New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation

In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Left. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Left. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii‘s generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.     

Baeicklund Transformation and Multiple Soliton Solutions for （3＋1）-Dimensional Potential-YTSF Equation

We study an approach to constructing multiple soliton solutions of the (3 1)-dimensional nonlinear evolution equation. We take the (3 1)-dimensional potential- YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3 1)-dimensional potential-YTSF equation into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3 1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions.     

Some Special Types of Solitary Wave Solutions for (3+1)-Dimensional Jimbo-Miwa Equation

Using the extended homogeneous balance method, we find some special types of single solitary wave solution and new types of the multisoliton solutions of the (3+1)-dimensional Jimbo-Miwa equation.     

New Ansaetze for Obtaining Exact Solutions of Nonlinear Schroedinger-Type Equation

We propose two simple ansaetze that allow us to obtain different analytical solutions for two generalizeal versions of the nonlinear Schrodinger equation, such as the averaged dispersive-managed fiber system equation and the extended nonlinear Schrodinger equation which describe the femtosecond pulse propagation in monomode optical fiber. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media.     

Symmetry Reduction, Exact Solutions, and Conservation Laws of （2＋1）-Dimensional Burgers Korteweg-de Vries Equation

Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.     

Visible-light-induced photocatalytic difluoroalkylation of 3-substituted benzo[d]isoxazoles via direct and regioselective CH functionalization

The difluoroalkylation of unactivated benzo[d]isoxazoles with ethyl difluorobromoacetate by visible-light photoredox catalysis via direct and regioselective CH functionalization has been efficiently achieved under mild reaction conditions. The difluoroalkylated adducts could be readily converted to a variety of corresponding CF₂-containing heterocycles, demonstrating the synthetic utility of the present approach.     

Symmetry Reduction, Exact Solutions, and Conservation Laws of (2+1)-Dimensional Burgers Korteweg-de Vries Equation

Using the classical Lie method of infinitesimals, we first obtain the symmetry of the (2 1)-dimensional Burgers-Korteweg-de-Vries (3D-BKdV) equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.     

Effect of variations in pore structure and acidity of alkali treated ZSM-5 on the isomerization performance

A series of alkali treated ZSM-5 samples were prepared and the effects of the alkali treatment conditions on the n-hexane isomerization performance of Pt/ZSM-5 were investigated. The characterization by XRD, N₂-adsorption, XRF, NH₃-TPD, Py-IR and NMR revealed that alkali treatment conditions had the effects on the crystallinity, textural property, Si/Al ratio and acidity of ZSM-5. Mild alkali treatment led to the reduction of the strong acid sites and did not distinctly change the pore structure, whereas severe alkali treatment resulted in the creation of the stronger acid sites and new mesopores. The correlation of the acidity and pore structure and isomerization behavior was established. It was proposed that the conversion of n-hexane was dependent on the amount of strong acid sites and irrelevant to the properties of acid sites and the pore structure. However, the selectivity for iso-hexanes was irrelevant to both the acidity and pore structure. The relative amount of dimethylbutanes (DMB) and methylpentanes (MP) in isomers was related not only to the pore structure, but to the acidity of ZSM-5. The suitable alkali treatment condition facilitated the high yield of isomers and the formation of more DMB.     

p-harmonic 1-forms on complete manifolds

Let (M ^m , g) be a complete non-compact manifold with asymptotically non-negative Ricci curvature and finite first Betti number. We prove that any bounded set of p-harmonic 1-forms in L ^q (M), 0 < q < ∞, is relatively compact with respect to the uniform convergence topology.     

光敏共聚物P(St/VM-co-MA)自组装胶体粒子及其性能

以苯乙烯类光敏单体7-(4-乙烯基苄氧基)-4-甲基香豆素(VM)、苯乙烯(St)、马来酸酐(MA)为共聚单体,采用自由基聚合法制备了光敏性双亲共聚物P(St/VM-co-MA).在选择性溶剂(N,N-二甲基甲酰胺(DMF)/H2O)中对P(St/VM-co-MA)进行自组装,用透射电镜(TEM)和动态激光光散射(DLS)表征了自组装胶体粒子的形态、粒径大小及其分布.利用紫外光照使胶体粒子中香豆素基元发生光二聚反应,形成交联胶体粒子,并用紫外-可见光分光光度计(UV-Vis)跟踪其交联过程.用DLS研究了交联和未经交联胶体粒子的粒径和结构稳定性,用激光扫描共聚焦显微镜(LSCM)和光学显微镜考察了胶体粒子的乳化、包覆性能.结果表明:交联和未经交联胶体粒子均具有乳化性,且在乳化过程中可实现对油溶性染料的包覆.胶体粒子交联后,粒径有所减小,结构稳定性、乳化性能、包覆性能均有所提高.