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The present paper is devoted to studying 2-local derivations on the planar Galilean conformal algebra. We prove that every 2-local derivation on the planar Galilean conformal algebra is a derivation., Comment: 13 pages

In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking tensor products of a finite number of irreducible modules $M(\lambda, \alpha, \beta, \gamma)$ with irreducible highest weight modules $V(\eta, \epsilon, \theta)$. We obtain the necessary and sufficient conditions for such tensor product modules to be irreducible, and determine the necessary and sufficient conditions for such two modules to be isomorphic. We also compare these modules with other known non-weight modules, showing that these irreducible modules are new., Comment: 21 pages. arXiv admin note: substantial text overlap with arXiv:2102.00979

BACKGROUND: The underlying cause of neurological sequelae after immature cerebral hypoxia-ischaemia (HI) white matter injury is impaired myelination. Previous studies have indicated that astrocyte activation is closely related to impaired myelination. However, the mechanism of reactive gliosis in white matter injury post-HI remains poorly understood. METHODS: Studies using adult ischaemic animal models demonstrated that hypoxia inducible factor-1α (HIF-1α) expression was involved in the formation of reactive astrocytes. Here, we investigated the temporal expression of HIF-1α and its impact on reactive gliosis and further myelination using a perinatal HI white matter injury model induced in rats at postnatal day 3. The temporal pattern of HIF-1α expression post-HI injury was tested by western blotting and immunofluorescence. Rats were treated with a HIF-1α inhibitor at 72 hours post-HI injury. Reactive gliosis and myelination were assessed with western blotting, immunofluorescence and electron microscopy, and neurological functions were examined by behavioural testing. RESULTS: Our results showed that the expression of HIF-1α was upregulated in neurons at 24 hours and in astrocytes at 7 days post-HI. Inhibiting delayed HIF-1α expression post-HI injury could restrain reactive gliosis, ameliorate hypomyelination, and improve the performance of rats in the Morris water maze test. CONCLUSIONS: Our findings suggest that a delayed increase in HIF-1α in astrocytes is involved in glial scar formation and leads to arrested oligodendrocyte maturation, impaired myelination, and long-term neurological function after experimental white matter injury in immature rats.

In this paper, we study quasi-Whittaker modules over the conformal Galilei algebras. We determine all quasi-Whittaker vectors and the simplicities of the universal quasi-Whittaker modules. For the reducible ones, we determine the corresponding simple quotient modules. Thus we classify all simple quasi-Whittaker modules for the conformal Galilei algebras.

In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras $\mathfrak{L}$ and a class of Block type Lie algebras $\mathfrak{B(q)}$, where $q$ is a nonzero complex number. We determine those modules whose restriction to the Cartan subalgebra (modulo center) are free of rank one. We also provide a sufficient and necessary condition for such modules to be simple, and determine their isomorphism classes. Moreover, we obtain the simplicity of modules over loop-Virasoro algebras by taking tensor products of some irreducible modules mentioned above with irreducible highest weight modules or Whittaker modules., Comment: 14 pages. Comments are welcome

It is well known that Tolls/Toll like receptors (TLRs), a family of pattern recognition receptors, play important roles in immune responses. Previously, we found that a Toll transcript was increased in a transcriptome library of haematopoietic tissue (Hpt) cells from the red claw crayfish Cherax quadricarinatus post white spot syndrome virus infection. In the present study, a full-length cDNA sequence of Toll receptor (named as CqToll) was identified with 3482 bp which contained an open reading frame of 3021 bp encoding 1006 amino acids. The predicted structure of CqToll protein was composed of three domains, including an extracellular domain of 19 leucine-rich repeats residues, a transmembrane domain and an intracellular domain of 138 amino acids. Tissue distribution analysis revealed that CqToll was expressed widely in various tissues determined from red claw crayfish with highest expression in haemocyte but lowest expression in eyestalk. Importantly, significant lower expression of the anti-lipopolysacchride factor (CqALF), an antiviral antimicrobial peptide (AMP) in crustaceans, but not CqCrustin was observed after gene silencing of CqToll in crayfish Hpt cell cultures, indicating that the CqALF was likely to be positively regulated via Toll pathway in red claw crayfish. Furthermore, the transcription of both an immediate early gene and a late envelope protein gene VP28 of WSSV were clearly enhanced in Hpt cells if silenced with CqToll, suggesting that the increase of WSSV replication was likely to be caused by the lower expression of the CqALF resulted from the loss-of-function of CqToll. Taken together, these data implied that CqToll might play a key role in anti-WSSV response via induction of CqALF in a crustacean C. quadricarinatus.