Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrödinger Equation

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.     

Semilinear wave models with friction and viscoelastic damping

In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.     

基于化学学科认知障碍突破的中考复习教学实践* ——以“二氧化碳的性质”为例

分析学生对二氧化碳的3个典型学科认知障碍,以“二氧化碳的捕捉”为情境,通过“尝试捕捉二氧化碳”“谁在捕捉二氧化碳”“捕捉背后的原理”等3个主要环节,实现对学科认知障碍的突破,展示了一种新的中考复习教学思路。     

Physical aging in amorphous poly(ethylene furanoate): Enthalpic recovery,density, and oxygen transport considerations

The current work utilizes three separate techniques to study the physical aging process in amorphous poly(ethylene furanoate) (PEF), which is a recently introduced engineering thermoplastic with enhanced properties compared to petroleum‐sourced poly(ethylene terephthalate). Differential scanning calorimetry aging experiments were conducted at multiple aging temperatures and times, and the resultant enthalpic recovery values compared to the theoretical maximum enthalpy loss evaluated from calculations involving extrapolation of the equilibrium liquid line. Density measurements reveal densification of the matrix for the aged versus unaged samples, and provide an estimate for the reduction in free volume for the aged samples. Complementary oxygen permeation and pressure‐decay sorption experiments provide independent verification of the free volume reduction mechanism for physical aging in glassy polymers. The current work provides the first detailed aging study for PEF. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 389–399     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Synthesis,Electronic Properties and WOLED Devices of Planar Phosphorus‐Containing Polycyclic Aromatic Hydrocarbons

We describe the synthesis and the physical properties of polyaromatic hydrocarbons (PAHs) containing a phosphorus atom at the edge. In particular, the impact of the successive addition of aromatic rings on the electronic properties was investigated by experimental (UV/Vis absorption, fluorescence, cyclic voltammetry) and theoretical studies (DFT). The physical properties recorded in solution and in the solid state showed that the P‐containing PAHs exhibit properties expected for an emitter in white organic light‐emitting diodes (WOLEDs).     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Arbitrage‐free call option surface construction using regression splines

In this work, we suggest a novel quadratic programming‐based algorithm to generate an arbitrage‐free call option surface. The empirical performance of the proposed method is evaluated using S&P 500 Index call options. Our results indicate that the proposed method provides a more precise fit to observed option prices than other alternative methodologies. Copyright © 2014 John Wiley & Sons, Ltd.