A New Multiplicity Formula for the Weyl Modules of Type A

A monomial basis and a filtration of subalgebras for the universal enveloping algebra $U(g_l)$ of a complex simple Lie algebra $g_l$ of type $A_l$ is given in this note. In particular, a new multiplicity formula for the Weyl module $V(\lambda)$ of $U(g_l)$ is obtained in this note.Comment: 13 page

Risk of hepatitis B virus reactivation and its effect on survival in advanced hepatocellular carcinoma patients treated with hepatic arterial infusion chemotherapy and lenvatinib plus programmed death receptor-1 inhibitors

BackgroundHepatitis B virus (HBV) reactivation is a common complication in hepatocellular carcinoma (HCC) patients treated with chemotherapy or immunotherapy. This study aimed to evaluate the risk of HBV reactivation and its effect on survival in HCC patients treated with HAIC and lenvatinib plus PD1s.MethodsWe retrospectively collected the data of 213 HBV-related HCC patients who underwent HAIC and lenvatinib plus PD1s treatment between June 2019 to June 2022 at Sun Yat-sen University, China. The primary outcome was the risk of HBV reactivation. The secondary outcomes were overall survival (OS), progression−free survival (PFS), and treatment−related adverse events.ResultsSixteen patients (7.5%) occurred HBV reactivation in our study. The incidence of HBV reactivation was 5% in patients with antiviral prophylaxis and 21.9% in patients without antiviral prophylaxis, respectively. The logistic regression model indicated that for HBV reactivation, lack of antiviral prophylaxis (P=0.003) and tumor diameter (P=0.036) were independent risk factors. The OS and PFS were significantly shorter in the HBV reactivation group than the non-reactivation group (P=0.0023 and P=0.00073, respectively). The number of AEs was more in HBV reactivation group than the non-reactivation group, especially hepatic AEs.ConclusionHBV reactivation may occur in HCC patients treated with HAIC and lenvatinib plus PD1s. Patients with HBV reactivation had shorter survival time compared with non-reactivation. Therefore, HBV-related HCC patients should undergo antiviral therapy and HBV-DNA monitoring before and during the combination treatment

Simulation of centrifugal pumps based on MPS solver

In this article, a three dimensional full-scale centrifugal pump is, for the first time, simulated using the moving particle semi-implicit method(MPS). The genetic smooth wall boundary(GSW) is used and extended to three dimension to deal with the complicated wall shape and thin blades in turbo-machines. The non-surface detection technique(NSD) based on conceptual particles is combined with this wall model to avoid the loss of particle number density near wall boundaries. A local wall particle refinement method is developed. Fine particles and coarse particles are applied to curved surface and flat surface respectively so as to reduce the computational cost while maintain the high discretization precision. The fully developed velocity inflow and pressure outflow boundary conditions are proposed. Three typical cases including hydrostatic cases with complicated geometry, flows over a two-dimensional backward-facing step, and flows in a three-dimensional tube are tested to verify the proposed models. This paper constructs a framework for the simulation of incompressible fluid machines, in which 3D complex revolving bodies can be integrally discretized and interactions between the stator and rotor can be integrally solved within a single coordinate. This paper provides a particle-based solver for incompressible fluid machinery and has the potential to study its inner flow with multiphase or phase change