A prediction-correction ADMM for multistage stochastic variational inequalities

The multistage stochastic variational inequality is reformulated into a variational inequality with separable structure through introducing a new variable. The prediction-correction ADMM which was originally proposed in [B.-S. He, L.-Z. Liao and M.-J. Qian, J. Comput. Math., 24 (2006), 693--710] for solving deterministic variational inequalities in finite dimensional spaces is adapted to solve the multistage stochastic variational inequality. Weak convergence of the sequence generated by that algorithm is proved under the conditions of monotonicity and Lipschitz continuity. When the sample space is a finite set, the corresponding multistage stochastic variational inequality is defined on a finite dimensional Hilbert space and the strong convergence of the sequence naturally holds true. A numerical example in that case is given to show the efficiency of the algorithm

Content determination of benzyl glucosinolate and anti–cancer activity of its hydrolysis product in Carica papaya L.

AbstractObjectiveTo determine the content of benzyl glucosinolate (BG) in the pulp and the seed and investigate the anti-cancer activity of its hydrolysis product in Carica papaya L.MethodsDetermination of BG was performed on an Hypersil BDS C18 column at the wavelength of 214 nm with 0.1% trifluoroacetic acid (TFA) aqueous solution (A) and 0.1%TFA acetonitrile (B) as the mobile phase. In vitro activity test was adopted with cultured human lung cancer H69 cell in vitro to investigate the inhibition rate of cell proliferation of benzyl isothiocyanate (BITC) against H69 cell.ResultsThe pulp has more BG before the maturation of papaya and it nearly disappeared after papaya matured, while the seed contains BG at every stage. Activity test demonstrated that the a higher concentration of BITC would have better inhibition rate of cell proliferation on H69 cell, and the IC50 was 6.5 μmol/L.ConclusionsBG also can be produced in the pulp of papaya and it will be stored in the seed after the fruit has been matured. The hydrolysis product of BG has certain cancer-prevention anti-cancer activities for human

Linear Displacement and Straightness Measurement by Fabry-Perot Interferometer Integrated with an Optoelectronic Module

This research develops a three degrees of freedom (DOF) measurement system by integrating Fabry-Perot interferometer and photoelectronic inspection module to determine linear displacement, horizontal and vertical straightness geometric error parameters simultaneously. The interferometer and the photoelectronic inspection module in a three DOF measurement system share the same light source, and the two structures are used to measure linear displacement and straightness errors. The experimental results are utilized to calculate the relevant error parameters according to ISO standards and numerical analysis. They show that after the machine error compensation, the positioning deviation of the system is reduced from 55 μm to 19 μm, corresponding to the reduction of 65%. The accuracy is promoted from 65 μm to 31 μm, about the improvement of 52%. The horizontal and vertical straightness errors of the machine are 4.30 μm and 5.71 μm respectively