• 호남수학학술지
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• 제1권1호
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• pp.21-25
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• 1979

Abelian군(群)의 presheaf에 관한 직적(直積)과 직화(直和)를 Category 입장에서 정의(定義)하고 presheaf $F_{\lambda}\;({\lambda}{\epsilon}{\Lambda})$들의 두 직적(直積)(또는 直和)은 서로 동형적(同型的) 관계(關係)에 있으며, 특히 ${\phi}:X{\rightarrow}Y$가 homeomorphism이라 하고 ${\phi}_*F$를 X상(上)의 presheaf F의 direct image이라 하면 (1) $({\phi}_*F, \;{\phi}_*(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직적(直積)일 때 오직 그때 한하여 $(F,\;(f_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직적(直積)이다. (2) $({\phi}_*F,\;{\phi}_*(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$가 $({\phi}_*F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}$의 직화(直和)일 때 오직 그때 한하여 $(F,\;(l_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$는 $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$의 직화(直和)이다. Let $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ be an indexed set of presheaves of abelian group on topological space X. We can define the cartesian product $$\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda}$$ of $(F_{\lambda})_{{\lambda}{\epsilon}{\Lambda}})$ by $$(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U)=\prod_{{\lambda}{\epsilon}{\Lambda}}(F_{\lambda}(U))$$ for U open in X $${\rho}_v^u:\;(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(U){\rightarrow}(\prod_{{\lambda}{\epsilon}{\Lambda}}\;F_{\lambda})(V)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}(_{\lambda}{\rho}_v^u(s_{\lambda}))_{{\lambda}{\epsilon}{\Lambda}})$$ for $V{\subseteq}U$ open in X where $_{\lambda}{\rho}^U_V$ is a restriction of $F_{\lambda}$, And we have natural presheaf morphisms ${\pi}_{\lambda}$ and ${\iota}_{\lambda}$ such that ${\pi}_{\lambda}(U):\;({\prod}_\;F_{\lambda})(U){\rightarrow}F_{\lambda}(U)((s_{\lambda})_{{\lambda}{\epsilon}{\Lambda}}{\rightarrow}s_{\lambda})$ ${\iota}_{\lambda}(U):\;F_{\lambda}(U){\rightarrow}({\prod}\;F_{\lambda})(U)(s_{\lambda}{\rightarrow}(o,o,{\cdots}\;{\cdots}o,s_{\lambda},o,{\cdots}\;{\cdots}o)$ for $(s_{\lambda}){\epsilon}{\prod}_{\lambda}\;F_{\lambda}(U)$ and $(s_{\lambda}){\epsilon}F_{\lambda}(U)$.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 춘계학술대회 논문집
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• pp.389-394
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• 1997

Consider a tetrhedron is composed of six dihedral angles .phi.(i=1,2..., 6), and a vertex of a tetrahedron is also three dihedral angles. It will assume that a vertex A, for an example, is composed of there angles definded such as .alpha..betha. and .gamma. !. then there is a corresponding angle can be given as .phi1.,.phi2.,.phi3.. Here, in order to differentiate between a conventional triangle and dihedral angle, if a dihedral angle degined in this paper is symbolized as .phi..LAMBDA.,the value of cos.theta.of .phi./sab a/, in a trigonometric function rule,can be defined to tecos.phi..LAMBD/sab A/., and it is defined as a tetradedral cosine .phi. or simply called a tecos.phi.. Moreover, in a simillar method, the dihedral angle of tetrahedron .phi..LAMBDA. is given as : value of sin .theta. can defind a tetra-sin.phi..LAMBDA., and value of tan .theta. of .phi..LAMBDA. is a tetra-tan .phi..LAMBDA. By induction it can derive that a tetrahedral geometry on the basis of suggesting a geometric tetrahedron

• 대한의생명과학회지
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• 제6권2호
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• pp.131-139
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• 2000

분리한 한국형 대장균파아지군($\phi$C1, $\phi$C2, $\phi$C3 및 $\phi$C4)과 잘 알려진 미국형 대장균파아지군($\phi$T2, $\phi$T4, $\phi$T5, $\phi$T7 및 ${\phi}{\lambda}$)의 유전적 유연관계를 조사하기 위하여 분자적 계통분류를 위한 방법인 RAPD-PCR을 실시하고 컴퓨터분석을 하였다. 그 결과, 9개의 대장균파아지들은 5개의 그룹으로 나위어지면서 한국형 대장균파아지들만이 그들간의 유전적 유사도가 매우 높으면서 하나의 클러스터를 형성하였다. 반면 이국형 대장균파아지들은 오직 하나의 서브클러스터를 가지며 나누어졌다. 즉, 미국형 대장균파아지 중 $\phi$T2와 $\phi$T4($T_{even}$ 파아지)만이 하나의 서브클러스터를 형성하면서 $\phi$T5, $\phi$T7 및 ${\phi}{\lambda}$들과 뚜렷히 구분되고 있었다. 그리고 한국형 대장균파아지들은 미국형 대장균차이지 중 오직 ${\phi}{\lambda}$와 유전적 유연관계를 갖고 있음을 확인하였다. 한편 한국형 대장균파아지의 게놈의 크기는 25,000 bp~35,000 bp 정도 였으며, 이 중 $\phi$C2가 그 크기가 가장 작고 $\phi$C1이 가장 컸다. 그리고 $\phi$C3과 $\phi$C4의 게놈은 중간 크기로 비슷하였다.

• Korean Journal of Mathematics
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• 제14권2호
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• pp.259-271
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• 2006

We consider a semilinear elliptic boundary value problem with Dirichlet boundary condition $Au+bu^+-au^-=t_{1{\phi}1}+t_{2{\phi}2}$ in ${\Omega}$ and ${\phi}_n$ is the eigenfuction corresponding to ${\lambda}_n(n=1,2,{\cdots})$. We have a concern with the multiplicity of solutions of the equation when ${\lambda}_1$ < a < ${\lambda}_2$ < b < ${\lambda}_3$.

• 천문학논총
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• 제9권1호
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• pp.69-84
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• 1994

The spectral types of stars can be classified by using Balmer discontinuity($D_B$) and wavelength(${\lambda}_B$) expressed in terms of effective temperatures appeared in Balmer discontinuity. In this research, in order to classify stars, we used the well established observational data of high dispersion spectrophotometry for the spectral types and luminosity classes of stars in the Breger(1976) catalogue. Balmer discontinuity by effective temperatures of stars was accurately measured, and the ${\lambda}_B$ was replaced to luminosity classes of MK system, because of the close relationship between the As and luminosity classes. We measured the energy gradients(${\phi}_R$) of stars which were expressed as a function of spectral types in the interval of ${\lambda}{\lambda}4,000{\sim}4600{\AA}$, and then obtained a new physical parameter(${\phi}$) from the $D_B$ and ${\phi}_B$. The new parameter, ${\phi}$ can be used instead of HD classifications of stars and can be used widely for spectrophotometrical classifications of stars.

• 대한수학회논문집
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• 제19권1호
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• pp.119-127
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• 2004

Suppose that $\psi{\;}\in{\;}L^2(\mathbb{R})$ generates a wavelet frame (resp. Riesz basis) with bounds A and B. If $\phi{\;}\in{\;}L^2(\mathbb{R})$ satisfies $$\mid$\^{\psi}(\xi)\;\^{\phi}(\xi)$\mid${\;}<{\;}{\lambda}\frac{$\mid$\xi$\mid$^{\alpha}}{(1+$\mid$\xi$\mid$)^{\gamma}}$ for some positive constants $\alpha,{\;}\gamma,{\;}\lambda$ such that $1{\;}<1{\;}+{\;}\alpha{\;}<{\;}\gamma{\;}and{\;}{\lambda}^2M{\;}<{\;}A$, then $\phi$ also generates a wavelet frame (resp. Riesz basis) with bounds $A(1{\;}-{\;}{\lambda}\sqrt{M/A})^2{\;}and{\;}B(1{\;}+{\;}{\lambda}\sqrt{M/A})^2$, where M is a constant depending only on $\alpha,{\;}\gamma$ the dilation step a, and the translation step b.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.97-103
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• 2009

Suppose F is a field of characteristic not 2 and $F\;{\neq}\;Z_3$. Let $M_n(F)$ be the linear space of all $n{\times}n$ matrices over F, and let ${\Gamma}_n(F)$ be the subset of $M_n(F)$ consisting of all $n{\times}n$ involutory matrices. We denote by ${\Phi}_n(F)$ the set of all maps from $M_n(F)$ to itself satisfying A - ${\lambda}B{\in}{\Gamma}_n(F)$ if and only if ${\phi}(A)$ - ${\lambda}{\phi}(B){\in}{\Gamma}_n(F)$ for every A, $B{\in}M_n(F)$ and ${\lambda}{\in}F$. It was showed that ${\phi}{\in}{\Phi}_n(F)$ if and only if there exist an invertible matrix $P{\in}M_n(F)$ and an involutory element ${\varepsilon}$ such that either ${\phi}(A)={\varepsilon}PAP^{-1}$ for every $A{\in}M_n(F)$ or ${\phi}(A)={\varepsilon}PA^{T}P^{-1}$ for every $A{\in}M_n(F)$. As an application, the maps preserving inverses of matrces also are characterized.

• 대한수학회논문집
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• 제12권3호
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• pp.603-617
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• 1997

Consider a Sobolev inner product on the space of polynomials such as $$ \phi(p,q) = \lambda p(c)q(c) + <\tau,p'(x)q'(x)> $$ where $\tau$ is a moment functional and c and $\lambda$ are real constants. We investigate properties of orthogonal polynomials relative to $\phi(\cdot,\cdot)$ and give necessary and sufficient conditions under which such Sobolev orthogonal polynomials satisfy a spectral type differential equation with polynomial coefficients.

• 대한수학회보
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• 제33권1호
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• pp.75-86
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• 1996

Let G be a finite simple connected graph with vertex set V(G) and edge set E(G). Let A(G) be the adjacency matrix of G. The characteristic polynomial of G is the characteristic polynomial $\Phi(G;\lambda) = det(\lambda I - A(G))$ of A(G). A zero of $\Phi(G;\lambda)$ is called an eigenvalue of G.

• 충청수학회지
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• 제20권3호
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• pp.261-267
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• 2007

We show the existence of the positive solution for the system of the following nonlinear wave equations with Dirichlet boundary conditions $$u_{tt}-u_{xx}+av^+=s{\phi}_{00}+f$$, $$v_{tt}-v_{xx}+bu^+=t{\phi}_{00}+g$$, $$u({\pm}\frac{\pi}{2},t)=v({\pm}\frac{\pi}{2},t)=0$$, where $u_+=max\{u,0\}$, s, $t{\in}R$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}=1$ of the eigenvalue problem $u_{tt}-u_{xx}={\lambda}_{mn}u$ with $u({\pm}\frac{\pi}{2},t)=0$, $u(x,t+{\pi})=u(x,t)=u(-x,t)=u(x,-t)$ and f, g are ${\pi}$-periodic, even in x and t and bounded functions in $[-\frac{\pi}{2},\frac{\pi}{2}]{\times}[-\frac{\pi}{2},\frac{\pi}{2}]$ with $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}f{\phi}_{00}=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}g{\phi}_{00}=0$.