The approximation of Laplace-Stieltjes transforms with finite order

In this paper, we study the irregular growth of an entire function defined by the Laplace-Stieltjes transform of finite order convergent in the whole complex plane and obtain some results about λ-lower type. In addition, we also investigate the problem on the error in approximating entire functions defined by the Laplace-Stieltjes transforms. Some results about the irregular growth, the error, and the coefficients of Laplace-Stieltjes transforms are obtained; they are generalization and improvement of the previous conclusions given by Luo and Kong, Singhal and Srivastava.

Approximate entropy in the electroencephalogram during wake and sleep

Entropy measurement can discriminate among complex systems, including deterministic, stochastic and composite systems. We evaluated the changes of approximate entropy (ApEn) in signals of the electroencephalogram (EEG) during sleep. EEG signals were recorded from eight healthy volunteers during nightly sleep. We estimated the values of ApEn in EEG signals in each sleep stage. The ApEn values for EEG signals (mean +/- SD) were 0.896 +/- 0.264 during eyes-closed waking state, 0.738 +/- 0.089 during Stage I, 0.615 +/- 0.107 during Stage II, 0.487 +/- 0.101 during Stage II, 0.397 +/- 0.078 during Stage IV and 0.789 +/- 0.182 during REM sleep. The ApEn values were found to differ with statistical significance among the six different stages of consciousness (ANOVA, p<0.001). ApEn of EEG was statistically significantly lower during Stage IV and higher during wake and REM sleep. We conclude that ApEn measurement can be useful to estimate sleep stages and the complexity in brain activity.