We show the results of a time series analysis of the long-term light curves of four blazars: 3C 279, 3C 345, 3C 446, and BL Lacertae. We used densely sampled light curves spanning 32 years at three frequency bands (4.8, 8, 14.5 GHz), provided by the University of Michigan Radio Astronomy Observatory monitoring program. The spectral indices of our sources are mostly at or inverted (-0:5 < α < 0), which is consistent with optically thick emission. Strong variability was seen in all light curves on various time scales. From the analyses of time lags between the light curves from different frequency bands and the evolution of the spectral indices with time, we find that we can distinguish high-peaking ares and lowpeaking ares according to the Valtaoja et al. classification. The periodograms (temporal power spectra) of the light curves are in good agreement with random-walk power-law noise without any indication of (quasi-)periodic variability. We note that random-walk noise light curves can originate from multiple shocks in jets. The fact that all our sources are in agreement with being random-walk noise emitters at radio wavelengths suggests that such behavior is a general property of blazars. We are going to generalize our approach by applying our methodology to a much larger blazar sample in the near future.

The efficient market hypothesis explains the random walk hypothesis suggesting that stock prices are independent of each other, hence, it is impossible to earn abnormal profits. The positive effect of a well-functioning and highly efficient stock market on the performance of an economy motivated the Philippine Stock Exchange to pursue massive modernization initiatives. This research provides evidence of the existence of random walk in the Philippine stock market employing the Augmented Dickey-Fuller (1981) and Phillips-Perron (1988) unit root tests, the Lo-MacKinlay’s (1988) conventional variance ratio test, and Chow-Denning’s (1993) simple multiple variance ratio test. Results of the ADF and PP unit root tests confirm the necessary condition for a random walk. The Chow-Denning (1993) maximum /z/ statistic and the Wald test statistic as in Richardson and Smith (1991) for the joint hypotheses and the Lo and MacKinlay (1988) individual statistics variance ratio test generally accepted the null hypothesis of a random walk. That is, the unit root and variance ratio tests consistently indicate that the null hypothesis of random walk cannot be rejected. The existence of a random walk in weak-form efficiency can be attributed to market liquidity as a result of continuous development and modernization of the Philippine equity market.

In this paper, an external torque estimation problem in one-degree-of-freedom (1-DOF) flexible-joint robot equipped with a joint-torque sensor is revisited. Since a sensor torque from the jointtorque sensor is distorted by two dynamics having a spring connection, i.e., motor dynamics and link dynamics of a flexible-joint robot, a model-based estimation, rather than a simple linear spring model, should be required to extract external torques accurately. In this paper, an external torque estimation algorithm for a 1-DOF flexible-joint robot is proposed. This algorithm estimates both an actuating motor torque from the motor dynamics and an external link torque from the link dynamics simultaneously by utilizing the flexible-joint robot model and the Kalman filter estimation based on random-walk model. The basic structure of the proposed algorithm is explained, and the performance is investigated through a custom-designed experimental testbed for a vertical situation under gravity.

자연하천에 유입된 오염물질의 확산거동을 해석하기 위하여 통계학적인 개념을 이용하여 오염물질 입자의 운동을 묘사하는 2차원 Random-Walk 모형을 개발하였다. 개발된 모형을 검정한 결과, 고정격자의 개수를 증가시키거나 각각의 고정격자 내에 포함된 입자개수의 평균값을 증가시키면 해의 정밀도가 증가하는 것으로 나타났다. 본 모형의 현장 적용성을 검토하기 위하여 캐나다에 위치한 Grand River에서 수행된 정상상태의 색소실험 결과와 본 모형에 의한 계