Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation \({\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial _x^2u + u{u_x} = 0\), where \({\cal H}\) denotes the Hilbert transform operator. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \({\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)\), which is a subspace of L²(ℝ). It is worth noting that the low-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is scaling critical, and thus the small data is necessary. The high-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is equal to the Sobolev space H^σ (ℝ) (σ ⩾ 0) and reduces to L²(ℝ). Furthermore, we also obtain its inviscid limit behavior in \({\tilde H^\sigma }(\mathbb{R})\) (σ ⩾ 0).

     

Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

化学法改性煤沥青脱除苯并芘的研究

在管式反应器中采用苯甲酸、聚乙二醇、固体古马隆树脂（S）、液体古马隆树脂（L）为添加剂来降低煤沥青中有害物质苯并芘的含量，以期使得煤沥青可绿色化应用。采用紫外-可见分光光度计分析煤沥青中苯并芘含量。考察了反应温度、反应时间、添加剂添加量、催化剂等工艺条件对添加剂脱除煤沥青中苯并芘的影响。结果表明，不同工艺条件能降低煤沥青中苯并芘的含量。在优化条件下，不同添加剂对苯并芘脱除率由高到低依次为：液体古马隆树脂、聚乙二醇、苯甲酸和固体古马隆树脂。分析其反应机理，这与催化剂的酸性相关，发生亲电取代反应。结果表明，液体古马隆树脂（L）在催化剂存在下对煤沥青中苯并芘脱除率可达73.0%，显示了良好的应用前景。     

Microwave‐assisted polycondensation of 4‐octylaniline with dibromoarylene

The Pd‐catalyzed polycondensation of 4‐octylaniline with various dibromoarylenes was carried out under microwave heating. Microwave heating led to a decrease in the reaction time and an increase in the molecular weight of the polymers as compared to conventional heating. Microwave heating also allowed the catalyst loading to be reduced to 1 mol %, yielding polymerization results that were comparable to those under conventional heating and 5 mol % catalyst. Investigations regarding field‐effect transistors and organic photovoltaic cells using the obtained poly(arylamine) with azobenzene units revealed that increasing the molecular weight of the polymer led to improved device performance, including hole mobility and power conversion efficiency. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 536–542     

Evaluation of Charged Defect Energy in Two-Dimensional Semiconductors for Nanoelectronics: The WLZ Extrapolation Method

Defects play a central role in controlling the electronic properties of two-dimensional (2D) materials and realizing the industrialization of 2D electronics. However, the evaluation of charged defects in 2D materials within first-principles calculation is very challenging and has triggered a recent development of the WLZ (Wang, Li, Zhang) extrapolation method. This method lays the foundation of the theoretical evaluation of energies of charged defects in 2D materials within the first-principles framework. Herein, the vital role of defects for advancing 2D electronics is discussed, followed by an introduction of the fundamentals of the WLZ extrapolation method. The ionization energies (IEs) obtained by this method for defects in various 2D semiconductors are then reviewed and summarized. Finally, the unique defect physics in 2D dimensions including the dielectric environment effects, defect ionization process, and carrier transport mechanism captured with the WLZ extrapolation method are presented. As an efficient and reasonable evaluation of charged defects in 2D materials for nanoelectronics and other emerging applications, this work can be of benefit to the community.     

On Fermat Diophantine functional equations,little Picard theorem and beyond

Aequationes mathematicae - We discuss equivalence conditions for the non-existence of non-trivial meromorphic solutions to the Fermat Diophantine equation $$f^m(z)+g^n(z)=1$$ with integers $$m,n\ge...     

Photo-Controlled Macroscopic Self-Assembly Based on Photo-Switchable Hetero-Complementary Quadruple Hydrogen Bonds

A photo-switchable hetero-complementary quadruple H-bonding array, which consists of an azobenzene-derived ureidopyrimidinone (UPy) module ( Azo-UPy ) and a nonphotoactive diamidonaphthyridine (DAN) derivative ( Napy-1 ), is constructed based on a reversible photo-locking approach. Upon UV (390 nm)/Vis (460 nm) light irradiations, photo-switchable quadruple H-bonded dimerization between Azo-UPy and Napy-1 can be achieved with exhibiting 4.8×10⁴-fold differences in binding strength (ON/OFF ratios). Furthermore, smart polymeric gels with unique photo-controlled macroscopic self-assembly behavior can be fabricated by introducing such quadruple H-bonding array as photo-regulable noncovalent interfacial connections.