The basic construction from the conditional expectation on the quantum double of a finite group

summary:Let $G$ be a finite group and $H$ a subgroup. Denote by $D(G;H)$ (or $D(G)$) the crossed product of $C(G)$ and $\Bbb {C}H$ (or $\Bbb {C}G$) with respect to the adjoint action of the latter on the former. Consider the algebra $\langle D(G), e\rangle$ generated by $D(G)$ and $e$, where we regard $E$ as an idempotent operator $e$ on $D(G)$ for a certain conditional expectation $E$ of $D(G)$ onto $D(G;H)$. Let us call $\langle D(G), e\rangle$ the basic construction from the conditional expectation $E\colon D(G)\rightarrow D(G;H)$. The paper constructs a crossed product algebra $C(G/H\times G)\rtimes \Bbb {C}G$, and proves that there is an algebra isomorphism between $\langle D(G),e\rangle$ and $C(G/H\times G)\rtimes \Bbb {C}G$

Involvement of MicroRNAs in Probiotics-Induced Reduction of the Cecal Inflammation by Salmonella Typhimurium

The microRNAs (miRNAs) have been shown to play important roles in the development of the immune system and in regulation of host inflammation responses. Probiotics can effectively alleviate the inflammation caused by Salmonella in chickens. However, whether and how miRNAs are involved in modulation of the inflammation response in the gut of chickens have not been reported. In this study, the impact of a probiotics, Lactobacillus plantarum Z01 (LPZ01), was investigated on the cecal miRNAs and cytokine secretions in Salmonella Typhimurium (S. Typhimurium)-infected chickens at the age of 3 days. Newly hatched chicks were assigned to four groups (1): NC (basal diet) (2): S (basal diet + S. Typhimurium challenged) (3): SP (basal diet + S. Typhimurium challenged + LPZ01) (4): P (basal diet + LPZ01). In comparison with the S group, chicks in the SP group reduced the number of S. Typhimurium and had lower levels of interferon-γ and lipopolysaccharide-induced tumor necrosis factor alpha factor (LITAF) in ceca post challenge. Expression of 14 miRNAs was significantly affected by the presence of S. Typhimurium and/or lactobacillus. Five differential expression miRNAs (gga-miR-215-5p, gga-miR-3525, gga-miR-193a-5p, gga-miR-122-5p, and gga-miR-375) were randomly selected for confirmation by the RT-PCR. Predicted target genes of differentially expressed miRNAs were enriched in regulation of cAMP-dependent protein kinase activity, stress-activated MAPK cascade, immune system development and regulation of immune system process as well as in immune related pathways such as MAPK and Wnt signaling pathways. The relationship between changes of miRNAs and changes of cytokines was explored. Finally, 119 novel miRNAs were identified in 36 libraries totally. Identification of novel miRNAs significantly expanded the repertoire of chicken miRNAs and provided the basis for understanding the function of miRNAs in the host. Our results suggest that the probiotics reduce the inflammation of the S. Typhimurium infection in neonatal broiler chicks, at least partially, through regulation of miRNAs expression

A multi-degree-of-freedom reconfigurable ankle rehabilitation robot with adjustable workspace for post-stroke lower limb ankle rehabilitation

Introduction: A multi-degree-of-freedom ankle rehabilitation robot with an adjustable workspace has been designed to facilitate ankle joint rehabilitation training. It features a rotation center adapted to the human body, making it suitable for patients with ankle dysfunction following a stroke.Method: In this study, a multi-degree-of-freedom reconfigurable ankle rehabilitation robot (RARR) with adaptable features, based on the principles of ergonomics, has been proposed to cater to the varying needs of patients. This robot offers an adjustable workspace, allowing for different types of ankle joint rehabilitation exercises to be performed. By adjusting the assembly of the RARR, personalized and targeted training can be provided to patients, circumventing issues of redundancy in degrees of freedom during its use. A kinematic model of the robot has been established, and finite element simulation has been employed to analyze the strength of critical components, ensuring the safety of the robot. An experimental platform has been set up to assess the smoothness of the rehabilitation process with RARR, with angle measurements conducted using an Inertial Measurement Unit (IMU).Results and discussion: In conclusion, both simulation and experimental results demonstrate that the robot offers an adjustable workspace and exhibits relatively smooth motion, thereby confirming the safety and effectiveness of the robot. These outcomes align with the intended design goals, facilitating ankle joint rehabilitation and advancing the field of reconfigurable robotics. The RARR boasts a compact structure and portability, making it suitable for various usage scenarios. It is easily deployable for at-home use by patients and holds practical application value for wider adoption in rehabilitation settings

Design of Lead-Free Inorganic Halide Perovskites for Solar Cells via Cation-Transmutation

Hybrid organic-inorganic halide perovskites with the prototype material of CH$_{3}$NH$_{3}$PbI$_{3}$ have recently attracted intense interest as low-cost and high-performance photovoltaic absorbers. Despite the high power conversion efficiency exceeding 20% achieved by their solar cells, two key issues -- the poor device stabilities associated with their intrinsic material instability and the toxicity due to water soluble Pb$^{2+}$ -- need to be resolved before large-scale commercialization. Here, we address these issues by exploiting the strategy of cation-transmutation to design stable inorganic Pb-free halide perovskites for solar cells. The idea is to convert two divalent Pb$^{2+}$ ions into one monovalent M$^{+}$ and one trivalent M$^{3+}$ ions, forming a rich class of quaternary halides in double-perovskite structure. We find through first-principles calculations this class of materials have good phase stability against decomposition and wide-range tunable optoelectronic properties. With photovoltaic-functionality-directed materials screening, we identify eleven optimal materials with intrinsic thermodynamic stability, suitable band gaps, small carrier effective masses, and low excitons binding energies as promising candidates to replace Pb-based photovoltaic absorbers in perovskite solar cells. The chemical trends of phase stabilities and electronic properties are also established for this class of materials, offering useful guidance for the development of perovskite solar cells fabricated with them.Comment: pages 19, 4 figures in main tex

Impact of Carbon Trading System on Green Economic Growth in China

Whether China’s economy can maintain sustainable growth has been debated both in China and internationally, and the most representative critique has been summarized in the “Krugman Query”. Faced with such doubts, how to achieve a “win-win” for economic growth and environmental protection has become one of the central objectives of local government work while striving for the new vision of development. Taking China’s carbon trading pilot policy as an example, and based on panel data of 30 provincial administrative regions in China from 2001 to 2018, this paper uses the Data Envelopment Analysis-Malmquist index model and the Propensity Score Matching-Difference in Difference method to measure the level of green economic growth from two aspects: green development mode and economic growth effect, and further explore the impact of China’s carbon trading system on green economic growth. The results show that the implementation of the carbon trading system promoted both the green development level and economic growth of pilot cities, and positively affected green total factor productivity, refuting the “Krugman Query”. Finally, the study puts forward a series of recommendations in strengthening environmental regulation, improving green technology innovation, and developing low-carbon industries