}$-constacyclic code are provided. Furthermore, the self-orthogonal and self-dual ${\gamma}$-constacyclic codes of length $2p^s$ over $GR(p^a,m)$ are also established. Finally, we determine the Rosenbloom-Tsfasman (RT) distances and weight distributions of all such codes.

• Journal of the Korean Ceramic Society
• /
• v.22 no.3
• /
• pp.67-71
• /
• 1985

2.5~40$mu extrm{m}$ 영역에서 $XAs_2S_3-(1-X)GeS_2$ 유리의 적외선 흡수에 관하여 연구했다/ Lucovsky와 그의 연구팀이 제창한 ""분자모델""에 의하면 $8-20\mu\textrm{m}$ 영역에서 위의 유리물질의 multiphonon 흡수대는 고립된 각 분자의 기본진동대의 overtone 및 combination 과 같다. 그러므로 multiphonon 흡수영역에서 AsY3 와 GeY3의 기본진동수를 모두 가지고 있는 combination 대는 관찰되지 않고 또한 혼합된 $XAs_2S_3-(1-X)GeS_2$ 유리의 흡수계수는 순수한 $As_2Y_3$ 및 $GeY_2$ 유리의 흡수계수를 더한 것으로 표현된다. 실험에서 얻은 흡수계수는 이 분자모델로부터 예상되는 값과 잘 일치한다.값과 잘 일치한다.

• Kyungpook Mathematical Journal
• /
• v.13 no.2
• /
• pp.235-240
• /
• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• Communications of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.185-191
• /
• 2006

This paper observes that the induced homomorphisms on cohomology groups by a cyclic map are trivial. For a CW-complex X, we use the fact to obtain some conditions of X so that the n-th Gottlieb group $G_n(X)$ is trivial for an even positive integer n. As corollaries, for any positive integer m, we obtain $G_{2m}(S^{2m})\;=\;0\;and\;G_2(CP^m)\;=\;0$ which are due to D. H. Gottlieb and G. Lang respectively, where $S^{2m}$ is the 2m- dimensional sphere and $CP^m$ is the complex projective m-space. Moreover, we show that $G_4(HP^m)\;=\;0\;and\;G_8(II)\;=\;0,\;where\;HP^m$ is the quaternionic projective m-space for any positive integer m and II is the Cayley projective space.

• Journal of the Korean Statistical Society
• /
• v.9 no.1
• /
• pp.31-38
• /
• 1980

The problem considered in this paper can be defiened as follows. Consider observations $x_1, x_2, \cdot, x_n$ which are assumed to come from a mixed population of the density function, $$f(x) = \sum^m_{k=1} pkf_k(x)$$ where m is the number of subpoulations and $p_k$ is the proportion of subpopulation k such that $\sum^m_{k=1} pk=1, 0