二元差分域上一阶差分方程的多项式解

本文研究了在二元域F(α,β)(α、β是域F上代数无关的超越元)上一阶线性差分方程aσ(f)+bf=g的多项式解f,式中a、b、g是二元域F(α,β)上的已知多项式,σ是域F(α,β)上满足σ(α)=β,σ(β)=uα+vβ的域同构,其中u,v≠0.通过多项式次数分解得到多项式解f存在的性质,然后根据待定系数法求得多项式f,并给出了这类差分方程多项式解在符号求和方面的应用.

EEMD能量熵分析及在齿轮箱故障诊断中的应用

针对齿轮箱振动信号的非平稳、非线性等特点,提出一种基于总体平均经验模态分解EEMD的能量熵信号分析及故障诊断方法。该方法利用EEMD方法能够有效抑制模式混叠现象的特点,先对原始振动信号进行EEMD分解,得到各阶本征模态函数(IMFs),然后求得将各阶本征模态函数的能量及其熵。指出能量熵的值能够反映系统的工作状态和故障类型。通过对白噪声幅值及分解次数对齿轮箱振动加速度信号分析对比,得出最优化选择方案。

Effects of AlN hydrolysis on fractal geometry characteristics of residue from secondary aluminium dross using response surface methodology

The effects of aluminium nitride(AlN)hydrolysis on fractal geometry characteristics of residue from secondary aluminium dross were studied using response surface methodology.The results show that the fractal dimensions of the residue can be significantly influenced by the AlN hydrolysis from secondary aluminium dross.The hydrolysis of AlN in the dross was spontaneous under temperatures of303-373K.The actual fractal dimensions of residue were significantly affected by the liquid-solid ratio(p<0.05)and changed from1.16to1.80,which accurately aligned with those from the calculations.Moreover,the fractal dimensions of residue were significantly affected by the interactions between hydrolysis temperature and hydrolysis time,liquid-solid ratio and hydrolysis time,respectively(p<0.01).The minimum fractal dimensions of the residue reached1.15under the optimized conditions,which included a hydrolysis temperature of30℃,liquid-solid ratio of5mL/g and hydrolysis time of10min.The results suggest that response surface methodology can guide in optimizing the conditions of AlN hydrolysis in order to obtain the minimum fractal dimensions of residue for improving the reutilization of the dross.

Exact Solutions for the Generalized KdV Equation： Modified Homogeneous Balance Method

In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact（new） solutions of the generalized KdV equation are obtained.

Real-variable characterizations of anisotropic product Musielak-Orlicz Hardy spaces

Let A :=(A_1, A_2) be a pair of expansive dilations and φ : R^n×R^m×[0, ∞) → [0, ∞) an anisotropic product Musielak-Orlicz function. In this article, we introduce the anisotropic product Musielak-Orlicz Hardy space H~φ_A(R^n× R^m) via the anisotropic Lusin-area function and establish its atomic characterization, the g-function characterization, the g_λ~*-function characterization and the discrete wavelet characterization via first giving out an anisotropic product Peetre inequality of Musielak-Orlicz type. Moreover, we prove that finite atomic decomposition norm on a dense subspace of H~φ_A(R^n× R^m) is equivalent to the standard infinite atomic decomposition norm. As an application, we show that, for a given admissible triplet(φ, q, s), if T is a sublinear operator and maps all(φ, q, s)-atoms into uniformly bounded elements of some quasi-Banach spaces B, then T uniquely extends to a bounded sublinear operator from H~φ_A(R^n× R^m) to B. Another application is that we obtain the boundedness of anisotropic product singular integral operators from H~φ_A(R^n× R^m) to L~φ(R^n× R^m)and from H~φ_A(R^n×R^m) to itself, whose kernels are adapted to the action of A. The results of this article essentially extend the existing results for weighted product Hardy spaces on R^n× R^m and are new even for classical product Orlicz-Hardy spaces.

Exact Solitary Wave Solutions of Nonlinear Evolution Equations with a Positive Fractional Power Term

The bounded and smooth solitary wave solutions of 10 nonlinear evolution equations with a positive fractional power term of dependent variable are successfully obtained by homogeneous balance principle and with the aid of sub-ODEs that admits a solution of sech-power or tanh-power type.In the special cases that the fractional power equals to 1 and 2,the solitary wave solutions of more than 10 important model equations arisen from mathematical physics are easily rediscovered.

SUBGROUPS OF CLASS GROUPS OF ALGEBRAIC QUADRATIC FUNCTION FIELDS

Ideal class groups H(K) of algebraic quadratic function fields K are studied. Necessaryand sufficient condition is given for the class group H(K) to contain a cyclic subgroup of anyorder n, which holds true for both real and imaginary fields K. Then several series of functionfields K, including real, inertia imaginary, and ramified imaginary quadratic function fields, aregiven, for which the class groups H(K) are proved to contain cyclic subgroups of order n.