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ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS
Kong, Xiangjun,Wang, Pei Korean Mathematical Society 2011 대한수학회논문집 Vol.26 No.1
In this paper, the connection of the inverse transversal with the adequate transversal is explored. It is proved that if S is an abundant semigroup with an adequate transversal $S^o$, then S is regular if and only if $S^o$ is an inverse semigroup. It is also shown that adequate transversals of a regular semigroup are just its inverse transversals. By means of a quasi-adequate semigroup and a right normal band, we construct an abundant semigroup containing a quasi-ideal S-adequate transversal and conversely, every such a semigroup can be constructed in this manner. It is simpler than the construction of Guo and Shum [9] through an SQ-system and the construction of El-Qallali [5] by W(E, S).
Tao Wang,Shuai Li,Xiangjun Pei,Yafan Yang,Bin Zhu,Guoqing Zhou 국제구조공학회 2022 Structural Engineering and Mechanics, An Int'l Jou Vol.81 No.2
The thermodynamic properties of shaft lining concrete (SLC) are important evidence for the design and construction, and the spatial variability of concrete materials can directly affect the stochastic thermal analysis of the concrete structures. In this work, an array of field experiments of the concrete materials are carried out, and the statistical characteristics of thermophysical parameters of SLC are obtained. The coefficient of variation (COV) and scale of fluctuation (SOF) of uncertain thermophysical parameters are estimated. A three-dimensional (3-D) stochastic thermal model of concrete materials with heat conduction and hydration heat is proposed, and the uncertain thermodynamic properties of SLC are computed by the self-compiled program. Model validation with the experimental and numerical temperatures is also presented. According to the relationship between autocorrelation functions distance (ACD) and SOF for the five theoretical autocorrelation functions (ACFs), the effects of the ACF, COV and ACD of concrete materials on the uncertain thermodynamic properties of SLC are analyzed. The results show that the spatial variability of concrete materials is subsistent. The average temperatures and standard deviation (SD) of inner SLC are the lowest while the outer SLC is the highest. The effects of five 3-D ACFs of concrete materials on uncertain thermodynamic properties of SLC are insignificant. The larger the COV of concrete materials is, the larger the SD of SLC will be. On the contrary, the longer the ACD of concrete materials is, the smaller the SD of SLC will be. The SD of temperature of SLC increases first and then decreases. This study can provide a reliable reference for the thermodynamic properties of SLC considering spatial variability of concrete materials.