Energy spectrum of multi-radiation of X-rays in a low energy Mather-type plasma focus device

The multi-radiation of X-rays was investigated with special attention to their energy spectrum in a Mather-type plasma focus device （operated with argon gas）. The analysis is based on the effect of anomalous resistances. To study the energy spectrum, a four-channel diode X-ray spectrometer was used along with a special set of filters. The filters were suitable for detection of medium range X-rays as well as hard X-rays with energy exceeding 30 keV. The results indicate that the anomalous resistivity effect during the post pinch phase may cause multi-radiation of X-rays with a total duration of 300 ± 50 ns. The significant contribution of Cu-Kα was due to the medium range X-rays, nonetheless, hard X-rays with energies greater than 15 keV also participate in the process. The total emitted X-ray energy in the forms of Cu-K and Cu-K/3 was around 0.14 ± 0.02 （J/Sr） and 0.04 ±0.01 （J/Sr）, respectively. The total energy of the emitted hard X-ray （〉 15 keV） was around 0.12± 0.02 （J/Sr）.     

一类差分系统边值问题在渐近线性下的多解存在性

应用临界点理论,获得了一类差分系统边值问题在渐近线性下存在多个非平凡解的条件.     

Uniform spin wave modes in antiferromagnetic nanoparticles with uncompensated moments

In magnetic nanoparticles the uniform precession (q = 0 spin wave) mode gives the predominant contribution to the magnetic excitations. We have calculated the energy of the uniform mode in antiferromagnetic nanoparticles with uncompensated magnetic moments, using the coherent potential approximation. In the presence of uncompensated moments, an antiferromagnetic nanoparticle must be considered as a kind of a ferrimagnet. Two magnetic anisotropy terms are considered, a planar term confining the spins to the basal plane, and an axial term determining an easy axis in this plane. Excitation energies are calculated for various combinations of these two anisotropy terms, ranging from the simple uniaxial case to the planar case with a strong out-of-plane anisotropy. In the simple uniaxial case, the uncompensated moment has a large influence on the excitation energy, but in the planar case it is much less important. The calculations explain recent neutron scattering measurements on nanoparticles of antiferromagnetic α-Fe₂O₃ and NiO.     

Inverse scattering method and soliton solutionfamily for the Einstein--Maxwell theory with multiple Abelian gauge fields

A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.     

二元合金多晶粒的枝晶生长的等温相场模型

基于Ginzburg-Landau理论和单晶粒的枝晶生长模型，发展了一个单相场控制的多个晶粒的枝晶生长模型. 采用相场和溶质场耦合的方法，以Al-2%Cu合金为例模拟了二元合金等温凝固过程中多个晶粒的生长过程. 结果表明，这个模型的计算结果展现了多个晶粒枝晶的竞争生长，能较真实的再现凝固过程中的枝晶的生长过程.     

多背包问题的半定松驰算法

The multiple knapsack problem denoted by MKP (B,S,rn,n) can be defined as follows. A set B of n items and a set S of rn knapsacks are given such that each item j has a profit pi and weight wj,and each knapsack i has a capacity Ci. The goal is to find a subset of items of maximum profit such that they have a feasible packing in the knapsacks. MKP (B,S,m,n) is strongly NP-Complete and no polynomial time approximation algorithm can have an approximation ratio better than 0.5. In the last ten years,semi-definite programming has been empolyed to solve some combinatorial problems successfully. This paper firstly presents a semi-definite relaxation algorithm (MKPS) for MKP (B,S,rn,n). It is proved that MKPS have a approximation ratio better than 0. 5 for a subclass of MKP (B,S,m,n) with n≤100, m≤5 and max^nj=1{wj}/min^mi=1={Ci}≤2/3.     

Solutions to a class of Schrödinger equations

We establish existence and multiplicity of solutions to a class of nonlinear Schrödinger equations with, e.g., ``atomic' Hamiltonians, via critical point theory.

     

Sets of uniqueness for spherically convergent multiple trigonometric series

A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.