Kq, Scaling of ac susceptibility and the nonlinear response function of high-temperature superconductors

The amplitude-dependent ac susceptibility of high-temperature superconductors is shown to obey some empirical scaling relations. We try to analyze this behavior by extending a dc nonlinear response function of mixed state to the ac cases. The derived equations for critical current and ac susceptibility ξ(T) agree with the scaling relations of experimental data.     

Influence of the chemical structure of dithiocarbamates with different N‐groups on the reversible addition–fragmentation chain transfer polymerization of styrene

Polymerizations of styrene with azobisisobutyronitrile initiation or thermal initiation have been performed in the presence of dithiocarbamates with different N‐groups, that is, benzyl 4,5‐diphenyl‐1H‐imidazole‐1‐carbodithioate ( 2a ), benzyl 1H‐1,2,4‐triazole‐1‐carbodithioate ( 2b ), benzyl indole‐1‐carbodithioate ( 2c ), benzyl 2‐phenyl‐indole‐1‐carbodithioate ( 2d ), benzyl phenothiazine‐10‐carbodithioate ( 2e ), benzyl 9H‐carbazole‐9‐carbodithioate ( 2f ), and benzyl dibenzo[b,f]azepine‐5‐carbodithioate ( 2g ). The results show that the structure of the N‐group of dithiocarbamates has significant effects on the activity of dithiocarbamates for the polymerization of styrene. 2a , 2b , 2c , 2d , and 2f are effective reversible addition–fragmentation chain transfer (RAFT) agents for the RAFT polymerization of styrene, and the polymerizations have good living characteristics. However, in the cases of 2e and 2g , the obtained polymers have uncontrolled molecular weights and broad molecular weight distributions. The polymerization rate is markedly influenced by the conjugation structure of the N‐group of the dithiocarbamate, and the polymerization rate of 2b is greater than that of 2a . For 2b , the rate of polymerization seems independent of the RAFT agent concentration. However, a significant retardation in the rate of polymerization can be observed in the case of 2c . 2d is more effective than 2c , and the substitution group of phenyl on this dithiocarbamate has obvious effects on the effectiveness of the controlled polymerization of styrene. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4849–4856, 2005     

Synthesis and characterization of proton‐conducting copolyimides bearing pendant sulfonic acid groups

A series of sulfonated copolyimides (co‐SPIs) bearing pendant sulfonic acid groups were synthesized from 1,4,5,8‐naphthalenetetracarboxylic dianhydride (NTDA), bis(3‐sulfopropoxy) benzidines (BSPBs), and common nonsulfonated diamines via statistical or sequenced polycondensation reactions. Membranes were prepared by casting their m‐cresol solutions. The co‐SPI membrane had a microphase‐separated structure composed of hydrophilic and hydrophobic domains, but the connecting behavior of hydrophilic domains was different from that of the homo‐SPIs. The co‐SPI membranes displayed clear anisotropic membrane swelling in water with negligibly small dimensional changes in the plane direction of the membrane. With water uptake values of 39–94 wt %, they showed dimensional changes in membrane thickness of about 0.11–0.58, which were much lower than those of homo‐SPIs. The proton conductivity σ values of co‐SPI membranes with ion exchange capacity values ranging from 1.95–2.32 meq/g increased sigmoidally with increasing relative humidity. They displayed σ values of 0.05–0.16 S/cm at 50 °C in liquid water. Increasing temperature up to 120 °C resulted in further increase in proton conductivity. The co‐SPI membranes showed relatively good conductivity stability during the aging treatment in water at 100 °C for 300 h. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1545–1553, 2005     

Phenanthrene removal in unsaturated soils treated by electrokinetics with different surfactants—Triton X-100 and rhamnolipid

In this study, the remediation performance of electrokinetic (EK) technology integrated with different surfactants for removing phenanthrene from unsaturated soils was investigated. A synthetic surfactant (Triton X-100) and a biosurfactant (rhamnolipid) were used to enhance phenanthrene solubility and removal efficiency during EK process. Results indicate that the electro-osmotic flow (EOF) rate in the rhamnolipid system is higher than that in Triton X-100. Using the EK technology for the removal of phenanthrene in the presence of rhamnolipid was more efficient than in the presence of Triton X-100. In addition to the transport mechanism of phenanthrene in EK system, the presence of rhamnolipid may promote microbial growth in the soil–water system and bring about biodegradation of phenanthrene. A diffusion–advection–sorption (DAS) model was solved by MATLAB, based on the linear sorption isotherm at the non-equilibrium condition, which is feasible to simulate the movement of phenanthrene during the EK + Triton X-100 treatment.     

Influence of substituents in the salicylaldehyde‐derived Schiff bases on vanadium‐catalyzed asymmetric oxidation of sulfides

A series of chiral Schiff bases ( L ¹ – L ⁵ ) with different substituents in the salicylidenyl unit were prepared from condensation of 3‐aryl‐5‐ tert ‐butylsalicylaldehyde derivatives and optically active amino alcohols. Bromination of 3‐phenyl‐5‐ tert ‐butylsalicylaldehyde gave an unexpected product 3‐(4‐bromophenyl)‐5‐bromosalicylaldehyde, from which the corresponding Schiff base ligands L ⁶ and L ⁷ , derived from (S)‐valinol and (S)‐ tert ‐leucinol, respectively, were prepared. Ligands L ¹ – L ⁷ were applied to the vanadium‐catalyzed asymmetric oxidation of aryl methyl sulfides. Under the optimal conditions, the oxidation of the thioanisole with H₂O₂ as oxidant in CH₂Cl₂ catalyzed by VO(acac)₂‐ L ¹ – L ⁷ gives good yields (74–83%) with moderate enantioselectivity (58–77% ee). Ligand L ⁷ , containing a 4‐bromophenyl group on the 3‐position and a Br atom on the 5‐position of the salicylidenyl moiety, displays an 80–90% ee for vanadium‐catalyzed oxidation of methyl 4‐bromophenyl sulfide and methyl 2‐naphthyl sulfide. Copyright © 2008 John Wiley & Sons, Ltd.     

A rapid and green approach to chiral α-hydroxy esters: asymmetric transfer hydrogenation (ATH) of α-keto esters in water by use of surfactants

A series of α-hydroxy esters were rapidly prepared (1.5 h) from α-keto esters via asymmetric transfer hydrogenation (ATH) in water by the use of surfactants for the first time. This green method, catalyzed by a water-soluble and recyclable Ru(II) complex, gave moderate to high enantioselectivities (up to 99.7% ee) with DTAB as an additive and HCOONa as the hydrogen source.     

An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems

We present a new active-set strategy which can be used in conjunction with exponential (entropic) smoothing for solving large-scale minimax problems arising from the discretization of semi-infinite minimax problems. The main effect of the active-set strategy is to dramatically reduce the number of gradient calculations needed in the optimization. Discretization of multidimensional domains gives rise to minimax problems with thousands of component functions. We present an application to minimizing the sum of squares of the Lagrange polynomials to find good points for polynomial interpolation on the unit sphere in ℝ³. Our numerical results show that the active-set strategy results in a modified Armijo gradient or Gauss-Newton like methods requiring less than a quarter of the gradients, as compared to the use of these methods without our active-set strategy. Finally, we show how this strategy can be incorporated in an algorithm for solving semi-infinite minimax problems.     

Tadpole‐shaped amphiphilic copolymers prepared via RAFT polymerization and click reaction

The tadpole‐shaped amphiphilic copolymers with cyclic polystyrene as the head and a linear poly(N‐isopropylacrylamide) as the tail have been successfully synthesized by combination of reversible addition‐fragmentation chain transfer (RAFT) polymerization and “click” reaction. The synthesis involves two main steps: (1) preparation of a linear acetylene‐terminated PNIPAAM‐b‐PS with a side azido group anchored at the junction between two blocks; (2) intramolecular cyclization reaction to produce the cyclic PS block using “click” chemistry under high dilution. The structures, molecular weights, and molecular weight distributions of the resulted intermediates and the target polymers were characterized by their ¹H NMR, FTIR, and gel permeation chromatography. The difference of surface property between tadpole‐shaped polymer and its linear precursor was observed, and the water contact angles on the former surface are larger than that of the latter surface. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2390–2401, 2008     

Asymptotics for solutions of a defective renewal equation with applications

In this paper, we derive non-exponential asymptotic forms for solutions of defective renewal equations. These include as special cases asymptotics for compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the Gerber-Shiu discounted penalty function in the classical risk model and the reliability of a two-unit cold standby system in reliability theory.      

Critical exponents for nonlinear diffusion equations with nonlinear boundary sources

This paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q₀ and the critical Fujita exponent qc for the problems considered, and show that q₀=qc for the multi-dimensional porous medium equation and non-Newtonian filtration equation with nonlinear boundary sources. This is quite different from the known results that q₀<qc for the one-dimensional case.