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.     

小麦液泡膜H~ -ATPase的Ca~(2 )激活特性

纯化小麦液泡膜H -ATPase,测定了纯化的小麦液泡膜H -ATPase 受Mg2 和Ca2 双重激活的特性及两种激活状态下酶的特性. Mg2 激活时酶水解活性受DCCD的抑制,受磷脂酰丝氨酸(PS)影响明显,ATP水解和泵质子活性相偶联.而在Ca2 激活时酶水解活性不受DCCD抑制,受PS影响微弱,Ca2 激活时ATP水解与泵质子活性解偶联. Mg2 和Ca2 对小麦液泡膜H -ATPase的激活作用不具有叠加效应.     

Synthesis and Characterization of New Adhesion Promoter for Grafting Conducting Polymer on Oxide Substrate

For grafting polypyrrole layers on oxidic substrates, the synthesis and characterization of a new adhesion promoter 11‐(pyrrol‐3‐yl) undecyl trimethoxysilane (PyTMS) were described in this article. The oxidation potential of PyTMS was determined by cyclic voltammetry. The grafting behavior of such an adhesion promoter on oxidized surface and chemical deposition of polypyrrole over the modified oxidized surface were studied. The adsorbed layer on the oxidized substrates thus formed was determined by both contact angle measurements and X‐ray photoelectron spectroscopy. Chemical polymerization of terminal pyrrole moieties on such substrates yielded adhesive polypyrrole films, and SEM image showed that the morphology of the polypyrrole films was influenced by the experimental conditions.     

Synthesis and characterization of hyperbranched polystyrene via click reaction of AB2 macromonomer

Well‐defined hyperbranched polystyrenes have been successfully prepared by polymerization of AB₂ macromonomer, polystyrene containing an azide group at its one end and two terminal propargyl groups at the other end via click reaction. For preparation of AB₂ macromonomers, an ATRP initiator, bispropargyl 2‐bromosuccinate (BPBS) with two propargyl groups and one bromine group was synthesized by the successive bromination and esterification reaction of L ‐aspartic acid. The resulting BPBS initiated the ATRP of St, and subsequently, the terminal bromine groups of (CH≡C)₂‐PS‐Brs were substituted by N₃ via the reaction with sodium azide resulting the AB₂ macromonomer, (CH≡C)₂‐PS‐N₃ with various molecular weights. All intermediates and the resultant polymers were characterized by GPC, ¹H NMR, FTIR, and MALLS methods. The polymerization kinetics study showed fast increase of DP at the initial stage of polymerization and then slow increase of their DP. The final “HyperMacs” have high‐molecular weight up to M_w,MALLS = 340,000 g/mol, their molecular weight distributions were moderately narrow (M_w/M_n = 1.47–1.65). The ratios of [η]_H/[η]_L of the HyperMacs formed in the polymerization system increased with evolution of polymerization. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 454–462, 2010     

闭系中硫(-Ⅱ)氧化的非线性动力学一般特征

The general dynamic features of the batch oxidation of Sulfur(-Ⅱ) compounds (S2- , thiosulfate,thiocynate and thiourea et al.) were discussed. The changes of Ph with reaction time consist of a rise and two separate drops. Dynamic model was proposed, further experimental studies on the batch oxidation of thiourea and thiocyanate by ClO2- were also carried out. Simulation curve was well consistent with experiment in a batch reactor. Non-catalytic oscillation of peroxide (hydrogen peroxide, persulfate et al.)- S(-Ⅱ) compound system resulted from the nonlinear dynamic of sulfur oxidation. In the oxidation of S(-Ⅱ) compounds by oxyhalogen compounds(ClO2- et al.), nonlinear dynamics of both oxyhalogen compound and sulfur compound should be considered simultaneously. So complex phenomena such as birhythmicity and chaos may be discovered.     

Performance-based design of permeation test cells for reliable evaluation of chemical protective materials

The test cell constitutes the core functionality of a permeation testing system. Accuracy of an experimental methodology depends on the ability of the test cell to efficiently deliver the challenge agents to the test material, collect all the transported permeate compounds from the test material and transfer those analytes to the online detector. Common test cell designs used in the US and internationally form the basis of their respective testing procedures. However, widespread usage does not necessarily equate to defensible assurance of analytical reliability. Consequently, chemical protective materials characterized with these cells may provide inadequate protection to users whose health and safety depend on barrier garments such as gloves and suits. Permeation test data, including those acquired in our laboratory, have emphasized the significance of test cell design on the accuracy of permeation measurements. This paper describes the key considerations necessary to ensure analytical reliability for a test cell, illustrates quantitative improvements demonstrated by existing prototypes and, finally, proposes a design which further advances the technology of permeation testing.     

Influence of fluorinated substituent and terminal length on phase behavior of mesogen‐jacketed liquid crystalline polymers with a biphenyl mesogen

A series of mesogen‐jacketed liquid crystalline polymers, poly{2,2,3,3,4,4,4‐heptafluorobutyl 4′‐hydroxy‐2‐vinylbiphenyl‐4‐carboxylate} (PF3Cm, where m is the number of carbon atoms in the alkoxy groups, and m = 1, 4, 6, and 8), the side chain of which contains a biphenyl core with a fluorocarbon substituent at one end and an alkoxy unit of varying length on the other end, were designed and successfully synthesized via atom transfer radical polymerization. For comparison, poly{butyl 4′‐hydroxy‐2‐vinylbiphenyl‐4‐carboxylate} (PC4Cm), similar to PF3Cm but with a butyl group instead of the fluorocarbon substituent, was also prepared. Differential scanning calorimetric results reveal that the glass transition temperatures (T_gs) of the two series of polymers decrease as m increases and T_gs of the fluorocarbon‐substituted polymers are higher than those of the corresponding butyl‐substituted polymers. Wide‐angle X‐ray diffraction measurements show that the mesophase structures of these polymers are dependent on the number of the carbon atoms in the fluorocarbon substituent and the property of the other terminal substituent. Polymers with fluorocarbon substituents enter into columnar nematic phases when m ≥ 4, whereas the polymer PF3C1 exhibits no liquid crystallinity. For polymers with butyl substituents, columnar nematic phases form when the number of carbon atoms at both ends of the side chain is not equal at high temperatures and disappear after the polymers are cooled to ambient temperature. However, when the polymer has the same number of carbon atoms at both ends of the side chain, a hexagonal columnar phase develops, and this phase remains after the polymer is cooled. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013