• The Pure and Applied Mathematics
• /
• v.21 no.2
• /
• pp.113-120
• /
• 2014

In this paper, we first show that for any space X, there is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) and that the subspace {${\alpha}{\mid}{\alpha}$ is a fixed ${\sigma}Z(X)^{\sharp}$-ultrafilter} of the Stone-space $S(Z({\Lambda}_X)^{\sharp})$ is the minimal basically disconnected cover of X. Using this, we will show that for any countably locally weakly Lindel$\ddot{o}$f space X, the set {$M{\mid}M$ is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) containing $Z(X)^{\sharp}$ and $s_M^{-1}(X)$ is basically disconnected}, when partially ordered by inclusion, becomes a complete lattice.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.221-229
• /
• 2013

We show that if X is a space such that ${\beta}QF(X)=QF({\beta}X)$ and each stable $Z(X)^{\sharp}$-ultrafilter has the countable intersection property, then there is a homeomorphism $h_X:vQF(X){\rightarrow}QF(vX)$ with $r_X={\Phi}_{vX}{\circ}h_X$. Moreover, if ${\beta}QF(X)=QF({\beta}X)$ and $vE(X)=E(vX)$ or $v{\Lambda}(X)={\Lambda}(vX)$, then $vQF(X)=QF(vX)$.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.655-672
• /
• 2011

Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

• Bulletin of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.119-126
• /
• 1989

Throughout this paper, X will always denote a Banach space over the complex numbers C, and L(X) will denote the Banach algebra of all continuous linear operators on X. Operator will always mean continuous linear operator. An n-tuple of operators T$_{1}$,..,T$_{n}$ on X will be denoted by over ^ T=(T$_{1}$,..,T$_{n}$ ). Let L$^{n}$ (X) be the set of all n-tuples of operators on X. X' will denote the dual space of X, S(X) its unit sphere and .PI.(X) the subset of X*X' defined by .PI.(X)={(x,f).mem.X*X': ∥x∥=∥f∥=f(x)=1}.

• Journal of Korean Medicine Rehabilitation
• /
• v.25 no.4
• /
• pp.75-81
• /
• 2015

Objectives To investigate the relationship between cervical intervertebral space narrowing in the X-ray and HIVD level of cervical spine in the CT image. Methods We studied 101 subjects who were taken cervical spine X-ray and CT. Intervertebral space were measured at the anterior, middle and posterior portion of each cervical disc in the X-ray. Considering individual difference, intervertebral space was set as value divided by upper width of lower vertebral body. We analyzed statistically adjusted intervertebral space of normal group and herniated disc group using student' t t-test. Results Intervertebral space of cervical spine was narrowed in the herniated disc group. But there was no significant difference at C2~C3. Conclusions We found that narrowing intervertebral space of cervical spine is associated with herniated disc. Further clinical observation is needed.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.717-722
• /
• 1999

The set of continuous maps of a space X to real usual space R equipped with the toplogy of pointwise convergence will be denoted by $C_p$(X). In this paper, we prove that; $C_p$(X) is hereditarily separable and hereditary Lindelof if and only if $X^n$ is hereditarily separable and hereditary Lindelof.

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.4
• /
• pp.461-466
• /
• 2018

$Let\;f:X{\rightarrow}X$ be a continuous surjection of a compact metric space X and let ${\sigma}_f:X_f{\rightarrow}X_f$ be the shift map on the inverse limit space $X_f$ constructed by f. We show that if a continuous surjective map f has some shadowing properties: the asymptotic average shadowing property, the average shadowing property, the two side limit shadowing property, then ${\sigma}_f$ also has the same properties.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.1
• /
• pp.35-43
• /
• 2011

In this paper we define the convergence of ${\delta}$-filters and study them. We show that ${\delta}$-filters on a Hausdorff space X converge at most one point in X. We also show that in a P-space X, ${\delta}$-filters on X converge at most one point in X if and only if X is a Hausdorff space.

• Communications of the Korean Mathematical Society
• /
• v.19 no.4
• /
• pp.715-720
• /
• 2004

Suppose X is a closed subspace of Z = ${({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}$ (1 < p < ${\infty}$, dim $Z_{n}$ < ${\infty}$). We investigate an isometrically isomorphic embedding of L(X)/K(X) into L(X, Z)/K(X, Z), where L(X, Z) (resp. L(X)) is the space of the bounded linear operators from X to Z (resp. from X to X) and K(X, Z) (resp. K(X)) is the space of the compact linear operators from X to Z (resp. from X to X).

• Journal of Astronomy and Space Sciences
• /
• v.5 no.2
• /
• pp.143-158
• /
• 1988

Since the successful observation by Uhuru, the first astronomical satellite, X-ray astronomy has become one of the rapidly developing fields in astronomy. The scientific results provide us the unique opportunity to understand the high energy nature of X-ray sources. We now know that our galaxy contains many different types of X-ray sources such as the compact X-ray sources, galactic bulge sources in addition to the Sun, the brightest X-ray sources in the sky. In this study we review the general properties of galactic X-ray sources, the characteristics of periodic compact X-ray sources, and bursters as well as the models.