On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators

Nemirovski’s analysis (SIAM J. Optim. 15:229–251, 2005) indicates that the extragradient method has the O(1/t) convergence rate for variational inequalities with Lipschitz continuous monotone operators. For the same problems, in the last decades, a class of Fejér monotone projection and contraction methods is developed. Until now, only convergence results are available to these projection and contraction methods, though the numerical experiments indicate that they always outperform the extragradient method. The reason is that the former benefits from the ‘optimal’ step size in the contraction sense. In this paper, we prove the convergence rate under a unified conceptual framework, which includes the projection and contraction methods as special cases and thus perfects the theory of the existing projection and contraction methods. Preliminary numerical results demonstrate that the projection and contraction methods converge twice faster than the extragradient method.     

Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach

This paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We treat these two classes of problems uniformly by a mixed variational inequality, and show how the application of PPA with customized metric proximal parameters can yield favorable algorithms which are able to make use of the models’ structures effectively. Our customized PPA revisit turns out to unify some algorithms including some existing ones in the literature and some new ones to be proposed. From the PPA perspective, we establish the global convergence and a worst-case O(1/t) convergence rate for this series of algorithms in a unified way.     

Application of an efficient strategy based on MAE,HPLC‐DAD‐MS/MS and HSCCC for the rapid extraction,identification, separation and purification of flavonoids from Fructus Aurantii Immaturus

This study presents an efficient strategy based on microwave‐assisted extraction (MAE), HPLC‐DAD‐MS/MS and high‐speed counter‐current chromatography (HSCCC) for the rapid extraction, identification, separation and purification of active components from the traditional Chinese medicine Fructus Aurantii Immaturus. An LC‐DAD‐MS/MS method was applied for the screening and structural identification of main components in crude extract, and five components were preliminarily identified as neoeriocitrin, narirutin, naringin, hesperidin and neohesperidin according to their UV and mass spectra. An efficient MAE method for the extraction of the three most abundant components (narirutin, naringin and neohesperidin) was optimized by the combination of univariate and multivariate approaches. The crude extract was then separated and purified by HSCCC and a total of 61.6 mg of narirutin, 207.3 mg of naringin and 159.5 mg of neohesperidin at high purities of 98.1, 97.2 and 99.5%, respectively, were obtained from 1.42 g of crude extract. The recoveries of these compounds were 86, 93 and 89%, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

An efficient and convenient method for preparation of disulfides from thiols using air as oxidant catalyzed by Co-Salophen

Disulfides have been synthesized by oxidation of thiols using air as oxidant catalyzed by Co-Salophen with high yields,mild and neutral conditions,and easy procedures of the catalyst.The products were confirmed by ~1H NMR and IR.     

Preface

Owing to the fast economic growing and the concern over greenhouse gases and air pollution,the development of nuclear energy is one important option to meet the expanded energy consumption in our future.To achieve that goal,continuing and reliable supplies of uranium are critical to future nuclear power projects.As is well known,global terrestrial reserves of uranium are limited and the deposits in China are relatively small.Given the projected big growth in nuclear power in the future,reliable supply of uranium at a reasonable price is essential for China.     

杨桦林普通大,中径材用材林定向培育技术的研究

采用固定标准地定位观测和临时标准地调查点面结合的方法，在立地分类的基础上＾「１」，研究了天然杨桦林林分的经营密度，确定杨桦林最佳经营密度为０．７０。根据各立地级林分平均胸径的生长进程规律、林分的经营密度模型以及林分胸径与小头直径的相关关系，提出了杨桦林大、中径材用材林定向培育技术。结果表明，采用该项技术，山杨林和白桦林林分单位面积生长量分别可提高９．５０％～２４．５２％，２７．６３％。     

A diode-pumped, self-starting, all-solid-state self-mode-locked Cr:LiSGAF laser

In this paper, a self-starting, diode-pumped self-mode-locked Cr:LiSGAF laser, which produced a stable pulse train of 45 fs duration with about 20 mW-average power at the repeated rate of 90 MHz, was presented. Self-mode-locked operation can be obtained whether there is the semiconductor saturable absorber mirror (SESAM) in the Cr:LiSGAF laser cavity or not, and with the SESAM in the cavity, the self-mode-locked operation could self-start. The shortest pulses, as short as 38 fs, which were not very stable, were obtain with the SESAM in the cavity.     

A Novel Ion‐Selective Electrode for Determination of the Mercury(II) Ion Based on Schiff Base as a Carrier

A new poly(vinyl chloride) (PVC) membrane ion‐selective electrode based on bis‐salicyladehyde‐diaminjodipropylamine (BSDDA) as an ion carrier was successfully applied to the detection of Hg²⁺ ions. This electrode displayed good selectivity toward Hg²⁺ in comparison with other metal ions and exhibited a Nernstian slope of 30.5 ± 0.4 mV per decade of Hg²⁺ over a concentration range of 9.5 × 10^?7 to 6.4 × 10^?2 M of Hg²⁺ in the pH range 1.5 to 3.5. The detection limit was 7.0 ± 0.2 × 10^?7 M and response time was about 10 s to 25 s. The electrode can be used at least 2 months without apparent divergence in potential. In addition, the effects of experimental parameters such as membrane composition, nature and amounts of plasticizer and additive were investigated. The proposed electrode could be used as an indicator electrode in the detection of Hg²⁺ in samples.     

Determination of rare earth elements in chloroplasts of Brassia napus by INAA and biochemical separation techniques

Intact chloroplasts were isolated from mesophyll protoplasts of Brassia napus. Concentrations of 8 rare earth elements (REEs) in the chloroplasts were determined by instrumental neutron activation analysis (INAA). The results showed that there were trace amounts of REEs in the chloroplasts, which corresponded to 1 atom of REEs per 2000 chlorophyll molecules. About 30% of the total REEs in the leaves are localized in the chloroplasts and the light REEs were enriched with respect to the heavy elements of the series.     

Compatible and tearing properties of poly(lactic acid)/poly(ethylene glutaric‐co‐terephthalate) copolyester blends

Fourier transform infrared and nuclear magnetic resonance results suggest that the carboxylic acid groups of poly(lactic acid) (PLA) molecules react with the hydroxyl groups of FePol (FP) molecules during the melt‐blending of PLA_xFP_y specimens. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) experiments of PLA and PLA/FP specimens suggest that only small amounts of poor PLA and/or FP crystals are present in their corresponding melt crystallized specimens. In fact, the percentage crystallinity, peak melting temperature, and onset re‐crystallization temperature values of PLA/FP specimens reduce gradually as their FP contents increase. However, the glass transition temperatures of PLA molecules found by DSC and DMA reduce to a minimum value as the FP contents of PLA_xFP_y specimens reach 6 wt %. Further DMA and morphological analysis of PLA/FP specimens reveal that FP molecules are compatible with PLA molecules at FP contents equal to or less than 6 wt %, as no distinguished phase‐separated FP droplets and tan δ transitions were found on fracture surfaces and tan δ curves of PLA/FP specimens, respectively. In contrast to PLA, the FP specimen exhibits highly deformable and tearing properties. After blending proper amounts of FP in PLA, the inherent brittle deformation and poor tearing behavior of PLA were successfully improved. Possible reasons accounting for these interesting crystallization, compatible and tearing properties of PLA/FP specimens are proposed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 913–920, 2010