Time-evolution-proof Scattering Data for the Focusing and Defocusing Zakharov-Shabat Systems

In this article we give sufficient conditions on the scattering data of a defocusing or focusing Zakharov-Shabat system in order that its potential is square integrable. For a dense subset of integrable as well as square integrable potentials, we show that the scattering data actually satisfy these sufficient conditions.     

Nonlinear interaction mechanisms of disturbances in supersonic flat-plate boundary layers

Due to the complexity of compressible flows, nonlinear hydrodynamic stability theories in supersonic boundary layers are not sufficient. In order to reveal the nonlinear interaction mechanisms of the rapidly amplified 3-D disturbances in supersonic boundary layers at high Mach numbers, the nonlinear evolutions of different disturbances in flat-plate boundary layers at Mach number 4.5, 6 and 8 are analyzed by numerical simulations. It can be concluded that the 3-D disturbances are amplified rapidly when the amplitude of the 2-D disturbance reaches a certain level. The most rapidly amplified 3-D disturbances are Klebanoff type (K-type) disturbances which have the same frequency as the 2-D disturbance. Among these K-type 3-D disturbances, the disturbances located at the junction of upper branch and lower branch of the neutral curve are amplified higher. Through analyzing the relationship between the amplification rate and the spanwise wavenumber of the 3-D disturbances at different evolution stages, the mechanism of the spanwise wavenumber selectivity of K-type 3-D disturbances in the presence of a finite amplitude 2-D disturbance is explained.     

Effect of permodified β‐cyclodextrin on the photophysical properties of poly[2,7‐(9,9‐dioctylfluorene)‐alt‐(5,5′‐bithiophene)] main chain polyrotaxanes

The photophysical properties of two polyrotaxanes ( PFBTh?PSβCD and PFBTh?PMeβCD ) composed of fluorene and bithiophene encapsulated into permodified β‐cyclodextrin cavities have been investigated and compared with those of the reference PFBTh . Rotaxane formation results in improvements of the thermal stability, solubility in common organic solvents, as well as better film forming ability combined with a high transparency. As expected PFBTh and its encapsulated forms absorb at wavelengths beyond 510 nm, and time‐resolved photoluminescence (PL) in solution shows a well‐define vibronic structures with a predominance of the 0‐0 transitions and an energy difference of 0.16 eV. The fluorescence lifetimes follow a monoexponential decay with a value τ = 630 ± 30 ps. Atomic force microscopy, AFM, indicated a tendency of polyrotaxanes to organize into fibers. The advancing contact angles indicated higher surface hydrophobicity and lower surface free‐energy values for polyrotaxanes compared with their unthreaded analogues. The device based on PFBTh?PSβCD: PCBM in a 1/1 w/w ratio under simulated AM 1.5G illumination at 100 mW cm^?2 exhibited improved photovoltaic parameters of cells, resulted in high V_oc (0.68 V), J_sc (1.65 mA cm^?2), FF (31.6%), and PCE (0.35) values, compared with PFBTh or PFBTh?PMeβCD , respectively. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 460–471     

A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy

In this Letter, a generalized Tu formula is firstly presented to construct Hamiltonian structures of fractional soliton equations. The obtained results can be reduced to the classical Hamiltonian hierarchy of AKNS in ordinary calculus.     

Evaluating nonlinear variability of mental fatigue behavioral indices during long‐term attentive task

This study investigates the behavioral indices of attention. A simple repetitive attentive task that resulted in mental fatigue was used consecutively in four trials. In the first step, reaction time and error responses were recorded to evaluate differences among trials. During the task, subjects showed different responses to stimulations. In the second part, to recognize the strategies, multiple clustering methods such as k‐means and fuzzy c‐means were performed in which behavioral indices and nonlinear features were used. In the last section, mental behavior was identified as a result of the chaotic properties of variations in reaction time. Therefore, the Lyapunov exponent of reaction times was evaluated. Results revealed that behavioral indices could distinguish attention from the occurrence of mental fatigue in trials. In addition, the three strategies used by subjects during the test protocol were assessed. Finally, variation of indices extracted from nonlinear analysis, that is, decrease in degree of chaotic behavior determined the transition from attention to mental fatigue. © 2012 Wiley Periodicals, Inc. Complexity, 2012     

SOLUTION WITH SHOCK-BOUNDARY LAYER AND SHOCK-INTERIOR LAYER TO A CLASS OF NONLINEAR PROBLEMS

In this paper,the shock behaviors of solution to a class of nonlinear singularly perturbed problems are considered.Under some appropriate conditions,the outer and interior solutions to the original problem are constructed.Using the special limit and matching theory,the expressions of solutions with the shock behavior near the boundary and some interior points are given and the domain for boundary values is obtained.     

New simple exact penalty function for constrained minimization

By adding one variable to the equality-or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.     

高硅煤中Si-Al-Fe-Ca四元体系碳热反应研究

研究了不同温度条件下高硅煤中矿物组成比例下的Si-Al-Fe-Ca多元体系的碳热反应以及其影响因素。通过XRD和FESEM-EDS技术对各还原产物进行分析。结果表明,Fe_2O_3对含硅矿物的碳热反应起促进作用,Fe可以有效提高Si反应活性。CaO在较低温度时与灰中的Al_2O_3和SiO_2反应形成致密的Ca-Al-Si相共熔体CaAl_2Si_2O_8,阻碍含硅矿物碳热反应的进行。随着温度的升高,继续反应生成SiC、CaAl_4O_7和CaSiO_3。热力学模拟计算与实验结果基本吻合。     

A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd.