In this paper, we define the semi-symmetric metric connection on the algebra of differential forms. We compute some special semi-symmetric metric connections and their curvature tensor and their Ricci tensor on the algebra of differential forms. We study the distribution on the algebra of differential forms and we get its Gauss-Codazzi-Ricci equations associated to the semi-symmetric metric connection. We also study the Lie derivative of the distribution on the algebra of differential forms. We define the canonical connection and the Schouten connection and the Vrancreanu connection on the algebra of differential forms and get some properties of these connections.
In this paper, we determine all left-invariant Ricci collineations associated to the Bott connection with three distributions on three-dimensional Lorentzian Lie groups . he author was supported in part by NSFC No.11771070.
Let [Formula: see text] be a finite-dimensional simple Lie algebra over [Formula: see text]. A [Formula: see text]-module is said to be weight if it is a weight [Formula: see text]-module. We give a complete classification of simple weight modules for [Formula: see text] which admits a one-dimensional weight space. We prove that there are four classes of such modules: finite, highest weight, lowest weight and dense modules. Different from the classical [Formula: see text]-representation theory, we show that there exists a class of [Formula: see text] irreducible modules which have uniformly two-dimensional weight spaces.
对内蒙古自治区乌梁素海湖泊及其周边河渠、地下水中放射性同位素氡(222Rn)含量的时空分布特征进行了调查分析.结果表明:乌梁素海非灌溉期(2021年9月上旬)湖水、出入湖河渠水、近湖岸地下水的222 Rn活度均小于灌溉期(2020年10月下旬),非灌溉期湖水的222 Rn活度约为灌溉期的39％,表明灌溉入渗、排水过程改变了区域地下水水动力条件,加速了区域地下水的循环流动,增大了水循环系统中的222 Rn活度;河湖222 Rn活度的时空差异性显著,灌溉期湖水222 Rn在总排干入湖区偏大,表明总排干退水是湖水222 Rn的主要源项.非灌溉期湖水222Rn活度(129.72～194.59 Bq/m3)和退水渠内湖水222Rn活度(277.25 Bq/m3)均大于总排干内湖水222Rn活度(110.72 Bq/m3),指示地下水对湖水存在一定的补给;非灌溉期西南岸地下水222 Rn活度仅为区域平均值的47.5％,指示该地区存在湖水的侧渗补给,稀释了地下水中的222 Rn.乌梁素海接受地下水的补给,但补给水量不大,在灌溉期总排干入湖水量对湖体水环境起主要的控制作用,在非灌溉期地下水对湖体水环境的影响程度可能要高于灌溉期.
考虑了一个带有反应速率系数扰动的随机连续搅拌釜式反应器模型.证明了随机反应模型正解的存在唯一性,得到了随机反应系统具有遍历性和平稳分布,通过数值模拟验证了本文理论结果的正确性.最有趣的结果是,即使确定性的连续搅拌釜式反应器模型的稳态可能会呈现9种不同性质的结构,但对应的随机模型无论确定性模型表现出什么样的动力学行为,它总是具有平稳分布的,而且不需要任何附加的条件.
