Initial‐Boundary Value Problems for the Coupled Nonlinear Schrödinger Equation on the Half‐Line

Initial‐boundary value problems for the coupled nonlinear Schrödinger equation on the half‐line are investigated via the Fokas method. It is shown that the solution can be expressed in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the complex k‐plane, whose jump matrix is defined in terms of the matrix spectral functions and that depend on the initial data and all boundary values, respectively. If there exist spectral functions satisfying the global relation, it can be proved that the function defined by the above Riemann–Hilbert problem solves the coupled nonlinear Schrödinger equation and agrees with the prescribed initial and boundary values. The most challenging problem in the implementation of this method is to characterize the unknown boundary values that appear in the spectral function . For a particular class of boundary conditions so‐called linearizable boundary conditions, it is possible to compute the spectral function in terms of and given boundary conditions by using the algebraic manipulation of the global relation. For the general case of boundary conditions, an effective characterization of the unknown boundary values can be obtained by employing perturbation expansion.     

广义sine-Gordon方程高精度隐式紧致差分方法

本文研究一类二维非线性的广义sine-Gordon(简称SG)方程的有限差分格式.首先构造三层时间的紧致交替方向隐式差分格式,并用能量分析法证明格式具有二阶时间精度和四阶空间精度.然后应用改进的Richardson外推算法将时间精度提高到四阶.最后,数值算例证实改进后的算法在空间和时间上均达到四阶精度.     

Synthesis and characterization of π-extended thienoacenes with up to 13 fused aromatic rings

π-Extended thienoacenes that comprise alternatively arranged anthracene and thieno[3,2-b]thiophene moieties and have 8 or 13 aromatic rings were synthesized. The delocalization of their HOMO and LUMO orbitals is over the entire molecules, and low-lying HOMO levels endow them good stability.     

Antibacterial cotton fabric prepared by a “grafting to” strategy using a QAC copolymer

Quaternary ammonium compounds (QACs) have outstanding antimicrobial effect, but covalent immobilization of plentiful QAC onto cotton fiber surface to realize a durable function remains a challenge. Herein, a quaternary ammonium monomer, [2-(methacryloyloxy) ethyl] trimethylammonium chloride (DMC) was co-polymerized with methyl acrylate (MA) to prepare an antibacterial copolymer, poly(DMC-co-MA). To graft the copolymer with an improved grafting efficiency, cotton fabric was treated using carboxymethyl chitosan (CMC) to establish an amino-functionalized fiber surface first. This treatment allows the amidation reactions between the amino groups and the pendant ester groups in the poly(DMC-co-MA) to take place, achieving a durable anionic polymer coating onto the fiber surfaces with remarkably antibacterial effect. Characterization results indicated that when DMC/MA monomer ratio was 100:1, the resulting copolymer endows the modified cotton fabric with antibacterial capability that inactivates all Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus). Even after 50 laundering cycles, more than 98.0% of the antibacterial rate could still be retained. Moreover, the wearing comfort properties such as softness, water absorption and air permeability of the finishing cotton fabrics have been insignificantly changed by comparing to the untreated cotton fabric.

     

金属草酸盐基负极材料——离子电池储能材料的新选择

商业化锂离子电池石墨负极和锂盐过渡金属氧化物正极材料的储锂容量都已接近各自的理论值,探索下一代高能量密度电极材料是解决现阶段锂离子电池容量限制的关键。近年来,新型金属草酸基负极材料,借助其在金属离子电池中多元化储能机制诱发的较高储能效应在碱金属离子电池绿色储能材料领域备受关注。本文就金属草酸基材料在锂、钠、钾金属离子电池方面的最新研究进行了综述,着重介绍了材料的晶型结构、多元化储能机制及储能过程中的动力学特征,简单阐述了材料在电化学储能中存在的问题,分析了金属草酸基负极材料在形貌晶型控制、界面碳复合改性和金属元素掺杂方面的改性策略。最后,预测了金属草酸基负极材料在碱金属离子电池体系的发展方向。     

Convergent architecting of multifunction-in-one hydrogels as wound dressings for surgical anti-infections

Surgical procedures are susceptible to the cause of infections, which could induce delayed wound healing, oxidative stress and tissue ischemia. Multifunctional wound dressings (e.g., hydrogels) without the induction of antibiotics is promising for the elimination of surgical site infections and the associated complications. Herein, we report a reductionism approach for the fabrication of bioactive hydrogels to recapitulate antibacterial functions as well as antioxidant, pro-angiogenic and hemostatic properties in surgical infection treatments. The hydrogels composed of naturally derived Cirsium setosum extracts (CE, a traditional medicinal herb) and carboxymethyl chitosan (CS) show their capacity for surgical anti-infections on three different models (i.e., infectious random skin flap model, infectious skin defect model and infectious femur fracture model). Due to the innate bioactivities of CE and CS, CECS hydrogels can also reduce the bleeding loss (85% reduction) on a hemorrhaging liver model and improve the vascularization for skin flap regeneration. Overall, bioactive CECS hydrogels integrated with the ease and scalability of assembly process and biological activities without the addition of antibiotics is promising to act as multifunctional wound dressings for surgical anti-infections.     

Janus 粒子在环境检测领域中的应用

Janus 粒子,也称为阴阳结构粒子或两面性非对称粒子,是指表面上具有两种或两种以上不同化学组成或性质的不对称粒子。目前,Janus 粒子因其独特的结构和功能已经逐渐成为生物医药、催化、材料以及防污等领域中的新型功能材料。在环境检测领域,Janus材料亦因其特殊的光学、磁学及电学性能,为提高检测灵敏度、选择性和稳定性等提供了新的研究方向。基于此,本文主要讨论了Janus材料在环境检测方面的特点、优势和相关应用。最后,本文基于本课题组的研究经验以及工作中所面临的问题,对本领域的发展和未来的研究方向提出了展望,以期对本领域的未来发展提供指导。     

变系数拟自回归模型下的测量误差分析

本文对雷达测量误差影响较大的因素进行了分析研究,并将其和雷达测量数据一起建立了变系数拟自回归的统计模型以实现对雷达测量值的纠偏,利用剖面最小二乘法估计模型参数,在一定条件下证明了模型的大样本性质,并结合残差的峰度和偏度构建了区间估计。实际数据的拟合和预测结果显示,我们提出的纠偏方法可将误差减少90%。     

CP violations in predictive neutrino mass structures

We study the CP-violation effects from two types of neutrino mass matrices with (i) \((M_\nu )_{ee}=0\), and (ii) \((M_\nu )_{ee}=(M_\nu )_{e\mu }=0\), which can be realized by the high-dimensional lepton number violating operators \(\bar{\ell }_R^c\gamma ^\mu L_L (D_\mu \Phi )\Phi ^2\) and \(\bar{\ell }_R^c l_R (D_\mu {\Phi })^2\Phi ^2\), respectively. In (i), the neutrino mass spectrum is in the normal ordering with the lightest neutrino mass within the range \(0.002\,\mathrm{eV}\lesssim m_0\lesssim 0.007\,\mathrm{eV}\). Furthermore, for a given value of \(m_0\), there are two solutions for the two Majorana phases \(\alpha _{21}\) and \(\alpha _{31}\), whereas the Dirac phase \(\delta \) is arbitrary. For (ii), the parameters of \(m_0\), \(\delta \), \(\alpha _{21}\), and \(\alpha _{31}\) can be completely determined. We calculate the CP-violating asymmetries in neutrino–antineutrino oscillations for both mass textures of (i) and (ii), which are closely related to the CP-violating Majorana phases.