Restricted testing conditions for the multilinear maximal operator

Restricted testing conditions were considered recently. For the maximal operator, Hytönen, Li and Sawyer [8] first obtained parental testing condition. Later, they [9] showed that it suffices to restrict testing to doubling cubes. Chen and Lacey [3] gave a similar restricted testing condition. In our paper, we discuss a version of the latter in the multilinear setting.

     

From differential equation solvers to accelerated first-order methods for convex optimization

Mathematical Programming - Convergence analysis of accelerated first-order methods for convex optimization problems are developed from the point of view of ordinary differential equation solvers. A...     

Visible light-driven acridone catalysis for atom transfer radical polymerization

Acridone as a new kind of visible light photocatalyst has been developed to catalyze metal free atom transfer radical polymerization (ATRP). The photocatalyst possess low excited state potential as can undergo an oxidative quenching pathway to initiate ATRP of vinyl monomers. Kinetic study and light on/off reaction demonstrate the “living”/controlled nature of the polymerization by light. Block copolymers can be achieved by using PMMA as macroinitiator to reinitiate polymerization of other vinyl monomers, which shows highly preserved Br chain-end functionality in the synthesized polymers. Moreover, the polymerization can be conducted under air atmosphere as most photocatalysts need anaerobic condition, which may give inspiration of further application of this kind of photocatalyst.     

A Note on Quantum Bell Nonlocality and Quantum Entanglement for High Dimensional Quantum Systems

We study the Bell nonlocality of high dimensional quantum systems based on quantum entanglement. A quantitative relationship between the maximal expectation value B of Bell operators and the quantum entanglement concurrence C is obtained for even dimension pure states, with the upper and lower bounds of B governed by C.

     

Chiral phase transition and equation of state in chiral imbalance

The chiral phase transition and equation of state are studied within a novel self-consistent mean-field approximation of the two-flavor Nambu-Jona-Lasinio model. In this newly developed model, modifications to the chemical μ and chiral chemical \begin{document}$\mu_5$\end{document} potentials are naturally included by introducing vector and axial-vector channels from Fierz-transformed Lagrangian to the standard Lagrangian. In the proper-time scheme, the chiral phase transition is a crossover in the \begin{document}$T-\mu$\end{document} plane. However, when \begin{document}$\mu_5$\end{document} is incorporated, our study demonstrates that a first order phase transition may emerge. Furthermore, the chiral imbalance will soften the equation of state of quark matter. The mass-radius relationship and tidal deformability of quark stars are calculated. The maximum mass and radius decrease as \begin{document}$\mu_5$\end{document} increases. Our study also indicates that the vector and axial-vector channels exhibit an opposite influence on the equation of state.     

Viscoelastic properties of ultrathin polycarbonate films by liquid dewetting

A liquid dewetting method for the determination of the viscoelastic properties of ultrathin polymer films has been extended to study thickness effects on the properties of ultrathin polycarbonate (PC) films. PC films with film thicknesses ranging from 4 to 299 nm were placed on glycerol at temperatures from below the macroscopic glass transition temperature (T_g) to above it with the dewetting responses being monitored. It is found that the isothermal creep results for films of the same thickness, but dewetted at different temperatures can be superposed into one master curve, which is consistent with the fact of PC being a thermorheologically simple material. Furthermore, the results show that the T_g of PC thin films is thickness dependent, but the dependence is weaker than the results for freely standing films and similar to literature data for PC films supported on rigid substrates. It was also found that the rubbery plateau region for the PC films stiffens dramatically, but still less than what has been observed for freely standing polycarbonate films. The rubbery stiffening is discussed in terms of a recently reported model that relates macroscopic segmental dynamics with the stiffening. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1559–1566     

Space-Confined Atomic Clusters Catalyze Superassembly of Silicon Nanodots within Carbon Frameworks for Use in Lithium-Ion Batteries

Incorporating nanoscale Si into a carbon matrix with high dispersity is desirable for the preparation of lithium-ion batteries (LIBs) but remains challenging. A space-confined catalytic strategy is proposed for direct superassembly of Si nanodots within a carbon (Si NDs⊂C) framework by copyrolysis of triphenyltin hydride (TPT) and diphenylsilane (DPS), where Sn atomic clusters created from TPT pyrolysis serve as the catalyst for DPS pyrolysis and Si catalytic growth. The use of Sn atomic cluster catalysts alters the reaction pathway to avoid SiC generation and enable formation of Si NDs with reduced dimensions. A typical Si NDs⊂C framework demonstrates a remarkable comprehensive performance comparable to other Si-based high-performance half LIBs, and higher energy densities compared to commercial full LIBs, as a consequence of the high dispersity of Si NDs with low lithiation stress. Supported by mechanic simulations, this study paves the way for construction of Si/C composites suitable for applications in future energy technologies.     

Transition-Metal Catalysis of Triene 6π Electrocyclization: The π-Complexation Strategy Realized

Triene 6π electrocyclization, wherein a conjugated triene undergoes a concerted stereospecific cycloisomerization to a cyclohexadiene, is a reaction of great historical and practical significance. In order to circumvent limitations imposed by the normally harsh reaction conditions, chemists have long sought to develop catalytic variants based upon the activating power of metal–alkene coordination. Herein, we demonstrate the first successful implementation of such a strategy by utilizing [(C₅H₅)Ru(NCMe)₃]PF₆ as a precatalyst for the disrotatory 6π electrocyclization of highly substituted trienes that are resistant to thermal cyclization. Mechanistic and computational studies implicate hexahapto transition-metal coordination as responsible for lowering the energetic barrier to ring closure. This work establishes a foundation for the development of new catalysts for stereoselective electrocyclizations.