On classification of second-order differential equations with complex coefficients

This paper is concerned with the deficiency index problem of second-order differential equations with complex coefficients. It is known that this class of equations is classified into cases I, II, and III according to the number of linearly independent solutions in suitable weighted square integrable spaces. In this study, the original equation is reformulated into a new formally self-adjoint differential system by introducing a new spectral parameter and the relationship between the classifications of the equation and the system is obtained. Moreover, the exact dependence of cases II and III on the corresponding half planes is given and some criteria of the three cases are established.     

Weighted Hardy's inequality in a limiting case and the perturbed Kolmogorov equation

In this paper, we show a weighted Hardy inequality in a limiting case for functions in weighted Sobolev spaces with respect to an invariant measure. We also prove that the constant on the left-hand side of the inequality is optimal. As applications, we establish the existence and nonexistence of positive exponentially bounded weak solutions to a parabolic problem involving the Ornstein–Uhlenbeck operator perturbed by a critical singular potential in a two-dimensional case, according to the size of the coefficient of the critical potential. These results can be considered as counterparts in the limiting case of results which are established in the work of Goldstein et al. [Weighted Hardy's inequality and the Kolmogorov equation perturbed by an inverse-square potential. Appl Anal. 2012;91(11):2057–2071] and Hauer and Rhandi [A weighted Hardy inequality and nonexistence of positive solutions. Arch Math. 2013;100:273–287] in the non-critical cases, and are also considered as extensions of a result in Cabré and Martel [Existence versus explosion instantanée pour des équations de la chaleur linéaires avec potential singulier. C R Acad Sci Paris Sér I Math. 1999;329:973–978] to the Kolmogorov operator case perturbed by a critical singular potential.     

Case studies in dynamic modelling of large-scale wastewater treatment plants

Several large-scale wastewater treatment plants have been modelled successfully using an extensive modelling library in the General Purpose Simulator, GPS-X. The mathematical models included all important processes on the selected wastewater treatment plants, i.e. primary sedimentation, activated sludge biokinetics and final clarification.The models have been used in different areas, such as: a)analysis of operational scenarios; b) determenation of sustained and peak capacity of plants(rated plant capacity) and c) investigation of plant expansion scenarios. Out of more than twenty documented cases four, involving simulation studies on large-scale wastewater plants are discussed.     

测试用例自动生成方法的现状及研究

软件测试数据生成在软件系统开发费用中占很大比重。如果该过程能自动实现,则会极大地减少软件开发的周期和费用。测试用例的生成工作包含选定被测任务、分析输入数据、确定其取值并分析对应的输出数据。其中分析对应的输出数据是决定测试是否成功的关键环节。测试用例选取的一个中心原则,就是以用最少的测试用例找到尽可能多的错误。目前的工具尚不能完成自动生成测试用例这个环节,往往是只能采用人工选取的方法。按所采用的方法和研究对象的不同,将测试用例自动生成方法主要分为5类:基于有限状态集的测试,基于标注的转换系统的测试,针对面向模型的需求规格说明的测试,针对面向对象软件的测试,以及运用模型检查生成测试用例的方法。在简单介绍前4种方法之后,重点对模型检查的方法进行详细的分析和探讨。     

非完全密封金属板电磁屏蔽方法分析

防止电磁泄漏的屏蔽机柜往往因某些需要如板间接缝、开关孔、线缆孔、散热孔、仪表以及机械接头等,使屏蔽机柜带有缝隙（孔隙）,这样,缝隙（孔隙）的电磁泄漏就会降低总的屏蔽效能。文中对非完全密封金属板的电磁屏蔽效能进行计算及分析,并给出一些有效方法与建议。     

Versatile transamination in quinonediimine chemistry: Towards a novel class of water soluble UV/violet chromophores

The transamination reaction of 2,5-diaminobenzoquinonediimine (QDI) with ethylenediamine gave fluorescent 1,2,3,4-tetrahydropyrazino[2,3-g]quinoxaline (1). When the same reaction was carried out with N,N’-bis(aminoethyl)-1,3-propanediamine, a novel cationic quinoxalinium species (2) was isolated, which can be further condensed with p-cyanobenzaldehyde to afford a benzimidazolo-fused quinoxaline dye (3) that is a water-soluble fluorophore in the UV–visible range.