Blow-up solutions and global solutions for nonlinear parabolic problems

This paper deals with the blow-up of positive solutions for a nonlinear parabolic equation subject to nonlinear boundary conditions. We obtain the conditions under which the solutions may exist globally or blow up in a finite time, by a new approach. Moreover, upper estimates of the “blow-up time”, blow-up rate and global solutions are obtained also.     

Design,synthesis, and characterization of a combined main-chain/side-chain liquid-crystalline polymer based on ethyl cellulose

A novel combined main-chain/side-chain liquid-crystalline polymer based on an ethyl cellulose main chain containing azobenzene mesogens (AzoEC) was successfully synthesized. Molecular characterization of the resulting polymers with different degrees of substitution (DS) was performed with proton nuclear magnetic resonance (¹H NMR), Fourier-transform infrared spectroscopy (FTIR), and gel permeation chromatography (GPC). Thermal stability was investigated by thermogravimetric analysis (TGA). The phase transitions and liquid-crystalline behavior of these polymers were investigated by differential-scanning calorimetry (DSC), polarized optical microscopy (POM), and wide-angle X-ray diffraction (WAXD). The results indicate that DS has substantial effect on the liquid-crystalline behavior of these polymers. AzoEC with low DS only shows the cholesteric phase similar to ethyl cellulose (EC). However, when DS increases to a specific value, AzoEC begins to show fascinating supramolecular structures. The supramolecular structure of AzoEC with maximum DS consisted of a large-scale ordered lamellar structure formed by EC main chains and a small-scale ordered structure formed by azobenzene mesogens.     

Portfolio optimization in a regime-switching market with derivatives

We consider the optimal asset allocation problem in a continuous-time regime-switching market. The problem is to maximize the expected utility of the terminal wealth of a portfolio that contains an option, an underlying stock and a risk-free bond. The difficulty that arises in our setting is finding a way to represent the return of the option by the returns of the stock and the risk-free bond in an incomplete regime-switching market. To overcome this difficulty, we introduce a functional operator to generate a sequence of value functions, and then show that the optimal value function is the limit of this sequence. The explicit form of each function in the sequence can be obtained by solving an auxiliary portfolio optimization problem in a single-regime market. And then the original optimal value function can be approximated by taking the limit. Additionally, we can also show that the optimal value function is a solution to a dynamic programming equation, which leads to the explicit forms for the optimal value function and the optimal portfolio process. Furthermore, we demonstrate that, as long as the current state of the Markov chain is given, it is still optimal for an investor in a multiple-regime market to simply allocate his/her wealth in the same way as in a single-regime market.     

Raman spectroscopic detection for liquid and solid targets using a spatial heterodyne spectrometer

Spatial heterodyne Raman spectroscopy (SHRS) is a new type of effective method for the analysis of structure and composition of liquid and solid targets with the characteristics of no moving parts, high spectral resolution, high optical throughput and large field of view. The technique is very suitable for detecting the targets from long distances or under the conditions with ambient light, which is essential for the exploration of planetary surface. In order to have a better understanding of the ability of SHRS for the detection of liquid and solid targets, a breadboard was designed, built and calibrated. Signal to noise was estimated at different integration time or laser power for carbon tetrachloride. Pure materials or materials contained in bottles were both tested. The mixture of organic liquids or inorganic solids were tested. In order to test the detection ability for natural targets, some composition‐unknown rocks and pebbles were tested. The results have shown that SHRS can meet the requirements for the detection of weak Raman signal scattered from artificial or natural targets. Standoff detection of sulfur from 5‐m or 10‐m distance without using any telescope or collimation optics was also tried to test the high optical throughput of SHRS. The potential feasibility of standoff detection has been proved. Copyright © 2015 John Wiley & Sons, Ltd.     

Superconvergence of the direct discontinuous Galerkin method for convection‐diffusion equations

This paper is concerned with superconvergence properties of the direct discontinuous Galerkin (DDG) method for one‐dimensional linear convection‐diffusion equations. We prove, under some suitable choice of numerical fluxes and initial discretization, a 2k‐th and ‐th order superconvergence rate of the DDG approximation at nodes and Lobatto points, respectively, and a ‐th order of the derivative approximation at Gauss points, where k is the polynomial degree. Moreover, we also prove that the DDG solution is superconvergent with an order k + 2 to a particular projection of the exact solution. Numerical experiments are presented to validate the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 290–317, 2017     

Controlled chlorine plasma reaction for noninvasive graphene doping

We investigated the chlorine plasma reaction with graphene and graphene nanoribbons and compared it with the hydrogen and fluorine plasma reactions. Unlike the rapid destruction of graphene by hydrogen and fluorine plasmas, much slower reaction kinetics between the chlorine plasma and graphene were observed, allowing for controlled chlorination. Electrical measurements on graphene sheets, graphene nanoribbons, and large graphene films grown by chemical vapor deposition showed p-type doping accompanied by a conductance increase, suggesting nondestructive doping via chlorination. Ab initio simulations were performed to rationalize the differences in fluorine, hydrogen, and chlorine functionalization of graphene.     

A novel pseudo simulated moving bed with solvent gradient for ternary separations

A novel pseudo simulated moving bed was suggested to separate a ternary mixture. A solvent gradient was created to make the solvent strength decreasing from zone II to zone III. Under suitable conditions, the least retained solute A moved forward and the most retained solute C moved backward in zones II and III whereas the medium retained solute B moved forward in zone II but backward in zone III to be trapped in the two zones consequently. Once the columns in zones II and III were saturated with solute B, the solvent dissolving the feed was introduced at the feed port to remove solute A from the raffinate-port and solute C from the extract-port. Finally, solute B was recovered from the extract port by stopping the liquid flow in zone II. This scheme was validated by the successful separation of dihydrocapsaicin from capsaicinoids.     

非凸双曲守恒律解的渐近性质

本文研究了非凸双曲守恒律ｕｔ＋（ｕ＾３）ｘ＝０解的渐近性态。对于初值具有紧支集或周期函数的情形，我们利用广义特征原理，建立了关于波速总变差的基本递推估计，给出了解的最优衰减速率。     

图T1,1,m与Q(3,n)中有路因子的充分必要条件及T1,1,m的匹配等价类

如果一个图的匹配多项式可以被一个路的匹配多项式整除,我们就称此路是该图的一个路因子,路因子在刻画图的匹配等价类,研究匹配唯一性方面有很重要的作用.本文得到了图T1,1.m与图Q(3,n)中有路因子的充分必要条件.     

Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors

The asymptotic behavior of classical solutions of the bipolar hydrodynamical model for semiconductors is considered in the present paper. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equation. The global existence of classical solutions is proven, and the nonlinear diffusive phenomena is observed in large time in the sense that both densities of electron and hole tend to the same unique nonlinear diffusive wave.