• Journal of the Korean Mathematical Society
• /
• 제53권2호
• /
• pp.287-304
• /
• 2016

In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of ${\mathbb{R}}^n$, $n{\geq}3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is ${\beta}{\in}[1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.

• Bulletin of the Korean Mathematical Society
• /
• 제51권5호
• /
• pp.1485-1502
• /
• 2014

The explicit formula for the hyperbolic metric ${\lambda}_{{\alpha},{\beta},{\gamma}}(z){\mid}dz{\mid}$ on the thrice-punctured sphere $\mathbb{P}{\backslash}\{0,1,{\infty}\}$ with singularities of order 0 < ${\alpha}$, ${\beta}$ < 1, ${\gamma}{\leq}1$, ${\alpha}+{\beta}+{\gamma}$ > 2 at 0, 1, ${\infty}$ was given by Kraus, Roth and Sugawa in [9]. In this article we investigate the asymptotic properties of the higher order derivatives of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$ near the origin and give more precise descriptions for the asymptotic behavior of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$.

• Bulletin of the Korean Mathematical Society
• /
• 제53권5호
• /
• pp.1457-1469
• /
• 2016

In this paper, we study a class of Finsler metric. First, we find some rigidity results of the dually flat (${\alpha}$, ${\beta}$)-metric where the underline Riemannian metric ${\alpha}$ satisfies nonnegative curvature properties. We give a new geometric approach of the Monge-$Amp{\acute{e}}re$ type equation on $R^n$ by using those results. We also get the non-existence of the compact globally dually flat Riemannian manifold.

• Journal of the Korean Mathematical Society
• /
• 제45권3호
• /
• pp.859-870
• /
• 2008

In the present paper, we investigate the geometric structures of the Dirichlet manifold composed of the Dirichlet distribution. We show that the Dirichlet distribution is an exponential family distribution. We consider its dual structures and give its geometric metrics, and obtain the geometric structures of the lower dimension cases of the Dirichlet manifold. In particularly, the Beta distribution is a 2-dimensional Dirich-let distribution. Also, we construct an affine immersion of the Dirichlet manifold. At last, we give the e-flat hierarchical structures and the orthogonal foliations of the Dirichlet manifold. All these work will enrich the theoretical work of the Dirichlet distribution and will be great help for its further applications.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• 제35권4호
• /
• pp.235-243
• /
• 2012

The Voronoi diagram of spheres and power diagram have been known as powerful tools to analyze spatial characteristics of weighted points, and these structures have variety range of applications including molecular spatial structure analysis, location based optimization, architectural design, etc. Due to the fact that both diagrams are based on different distance metrics, one has better usability than another depending on application problems. In this paper, we compare these diagrams in various situations from the user's viewpoint, and show the Voronoi diagram of spheres is more effective in the problems based on the Euclidean distance metric such as nearest neighbor search, path bottleneck locating, and internal void finding.

• Journal of Pharmacopuncture
• /
• 제22권3호
• /
• pp.166-170
• /
• 2019

Objectives: Attentional and memory functions are important aspects of neural plasticity that, theoretically, should be amenable to pharmacopuncture treatments. A previous study from our laboratory suggested that quantitative electroencephalographic (qEEG) measurements of theta/beta ratio (TBR), an index of attentional control, may be indicative of academic performance in a first-semester medical school course. The present study expands our prior report by extracting and analyzing data on frontal theta and beta asymmetries. We test the hypothesis that the amount of frontal theta and beta asymmetries (fTA, fBA), are correlated with TBR and academic performance, thereby providing novel targets for pharmacopuncture treatments to improve cognitive performance. Methods: Ten healthy male volunteers were subjected to 5-10 min of qEEG measurements under eyes-closed conditions. The qEEG measurements were performed 3 days before each of first two block examinations in anatomy-physiology, separated by five weeks. Amplitudes of the theta and beta waveforms, expressed in ${\mu}V$, were used to compute TBR, fTA and fBA. Significance of changes in theta and beta EEG wave amplitude was assessed by ANOVA with post-hoc t-testing. Correlations between TBR, fTA, fBA and the raw examination scores were evaluated by Pearson's product-moment coefficients and linear regression analysis. Results: fTA and fBA were found to be negatively correlated with TBR (P<0.03, P<0.05, respectively) and were positively correlated with the second examination score (P<0.03, P=0.1, respectively). Conclusion: Smaller fTA and fBA were associated with lower academic performance in the second of two first-semester medical school anatomy-physiology block examination. Future studies should determine whether these qEEG metrics are useful for monitoring changes associated with the brain's cognitive adaptations to academic challenges, for predicting academic performance and for targeting phamacopuncture treatments to improve cognitive performance.

• Journal of Internet Computing and Services
• /
• 제6권4호
• /
• pp.37-46
• /
• 2005

Computer are being used in an increasingly wide variety of application areas, and their correct operation is often critical for business success and humasn safety. Developing high quality software products is therefore of prime important. The recent game software become popular, so we are interest in the game software testing. According to the kinds of game software, because it has the different characters, so game software testing is very difficult. According to enviroment change, Recently, online game is popular, so online game trade in the world market. In the company, developers try to develop the reliable game software. But we can experience many fault of game software in spite of the beta testing. Especially, Testing is very difficult on the game software because of various environment and functionality. We tried the survey for game user. In this paper, we study the quality testing metric of game software fault basis on the ISO/IEC 9126. Also, we consist of the check list of game software a point of view user. It apply for the reliability testing metrics of ISO/IEC 9126.

• Korean Journal of Exercise Nutrition
• /
• 제25권4호
• /
• pp.24-37
• /
• 2021

[Purpose] To determine whether physical activity (PA), primarily the recommended 60 minutes of moderate-to-vigorous PA, is associated with gut bacterial microbiota in 10-year-old children. [Methods] The Block Physical Activity Screener, which provides minutes/day PA variables, was used to determine whether the child met the PA recommendations. 16S rRNA sequencing was performed on stool samples from the children to profile the composition of their gut bacterial microbiota. Differences in alpha diversity metrics (richness, Pielou's evenness, and Faith's phylogenetic diversity) by PA were determined using linear regression, whereas beta diversity (unweighted and weighted UniFrac) relationships were assessed using PERMANOVA. Taxon relative abundance differentials were determined using DESeq2. [Results] The analytic sample included 321 children with both PA and 16S rRNA sequencing data (mean age [SD] =10.2 [0.8] years; 54.2% male; 62.9% African American), where 189 (58.9%) met the PA recommendations. After adjusting for covariates, meeting the PA recommendations as well as minutes/day PA variables were not significantly associated with gut richness, evenness, or diversity (p ≥ 0.19). However, meeting the PA recommendations (weighted UniFrac R² = 0.014, p = 0.001) was significantly associated with distinct gut bacterial composition. These compositional differences were partly characterized by increased abundance of Megamonas and Anaerovorax as well as specific Christensenellaceae_R-7_group taxa in children with higher PA. [Conclusion] Children who met the recommendations of PA had altered gut microbiota compositions. Whether this translates to a reduced risk of obesity or associated metabolic diseases is still unclear.