Nonclassical symmetries of a class of nonlinear partial differential equations with arbitrary order and compatibility

In this paper, we show that for a class of nonlinear partial differential equations with arbitrary order the determining equations for the nonclassical reduction can be obtained by requiring the compatibility between the original equation and the invariant surface condition. The nonlinear wave equation and the Boussinesq equation all serve as examples illustrating this fact.     

Exact solutions for the coupled Klein-Gordon-Schrǒdinger equations using the extended F-expansion method

The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.     

拓扑交性质与极大极小定理

本文得到一个一般的拓扑型有限交性质,并将所得结果应用于研究拓扑型极大极小定理     

A study of conduction band edge states in complex oxides by X-ray absorption spectroscopy

Conduction band edge d-states are compared for complex oxides: (i) mixed tetravalent–trivalent ZrO₂–Y₂O₃ alloys, (ii) tetravalent Zr(Hf)O₂–TiO₂ alloys, and (iii) trivalent La scandate and aluminate. Low Y₂O₃ content cubic ZrO₂–Y₂O₃ alloys display two crystal-field split 4d-features in O K₁ spectra. Alloys with higher Y₂O₃ content, as well as Zr(Hf)O₂–TiO₂ alloys display increased d-state multiplicity. O K₁ spectra of perovskite-structured LaScO₃ and LaAlO₃ indicate Jahn–Teller d-state term-splittings with contributions from both trivalent atomic species.     

稠密的s维分形集

对任意给定的0≤s≤1,本文构造Cantor型集E_s,使dim_H E_s=s,且E_s在[0,1]内稠密。     

Double photoionisation spectra of HI,CH3I and CF3I from TOF-PEPECO measurements

Double photoionisation spectra of HI, CH₃I and CF₃I have been measured by the TOF-PEPECO technique, providing complete information on electron energy distributions. The lowest energy states of HI²⁺ and CH₃I²⁺ are identified and their vibrations are resolved. Possible reasons for the markedly different CF₃I spectrum are discussed. There is evidence for atomic autoionisation of iodine as a pathway contributing to the double photoionisation.     

Perturbation methods in semilinear elliptic problems involving critical hardy-sobolev exponent

In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory.     

On the Sizes of k-edge-maximal r-uniform Hypergraphs

Acta Mathematicae Applicatae Sinica, English Series - Let H = (V, E) be a hypergraph, where V is a set of vertices and E is a set of non-empty subsets of V called edges. If all edges of H have the...     

Bäcklund transformation,infinite conservation laws and periodic wave solutions to a generalized (2+1)-dimensional Boussinesq equation

Under investigation in this paper is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the water wave interaction. By using Bell polynomials, a lucid and systematic approach is proposed to systematically study the integrability of the equation, including its bilinear representation, soliton solutions, periodic wave solutions, Bäcklund transformation and Lax pairs, respectively. Furthermore, by virtue of its Lax equations, the infinite conservation laws of the equation are also derived with the recursion formulas. Finally, the asymptotic behavior of periodic wave solutions is shown with a limiting procedure.