Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

Modified layered bimetallic compound used as a novel adsorbent for the solid-phase extraction of monoaromatic hydrocarbons from water samples prior to gas chromatography–mass spectrometry

This study reports a promising method of solid-phase extraction for determining the toluene, ethylbenzene, p-xylene, m-xylene, o-xylene, 1,3,5-trimethylbenzene, and 1,2,4-trimethylbenzene in water samples by gas chromatography–mass spectrometry (GC–MS). Prior to this procedure, the magnesium–aluminum bimetallic hydroxides modified with sodium dodecylbenzenesulfonate (Mg/Al-SDBS-LDH) were prepared and served as the novel solid-phase extractant. The Mg/Al-SDBS-LDH has advantage of good hydrophobicity and larger spacing which facilitates the monoaromatic hydrocarbons (MAHCs) into the interlayer for adsorption. As a result, the seven MAHCs in 500 mL water samples were enriched greatly, and the theoretical enrichment factor reached to 125 times. Under the optimized conditions of solid-phase extraction (SPE) and GC–MS, the mass concentration of each MAHC (0.005–10, 0.01–10, or 0.05–10 ng/mL) had a fine linear relationship with peak area. The correlation coefficients were more than 0.995. The detection limits were between 0.001 and 0.01 ng/mL, and the RSD were between 3.1% and 6.6%. The method had been applied to determine the seven MAHCs in the Dongfengqu river water and laboratory wastewater of Chengdu University of Technology successfully.     

Fano profile in a novel double cavity optomechanical system with harmonically bound mirrors

We investigate a double cavity optomechanical system generating single and double Fano resonance (multi-Fano). By altering a single parameter, the tunnelling rate g of the middle mirror, we are able to switch between single and double Fano line shapes. The first spectral line shape is stronger in the case of multi-Fano than in the case of single Fano. Also the behaviour of the steady state value of the displacement of the middle mirror, with respect to g, heavily influences the behaviour of double Fano lines in our scheme. This tunability along with using a single pump and signal/probe laser has an added advantage in situations where only low power consumption is available.     

2个位势的Ablowitz-Ladik等谱方程的Complexiton解

借助双Casoratian技巧和构造双Wronski行列式元素的矩阵方法,求出2个位势的Ablowitz-Ladik等谱方程的Complexiton解和周期解,并通过将矩阵取成不同的组合类型,进而分别得到该方程具有双Casorati行列式形式的新解,即Complexiton解与类有理解的混合解、Complexiton解与Matveev解的混合解.     

Crystalline Boragermenes

Boragermene 3 featuring a double bond between the Ge and dicoordinate B atoms has been synthesized for the first time by reacting the cyclic (alkyl)(boryl)germylene–PMe₃ adduct 1 with Cl₂BN(SiMe₃)₂ followed by reductive dehalogenation with KC₈. Addition of a Lewis base (^MeNHC) to 3 leads to the formation of the corresponding adduct 4 , which shows double bond character between the Ge and tricoordinate B atoms. Compound 3 undergoes hydrogenation with H₂ concomitant with a complete scission of the Ge=B bond.     

应变对单层砷烯结构拉曼散射的影响

应用密度泛函理论对应变下的单层砷烯拉曼光谱的变化进行研究.由于材料的结构对称性较低，由外部应力诱发的形变不仅可以造成拉曼模式分裂，还可以引发拉曼模式偏移.计算表明：拉曼峰位的变化与应变正相关，建立了应变与峰位移动间的定量关系，为在实验中识别砷烯结构的应变提供依据.     

通过超宽139La固体核磁共振波谱研究层状La(OH)2NO3

层状稀土氢氧化物是一类新型的稀土功能材料，本文采用固体核磁共振（SSNMR）方法研究了同时具备离子交换能力和非线性光学特性的层状La（OH）₂NO₃化合物，探讨了通过四极核CPMG（QCPMG）脉冲序列和变频谱图采集获取超宽¹³⁹La SSNMR谱图的方法，并描述了适用于此类实验的滤波方程和谱图重建方法.重建谱图同时包含四极核中心跃迁和卫星跃迁信息，本文使用QUEST软件对超宽¹³⁹La NMR谱图进行了模拟，获取的四极耦合常数C_Q和非对称因子η_Q均与CASTEP密度泛函理论计算值高度吻合.SSNMR实验结果证实层状La（OH）₂NO₃化合物属于非中心对称结构（P2₁），解决了对其结构长期以来存在的争论.     

若干高维可积和不可积模型的严格解

可积和不可积模型可以描述自然科学中的诸多现象, 寻找高维非线性模型的严格解已成为可积系统的一个重要研究内容. 结合达布变换法和多线性分离变量法, 可以得到多个(2+1)维非线性模型包含任意函数的严格解, 通过选取不同的任意函数, 构造这些非线性模型新的相互激发模式. 进一步推广了形变映射理论, 建立了变系数 场和sine-Gordon以及双sine-Gordon场的形变映射关系, 从而得到高维不可积模型包含任意函数的新严格解. 对任意函数的不同选择, 构造了sine-Gordon和双sine-Gordon可积模型丰富的局域解和周期解, 如多solitoff解及其周期波推广、周期形变的蛇形孤波解以及变模的拟周期解等.