• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.163-171
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• 1996

Observing that a locally weakly Lindel$\"{o}$f space is a quasi-F space if and only if it has an F-base, we show that every dense weakly Lindel$\"{o}$f subspace of an almost-p-space is C-embedded, every locally weakly Lindel$\"{o}$f space with a cocompact F-base is a locally compact and quasi-F space and that if Y is a dense weakly Lindel$\"{o}$f subspace of X which has a cocompact F-base, then $\beta$Y and X are homeomorphic. We also show that for any a separating nest generated intersection ring F on a space X, there is a separating nest generated intersection ring g on $\phi_{Y}^{-1}$(X) such that QF(w(X, F)) and ($\phi_{Y}^{-1}$(X),g) are homeomorphic and $\phi_{Y}_{x}$(g$^#$)=F$^#$.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.347-353
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• 2006

In this paper, we show that if the minimal basically disconnected cover ${\wedge}X_\imath\;of\;X_\imath$ is given by the space of fixed a $Z(X)^#$-ultrafilters on $X_\imath\;(\imath=1,2)\;and\;{\wedge}X_1\;{\times}\;{\wedge}X_2$ is a basically disconnected space, then ${\wedge}X_1\;{\times}\;{\wedge}X_2$ is the minimal basically disconnected cover of $X_1\;{\times}\;X_2$. Moreover, observing that the product space of a P-space and a countably locally weakly Lindelof basically disconnected space is basically disconnected, we show that if X is a weakly Lindelof almost P-space and Y is a countably locally weakly Lindelof space, then (${\wedge}X\;{\times}\;{\wedge}Y,\;{\wedge}_X\;{\times}\;{\wedge}_Y$) is the minimal basically disconnected cover of $X\;{\times}\;Y$.

• Journal of Korean Neurosurgical Society
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• v.55 no.5
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• pp.261-266
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• 2014

Objective : With the increased use of interspinous spacers in the treatment of lumbar stenosis, knowledge of the geometry of the interspinous space is important. To prevent dislodgment of an interspinous spacer, the accurate depth and width of the interspinous space needs to be established to facilitate the best intraoperative selection of correct spacer size. Methods : To determine the depth and width of the interspinous space, two methods are available which utilize plain film and magnetic resonance imaging (MRI). Data analysis of the interspinous depth and width was undertaken in 100 patients. Results : The standard deviations were variable, since skin thickness (zone 1) was altered by sex and age. The difference in the zone 1 distance between adjacent interspinous processes varied according to gender (p<0.05), but was not influenced by age [p=0.32 by analysis of variance between groups (ANOVA)]. Zone 2, the supraspinous, and zone 3, the interspinous ligament depths, comprise the operative working area during insertion of an interspinous spacer. There were no differences with regard to gender or age (p>0.05). For zones 6 and 7, the interspinous distances at the narrowest and widest points, respectively, were found to decrease with the aging process, but the decrease was not statistically significant. There were no differences with regard to gender (p>0.05). Conclusion : This study provides additional information on the interspinous space. This statistical data are valuable for use in the design of interspinous spacers.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.657-669
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• 2005

Calculations of some integrals on the n-dimensional vector space over $\mathbb{Q}_p$ are useful in getting some other formulations of quantum mechanics and the field theory of p-adic mathematical physics. For reasons of these, we estimate several integrals. As an application, we derive some properties for the p-adic Green functions.

• The Mathematical Education
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• v.22 no.2
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• pp.5-12
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• 1984

Steenrod algebra $\alpha$$_{p}$(mod p) was generated for algebra on steenrod reduced powers p$^n$ and Bochstein coboudary operation $\beta$. We know the relation between them. In this thesis I have verified the theorem: (equation omitted)

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.1
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• pp.128-133
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• 2022

This paper deals with the graph in which the weights of edges are given the distances between two end vertices on a metric space. In particular, we will study about a path P with n vertices for these graphs. We obtain a new graph $\bar{P}$ by augmenting an edge to P. Then the length of the shortest path between two vertices on $\bar{P}$ is considered and we focus on the maximum of these lengths. This maximum is called the diameter of the graph $\bar{P}$. We wish to find the augmented edge to minimize the diameter of $\bar{P}$. Especially, for an arbitrary real number λ > 0, we should determine whether the diameter of $\bar{P}$ is less than or equal to λ and we propose an O(n)-time algorithm for this problem, which improves on the time complexity O(nlogn) previously known. Using this decision algorithm, for the length D of P, we provide an O(nlogD)-time algorithm to find the minimum of the diameter of $\bar{P}$.

• Journal of Korean Neurosurgical Society
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• v.40 no.2
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• pp.84-89
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• 2006

Objective : The purpose of this study is to compare the outcomes of two methods for stabilization and fusion : Postero-Lateral Fusion [PLF, pedicle screw fixation with bone graft] and Posterior Lumbar Interbody Fusion [PLIF, cage insertion] for spinal stenosis and recurred disc herniation except degenerative spondylolisthesis. Methods : Seventy one patients who underwent PLF [n=36] or PLIF [n=35] between 1997 and 2001 were evaluated prospectively. These two groups were compared for the change of interbody space, the range of segmental angle, the angle of lumbar motion, and clinical outcomes by Prolo scale. Results : The mean follow-up period was 32.6 months. The PLIF group showed statistically significant increase of the interbody space after surgery. However, the difference in the change of interbody space between two groups was insignificant [P value=0.05]. The range of segmental angle was better in the PLIF group, but the difference in the change of segmental angle was not statistically significant [P value=0.0l7]. Angle of lumbar motion was similar in the two groups. Changes of Prolo economic scale were not statistically significant [P value=0.193]. The PLIF group showed statistically significant improvement in Prolo functional scale [P value=0.003]. In Prolo economic and functional scale, there were statistically significant relationships between follow-up duration [P value<0.001]. change of interbody space [P value<0.001], and range of segmental angle [P value<0.001]. Conclusion : Results of this study indicate that PLIF is superior to PLF in interbody space augmentation and clinical outcomes by Prolo functional scale. Analysis of clinical outcomes showed significant relationships among various factors [fusion type, follow-up duration, change of interbody space, and range of segmental angle]. Therefore, the authors recommend instrumented PLIF to offer better clinical outcomes in patients who needed instrumented lumbar fusion for spinal stenosis and recurred disc herniation.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1241-1257
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• 2014

We consider a class of hypoelliptic operators of the following type $$L=\sum_{i,j=1}^{p_0}a_{ij}{\partial}^2_{x_ix_j}+\sum_{i,j=1}^{N}b_{ij}x_i{\partial}_{x_j}-{\partial}_t$$, where ($a_{ij}$), ($b_{ij}$) are constant matrices and ($a_{ij}$) is symmetric positive definite on $\mathbb{R}^{p_0}$ ($p_0{\leqslant}N$). By establishing global Morrey estimates of singular integral on the homogenous space and the relation between Morrey space and weak Morrey space, we obtain the global weak Morrey estimates of the operator L on the whole space $\mathbb{R}^{N+1}$.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.1-8
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• 2006

In this paper, we obtain some unique common fixed point theorems for four self-maps and pair of maps in D-metric space using orbitally lower semi continuity conditions.

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