Functionally separable solutions to nonlinear wave equations by group foliation method

We apply functional separation of variables within the approach of the group foliation method to the nonlinear wave equation with variable speed and external force: utt=A(x)(Dx(u)ux)+B(x)Q(u), Ax≠0. A classification of these equations admitting functionally separable solutions is performed and the resulting solutions are obtained in explicit form in many cases.     

Large sets in finite fields are sumsets

For a prime p, a subset S of Zp is a sumset if S=A+A for some A⊂Zp. Let f(p) denote the maximum integer so that every subset S⊂Zp of size at least p−f(p) is a sumset. The question of determining or estimating f(p) was raised by Green. He showed that for all sufficiently large p, and proved, with Gowers, that f(p)<cp2/3log1/3p for some absolute constant c. Here we improve these estimates, showing that there are two absolute positive constants c₁,c₂ so that for all sufficiently large p,

     

NaYF4∶Eu3+, Tm3+, Yb3+材料中Stokes和反Stokes发光研究

合成了Eu3+,Tm3+和Yb3+掺杂的NaYF₄材料。360 nm光激发呈蓝色发光,峰值位于452 nm,对应Tm3+的1D₂→3F₄跃迁;395 nm光激发呈橙色发光,峰值位于591 nm,对应Eu3+的5D₀→7F₁跃迁;409 nm光激发呈红色发光,峰值位于613 nm,对应Eu3+的5D₀→7F₂跃迁;980 nm光激发呈蓝色和红色发光,发光峰位于474和646 nm。蓝光来源Tm3+的1G₄ →3H₆跃迁,红光来源Tm3+的1G₄→3F₄跃迁。在双对数曲线中,蓝光474 nm和红光646 nm的斜率分别为2.1和2.4,在980 nm光激发下,蓝光和红光发射都是双光子过程。还研究了材料的吸收光谱,并利用X射线衍射,扫描电镜测试了材料的物相结构和微观形貌。结果表明：NaYF₄∶Eu3+, Tm3+, Yb3+材料具有较规则的六方相结构,结晶良好。     

A chi-square method for obtaining a priority vector from multiplicative and fuzzy preference relations

Decision makers (DMs)’ preferences on decision alternatives are often characterized by multiplicative or fuzzy preference relations. This paper proposes a chi-square method (CSM) for obtaining a priority vector from multiplicative and fuzzy preference relations. The proposed CSM can be used to obtain a priority vector from either a multiplicative preference relation (i.e. a pairwise comparison matrix) or a fuzzy preference relation or a group of multiplicative preference relations or a group of fuzzy preference relations or their mixtures. Theorems and algorithm about the CSM are developed. Three numerical examples are examined to illustrate the applications of the CSM and its advantages.     

Digital pulse shape discrimination methods for n-γ separation in an EJ-301 liquid scintillation detector

A digital pulse shape discrimination system based on a programmable module NI-5772 has been established and tested with an EJ-301 liquid scintillation detector. The module was operated by running programs developed in Lab VIEW, with a sampling frequency up to 1.6 GS/s. Standard gamma sources22 Na,137Cs and60 Co were used to calibrate the EJ-301 liquid scintillation detector, and the gamma response function was obtained. Digital algorithms for the charge comparison method and zero-crossing method have been developed. The experimental results show that both digital signal processing(DSP) algorithms can discriminate neutrons from γ-rays. Moreover,the zero-crossing method shows better n-γ discrimination at 80 ke Vee and lower, whereas the charge comparison method gives better results at higher thresholds. In addition, the figure-of-merit(FOM) for detectors of two different dimensions were extracted at 9 energy thresholds, and it was found that the smaller detector presented better n-γseparation for fission neutrons.     

关于一个素数和一个素数的k次方和问题

设k≥2,且Hk表示一个正整数n的集合,使得该集合中的元素满足a+bk≡n(modq)对任意的q,在模q的既约剩余系中有解,令Dk(N)表示所有的n≤N,且n∈Hk且不能表成p1+p2k=n形式的整数.那么在GRH下, Dk(N)相似文献   

基于粗糙集理论的知识约简及应用实例

在保持分类能力不变的前提下 ,通过利用粗糙集理论中的知识约简方法 ,在保护知识库分类不变的条件下 ,删除其中不相关或不重要的知识 ,从而导出问题的决策 .利用基于决策表的粗糙集模型算法 ,实例分析如何数字化表示决策表 ,并对其进行属性约简和属性值的约简 ,从而提取决策规则 .     

Navier-Stokes方程带Backtracking技巧的两重网格算法

1 引 言考虑二维不可压 Navier-Stokes方程:     

基于哈密顿体系的平面无限解析元

在有限元法中,无限域的问题不便于处理求解。但无限域往往可以由规则的无限外域再加上有限的局部域组成。将无限域问题中的有限局部域用有限元法处理,在规则的无限外域中建立极坐标系,将规则无限域问题导向哈密顿体系,利用本征向量展开的方法,推导出一种新的半解析无限解析元,其刚度阵是精确的。该单元可用常规方法作为一个超级有限单元与有限的局部域连接。数值计算结果表明,该单元具有精度高,应用方便,数据处理非常简单的特点。对无限域问题的数值求解有重要意义。该方法可推广到三维无限域问题中。     

模糊随机参数二维声场数值计算

解决声场参数同时具有模糊性和随机性的问题,实现模糊随机声场声压响应的预测,引入了信息熵理论,利用信息熵的等效转换,将模糊随机声场转化为纯随机声场或者纯模糊声场进行求解,推导了基于摄动法的二维随机声场和模糊声场的有限元计算公式。以模糊随机参数下的二维管道声场模型和某轿车二维声腔模型为例进行了数值计算,所得结果与蒙特卡洛法(Monte Carlo Method)所预测声压变化范围基本一致,同时,转化为纯随机声场和纯模糊声场所求得声压响应变化范围也基本一致,说明了本文方法计算结果的准确性。因此本文方法能很好地应用于模糊随机参数下二维声场的预测,具有重要的工程应用价值。