On the Harish-Chandra Homomorphism for Quantum Superalgebras

In this paper, we introduce the Harish-Chandra homomorphism for the quantum superalgebra $\mathrm{U}_q(\mathfrak{g})$ associated with a simple basic Lie superalgebra $\mathfrak{g}$ and give an explicit description of its image. We use it to prove that the center of $\mathrm{U}_q(\mathfrak{g})$ is isomorphic to a subring of the ring $J(\mathfrak{g})$ of exponential super-invariants in the sense of Sergeev and Veselov, establishing a Harish-Chandra type theorem for $\mathrm{U}_q(\mathfrak{g})$. As a byproduct, we obtain a basis of the center of $\mathrm{U}_q(\mathfrak{g})$ with the aid of quasi-R-matrix.Comment: 35 pages, comments are welcome

Sliding mode control for pulsed load power supply converters in DC shipboard microgrids

Pulsed power load (PPL) is a special load type in shipboard microgrids (SMGs), which consists of the generation module, energy storage system, and various types of loads. Having a reliable power supply to shipboard loads is a challenge as the SMG operates in islanded mode in most cases. Particularly, the PPLs require high transient power transfer with fast dynamics and strong robustness. Conventional solution to supply for the PPL is based on proportional-integral (PI) control, which can be used by linearizing the system around the equilibrium operation point. However, for a pulsed power supply (PPS) system, the load demand drastically changes in a short time, usually in millisecond level, making the operating point changes when the pulsed power is triggered or terminated. To supply the PPL with fast dynamics and robustness, an improved PPS control method is presented in this paper. By adopting a nonlinear sliding mode control (SMC) method, fast voltage regulation and robust pulse power tracking can be achieved. In the PPS, the PPL power demand is divided into two terms: one is the average power that is supplied by the SMG and the other is the fast pulsed power that is supplied by the storage capacitor. The size and cost of the storage capacitor are reduced as it is intentionally driven to a deep discharge. The PPS system configuration and coordination principle, SMC controllers, and sizing of passive elements in the PPS are analyzed in detail. The effectiveness of the presented PPS is verified by simulation results.Peer ReviewedPostprint (published version

Resveratrol Ameliorates Glucocorticoid-Induced Bone Damage in a Zebrafish Model

Resveratrol (Res) is a multi-functional polyphenol compound that has protective functions in cardiovascular and neurodegenerative diseases. This study aimed to determine the effect of Res on osteogenic differentiation and bone mineralization in zebrafish (Danio rerio) with dexamethasone (Dex)-induced bone damage. Our results showed that Dex exposure (15 μmol/l) decreased the green fluorescence areas and the integrated optic density (IOD) values in the skull bones of zebrafish larvae of the TG(SP7:EGFP) strain in a dose-dependent manner (p < 0.01). Furthermore, Dex exposure decreased the alizarin red S-stained areas (bone mineralization area) in the skeleton and spinal bones of zebrafish larvae of the AB strain in a dose-dependent manner (p < 0.01). By contrast, Res treatment (150 μmol/l) significantly increased both the green fluorescence and bone mineralization area in Dex-exposed zebrafish larvae. Thus, our data show that Res improves bone mineralization after glucocorticoid-induced bone damage in a zebrafish model. Res may be a candidate drug for the prevention of osteoporosis