Smash Products of H-Simple Module Algebras

Let H be a finite-dimensional Hopf algebra and A a finite-dimensional H-simple left H-module algebra. We show that the smash product A#H is isomorphic to End _A′(V ? H*), where V ≠ 0 is a finite-dimensional left A-module and (A′, V′) the stabilizer of (A, V). As an application it is proved that A#H is isomorphic to a full matrix algebra over A′ when H is semisimple and dim V|dim A.     

The strong convergence of a three-step algorithm for the split feasibility problem

Based on the very recent work by Dang and Gao (Invers Probl 27:1–9, 2011) and Wang and Xu (J Inequal Appl, doi:10.1155/2010/102085, 2010), and inspired by Yao (Appl Math Comput 186:1551–1558, 2007), Noor (J Math Anal Appl 251:217–229, 2000), and Xu (Invers Probl 22:2021–2034, 2006), we suggest a three-step KM-CQ-like method for solving the split common fixed-point problems in Hilbert spaces. Our results improve and develop previously discussed feasibility problem and related algorithms.     

Strong convergence of a regularization method for Rockafellar’s proximal point algorithm

In this paper, for a monotone operator T, we shall show strong convergence of the regularization method for Rockafellar’s proximal point algorithm under more relaxed conditions on the sequences {r _k } and {t _k }, $$\lim\limits_{k\to\infty}t_k = 0;\quad \sum\limits_{k=0}^{+\infty}t_k = \infty;\quad\ \liminf\limits_{k\to\infty}r_k > 0.$$ Our results unify and improve some existing results.     

Temperature evolution associated with dynamic phase transformation in shape-memory TiNi alloys

In this paper, temperature evolution in shape-memory TiNi alloys was in situ measured in the process of phase transition under shock loading tests. It was shown that the temperature increased during loading, while unloading, it would keep the maximum value constant or decreased, depending on the strain rate. The corresponding dynamic response indicated that the hardening property is related to phase transition strain and the transformation path has remarkable strain-rate effect. The reason for this phenomenon is essentially due to the temperature dependence of the phase transformation stress. Moreover, the evolution of temperature was consistent with the change of stress, suggesting that this dynamic phase transition deformation is uniform. The theoretical calculation shows that the mechanism of temperature evolution results from the release of latent heat and the hysteresis dissipated energy. The results of this investigation provide insight into intriguing strain-rate-dependent phenomena intrinsic of TiNi alloys.     

Aromaticity of the most stable adenine and purine tautomers in terms of Hückel's 4N+2 principle

Electron structures of the fused rings in 7H and 9H tautomers of purine and adenine follow the 4N + 2 rule; the values of pEDA, HOMA, NICS and FLU indices document their aromatic character. In the 1H and 3H tautomers, these rings contain five or seven π electrons, hence they do not follow this rule and consequently exhibit lower aromaticity. This also applies to the aromaticity of whole molecules.     

Dependence of Crystal Quality and β Value on Synthesis Temperature in Growing Gem Diamond Crystals

High quality Ib gem diamond single crystals were synthesized in cubic anvil high-pressure apparatus （SPD- 6 × 1200） under 5.4GPa and 1230℃-1280℃. The （100） face of seed crystal was used as growth face, and Ni70Mn25Co5 alloy was used as solvent/catalyst. The dependence of crystal quality andβ value （the ratio of height to diameter of diamond crystal） on synthesis temperature was studied. When the synthesis temperature is between 1230℃ and 1280℃, theβ value of the synthetic high-quality gem diamond crystals is between 0.4 and 0.6. The results show that when theβ value is between 0.4 and O. 45, the synthetic diamonds are sheet-shape crystals; however, when theβ value is between 0.45 and 0.6, the synthetic diamonds are tower-shape crystals. In addition, when theβ value is less than 0.4, skeleton crystals will appear. When theβ value is more than 0.6, most of the synthetic diamond crystals are inferior crystals.     

课程思政理念在《常微分方程》教学改革中的应用

本文研究《常微分方程》课程教学改革过程中课程思政理念的应用.基于课程原有的知识体系,从哲学层面思考课程内容和研究方法,通过分析课程中蕴含的马克思主义观点和方法进行教学、微分方程建模教学、课程发展史和重要科学家生平事迹教学,培养学生的数学素养和科学精神,增强学生的民族自信和家国情怀,激励学生刻苦钻研、勇攀科学高峰.     

Effects of temperature on performances and hydration process of sulphoaluminate cement-based dual liquid grouting material and its mechanisms

Journal of Thermal Analysis and Calorimetry - In order to find out the rules of the effect of temperature on performances and hydration process of sulphoaluminate cement-based dual liquid grouting...