Relationships between the canonical ascending and descending central series of ideals of an associative algebra

We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results.     

Generalized harmonic number summation formulae via hypergeometric series and digamma functions

By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae for generalized harmonic numbers.     

Erdélyi-type integrals for generalized hypergeometric functions with integral parameter differences

In this paper, we extend one of Erdélyi's classical integrals for the Gauss hypergeometric functions to a special class of generalized hypergeometric functions in which certain pairs of numerator and denomiator parameters differ by positive integers. Our main results are achieved by applying the fractional integration by parts and series manipulation technique. Some special cases are also pointed out which includes a new extension of a Thomae-type transformation.     

Hypergeometric approach to Apéry-like series

By reformulating four hypergeometric series formulae, we derive 36 Apéry-like series expressions for the Riemann zeta function, including a couple of identities conjectured by Sun [New series for some special values of L-functions. Nanjing Univ J Math. 2015;32(2): 189–218].     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.     

锰氧化物中氧空位的构建及其催化氧化苯系物作用机制研究进展

作为一种过渡金属氧化物,锰氧化物以其多晶型、储/释氧能力强、蕴含丰富氧物种、结构缺陷可控等优点被广泛应用于苯系物的热催化氧化。其中,具有众多特性的氧空位能有效促进苯系物的完全催化氧化,因而成为各界研究的焦点。我们综述了常见的氧空位构建方法及表征技术,并总结了在苯系物催化氧化过程中,锰氧化物中氧空位的几种重要作用机制对催化活性和抗水性能的积极影响。最后文章对氧空位构建新方法、形成机理、具体过程及其在锰氧化物热催化氧化苯系物领域中的应用进行了总结和展望。     

点支承四边自由各向异性平行四边形板自由振动、屈曲和弯曲分析

一个精确的重富立叶级数解析解用于分析四边形自由的点支横观各向异性平行四边形板的自由振动、屈曲和弯曲。解析解用叠加法得到,此解收敛迅速。与现有结果的比较证实了由本法得到的解析解的精确性。文后用图表给出高精度的自由振动、屈曲和弯曲计算结果。