[3, 3] Padé approximation method for solving space fractional Fokker–Planck equations

The fractional Fokker–Planck equation has been used in various areas of engineering and physics. In this paper, we proposed a novel numerical scheme for solving the space fractional Fokker–Planck equation with the help of the [3, 3] Padé approximation. It is proved that the numerical method is unconditionally stable in view of the matrix analysis method. Finally, a numerical example is proposed to prove the effectiveness of the numerical scheme.     

Solving Ck/Cm/1/N queues by using characteristic roots in matrix analytic methods

In this paper, we study a C_k/C_m/1/N open queueing system with finite capacity. We investigate the property which shows that a product of the Laplace Stieltjes Transforms of interarrival and service times distributions satisfies an equation of a simple form. According to this equation, we present that the stationary probabilities on the unboundary states can be written as a linear combination of vector product-forms. Each component of these products is expressed in terms of roots of an associated characteristic polynomial. As a result, we carry out an algorithm for solving stationary probabilities in C_k/C_m/1/N systems, which is independent of N, hence greatly reducing the computational complexity.     

Chemometric methods in energy dispersive X-ray fluorescence

Chemometric methods like principal component regression (PCR) are an excellent tool for the determination of matrix parameters from scattered radiation. PCR is used for the determination of carbon, hydrogen and oxygen from water and oil-based samples. This information is used in combination with fundamental parameters to determine zink in liquid samples. The method allows an accurate prediction of element concentrations in strong varying matrices.     

临界情况下模糊矩阵对策的性质

讨论临界情况下模糊矩阵对策的性抽，对模型问题各种情况给出了临界值c*的定义，证明了当d(f1,f2)＜ε≤c*时，模糊矩阵对策模型问题关于价值函数f1(x)、f2(x)具有连续依赖性和可调和性。     

激光剥蚀-电感耦合等离子体质谱:双外标结合基体归一定量校准策略

定量校准策略是激光剥蚀电感耦合等离子体质谱(AICP-MS)分析技术的重要组成部分,直接影响分析数据的质量.本研究评估了现有玻璃标准物质定值不确定度的相对大小,并探究了NIST、MPI-DING和USGS系列玻璃标准物质之间的基体效应.结果表明,NIST610的定值不确定度优于其它玻璃标准物质,在本实验条件下,NIST、MPI-DING和USGS系列玻璃标准物质之间的基体效应可忽略不计.在此基础上提出了双外标结合基体归一定量校准策略,外标分别为NIST610和StHs6/80-G.此策略克服了由于NIST610主量成分与地质样品差别大而造成的主量元素准确度差以及StHs6/80-G中某些微量元素含量低、定值不确定度较大等缺点.对比采用3种定量校准策略(单外标NSIT610基体归一法、单外标StHs6/80G基体归一法和双外标基体归一法)校准的ML3B-G数据可知,双外标基体归一法有效避免了单外标基体归一法的不足,并提高了分析数据的准确度.采用双外标结合基体归一定量校准策略校准了BCR-2G、CGSG-2和KL-2G中的主量元素和微量元素.结果表明,绝大多数分析数据在定值不确定度范围内,验证了此校准策略的实用性.同时,本研究得到的主量微量元素数据进一步补充了BCR-2G、CGSG-2和KL-2G的定值数据库.     

Irreducible Representations of the Quantum Weyl Algebra at Roots of Unity Given by Matrices

To describe the representation theory of the quantum Weyl algebra at an lth primitive root γ of unity, Boyette, Leyk, Plunkett, Sipe, and Talley found all nonsingular irreducible matrix solutions to the equation yx ? γxy = 1, assuming yx ≠ xy. In this note, we complete their result by finding and classifying, up to equivalence, all irreducible matrix solutions (X, Y), where X is singular.     

CPA矩阵分光光度法同时测定三种酚

在无水乙醇介质中，对乙酰胺基酚，对氨基酚、对硝基酚三者的紫外吸收光谱相互严重重叠，用一般的光度分析手段无法同时测定。本文首次采用CPA矩阵法，不经分离直接测定了上述三组分的含量，实验结果表明：当选取216、234、260、292、312nm5个波长点作为CPA矩阵程序的最佳波长点时，该法对样品中各组分的平均回收率在100.2%－103.5%之间，结果较满意，与现行分析方法相比，本方法具有简便、快速的优点。本法已用于扑热息痛合成物中三组分含量的测定。     

Application of computer algebra to Jones polynomials

In this paper we apply computer algebra (Maple) techniques to calculate Jones polynomial of graphs of K(2,q)-Torus knots. For this purpose, a computer program was developed. When a positive integer q is given, the program calculate Jones polynomial of graph of K(2,q)-Torus knots.