• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.681-689
• /
• 2019

The $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is an orbit of a subgroup of the $M{\ddot{o}}bius$ transformation group of ${\mathbb{S}}^{n+1}$. In this note, We prove that a compact $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is the image of a $M{\ddot{o}}bius$ transformation of the isometric homogeneous submanifold in ${\mathbb{S}}^{n+1}$.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.3
• /
• pp.29-36
• /
• 2007

Let T be an ergodic measure preserving transformation on (X, B, ${\mu}$). It is called 2-simple if every 2-fold ergodic joining is either a product measure or an off-diagonal measure. In general, factors of simple maps are not simple. So far, there has been no characterization of the factor of simple maps. In this paper, we give a joining characterization of factors of simple maps.

• Physical Therapy Korea
• /
• v.6 no.2
• /
• pp.16-31
• /
• 1999

The purpose of this study was to assess the fatigue in lumbar and abdominal muscles in patients with chronic low back pain compared with normal subjects using spectral analysis with mean power frequency and median power frequency. The experimental group consisted of twenty subjects who had experienced chronic low back pain for over one year after the onset day. A control group consisted of twenty normal subjects with no history of low back pain. All subjects stood in an apparatus to perform sustained contraction in the lumbar and abdominal muscles for 30 seconds with 60% maximal voluntary isometric contraction (MVIC). The resulting electromyographic (EMG) recorded time serial data were transformed into frequency serial data by Fast Fourier Transformation (FFT). The results were as follows: 1) lumbar muscles measured, the frequency change ratio of both median power frequency and mean power frequency was significantly greater for experimental group compared with control group group (p<0.05). In measured two abdominal muscles (inferior rectus abdominis, obliquus externus abdominis) except superior rectus abdominis, the frequency change ratio of both median power frequency and mean power frequency was significantly greater for experimental group compared with control group (p<0.05). 2) In all three (longissimus thoracis, iliocostalis lumborum, multifidus) lumbar muscles measured, the initial frequency value of both median power frequency and mean power frequency was significantly lower for the experimental group compared with the control group (p<0.05). In the two (inferior rectus abdominis, obliquus externus abdominis) abdominal muscles measured (superior rectus abdominis not included), the initial frequency value of both median power frequency and mean power frequency was significantly lower for the experimental group compared with the control group (p<0.05). These results suggest that in patients with chronic low back pain there is a trend for more fatigue to occur in both lumbar and abdominal muscles than in the normal control group. This would seem to suggest that in treatment programs for patients with chronic low back pain, improvement of endurance in all trunk muscles should be considered.