Ancient Chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method

Air exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.

Absolute measurement of roughness and lateral-correlation length of random surfaces by use of the simplified model of image-speckle contrast

We present a method of image-speckle contrast for the nonprecalibration measurement of the root-mean-square roughness and the lateral-correlation length of random surfaces with Gaussian correlation. We use the simplified model of the speckle fields produced by the weak scattering object in the theoretical analysis. The explicit mathematical relation shows that the saturation value of the image-speckle contrast at a large aperture radius determines the roughness, while the variation of the contrast with the aperture radius determines the lateral-correlation length. In the experimental performance, we specially fabricate the random surface samples with Gaussian correlation. The square of the image-speckle contrast is measured versus the radius of the aperture in the 4f system, and the roughness and the lateral-correlation length are extracted by fitting the theoretical result to the experimental data. Comparison of the measurement with that by an atomic force microscope shows our method has a satisfying accuracy. (C) 2002 Optical Society of America.

Photodegradation dynamics of pure microcystin variants with illumination of fixed wavelength UV-lights

Photolysis of microcystins by UV irradiation and the effects of different environmental factors on efficiency of UV degradation were studied. The results indicated that the rates of the photolytical degradation reactions of microcystin-LR and RR-follow pseudo-first-order kinetic process. The results also showed that the concentrations of two microcystin variants decreased significantly by UV-C Irradiation; the wavelength and intensitiy of UV irradiation are two very important factors affecting the rate of degradation; temperature and pH value could also affect the half life of degradation rates. When irradiated by weaker UV-Iight, isomerization could be detected in the course of photolytical degradation. The concentrations of two isomers transformed from microcystin-LR reached its maximum at the third minute and decreased with the time afterwards. To simulate photolysis of microcystins in the field water body, microcystins with low concentration were used. It was found that UV-C illumination was capable of decomposing over 95% of microcystins within 40 min. In the presence of humic substances the photodecomposition slowed down to a certain extent. These results are valuable in using UV irradiation for elimination microcystins from raw water.

THEORETICAL INVESTIGATION OF THE DYNAMIC PROCESS OF THE ILLUMINATION OF GAAS

The dynamic process of light illumination of GaAs is studied numerically in this paper to understand the photoquenching characteristics of the material. This peculiar behavior of GaAs is usally ascribed to the existence of EL2 states and their photodriven metastable states. To understand the conductivity quenching, we have introduced nonlinear terms describing the recombination of the nonequilibrium free electrons and holes into the calculation. Though some photoquenching such as photocapacitance, infrared absorption, and electron-paramagnetic-resonance quenching can be explained qualitatively by only considering the internal transfer between the EL2 state and its metastability, it is essential to take the recombination into consideration for a clear understanding of the photoquenching process. The numerical results and approximate analytical approach are presented in this paper for the first time to our knowledge. The calculation gives quite a reasonable explanation for n-type semiconducting GaAs to have infrared absorption quenching while lacking photoconductance quenching. Also, the calculation results have allowed us to interpret the enhanced photoconductance phenomenon following the conductance quenching in typical semi-insulating GaAs and have shown the expected thermal recovery temperature of about 120 K. The numerical results are in agreement with the reported experiments and have diminished some ambiguities in previous works.

RELATION BETWEEN THE METASTABILITY OF EL2 AND THE PHOTOSENSITIVITY OF LOCAL VIBRATIONAL-MODES IN SEMIINSULATING GAAS

Recent infrared spectroscpic observations of local vibrational mode absorptions have revealed a number of photosensitive centers in semi-insulating GaAs. They include (OVAs) center which has three modes at 730 cm(-1) (A), 715 cm(-1) (B), and 714 cm(-1) (C), respectively, a suggested NH center related to a line at 983 cm(-1) (X(1)), and centers related to hydrogen, such as (H-O) or (H-N) bonds, corresponding to a group of peaks in the region of 2900-3500 cm(-1). The photosensitivity of various local vibration centers was observed to have similar time dependence under near-infrared illumination and was suggested to be due to their charge-state interconversion. Mainly described in this work is the effect of the 1.25-eV illumination. It is confirmed that this photoinduced kinetic process results from both electron capture and hole capture, which are closely related to the photoionization behavior and metastability of the EL2 center.