The least common multiple of a sequence of products of linear polynomials

Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty$, where $A$ is a constant depending on $f$.Comment: To appear in Acta Mathematica Hungaric

Protective role of curcumin in disease progression from non-alcoholic fatty liver disease to hepatocellular carcinoma: a meta-analysis

Background: Pathological progression from non-alcoholic fatty liver disease (NAFLD) to liver fibrosis (LF) to hepatocellular carcinoma (HCC) is a common dynamic state in many patients. Curcumin, a dietary supplement derived from the turmeric family, is expected to specifically inhibit the development of this progression. However, there is a lack of convincing evidence.Methods: The studies published until June 2023 were searched in PubMed, Web of Science, Embase, and the Cochrane Library databases. The SYstematic Review Center for Laboratory animal Experimentation (SYRCLE) approach was used to evaluate the certainty of evidence. StataSE (version 15.1) and Origin 2021 software programs were used to analyze the critical indicators.Results: Fifty-two studies involving 792 animals were included, and three disease models were reported. Curcumin demonstrates a significant improvement in key indicators across the stages of NAFLD, liver fibrosis, and HCC. We conducted a detailed analysis of common inflammatory markers IL-1β, IL-6, and TNF-α, which traverse the entire disease process. The research results reveal that curcumin effectively hinders disease progression at each stage by suppressing inflammation. Curcumin exerted hepatoprotective effects in the dose range from 100 to 400 mg/kg and treatment duration from 4 to 10 weeks. The mechanistic analysis reveals that curcumin primarily exerts its hepatoprotective effects by modulating multiple signaling pathways, including TLR4/NF-κB, Keap1/Nrf2, Bax/Bcl-2/Caspase 3, and TGF-β/Smad3.Conclusion: In summary, curcumin has shown promising therapeutic effects during the overall progression of NAFLD–LF–HCC. It inhibited the pathological progression by synergistic mechanisms related to multiple pathways, including anti-inflammatory, antioxidant, and apoptosis regulation

Inhibition of Endothelial Cell Proliferation and Tumor Angiogenesis by Up-Regulating NDRG2 Expression in Breast Cancer Cells

The N-myc downstream-regulated gene 2 (NDRG2) is involved in tumor cell differentiation and apoptosis, but its function in tumor angiogenesis remains to be established. Here, we employed adenovirus overexpressing NDRG2 (Ad-NDRG2) to efficiently up-regulate target gene expression in the NDRG2-low-expressing, breast cancer cell line MCF-7. Moreover, VEGF secretion was decreased in MCF-7 cells infected by Ad-NDRG2, and medium conditioned by these infected cells could significantly inhibit the proliferation, tube formation and invasion of human umbilical vein endothelial cells (HUVECs). Further study indicated that the angiogenesis promoting factors VEGF and HIF-1α were down-regulated, whereas the angiogenesis suppressing factors p53 and VHL were up-regulated in MCF-7 cells infected by Ad-NDRG2. Finally, in a nude mouse model, intratumoral injections of Ad-NDRG2 every 3 days for 20 days significantly inhibited the growth and angiogenesis of xenografted MCF-7 tumors. In summary, these data indicate that NDRG2 may be involved in angiogenesis by impacting the expression of angiogenesis related factors. Thus, specific overexpression of NDRG2 by adenovirus represents a promising approach for the treatment of tumor angiogenesis

Delay-dependent stability criterion of arbitrary switched linear systems with time-varying delay,”

This paper deals with the problem of delay-dependent stability criterion of arbitrary switched linear systems with time-varying delay. Based on switched quadratic Lyapunov functional approach and free-weighting matrix approach, some linear matrix inequality criterions are found to guarantee delay-dependent asymptotically stability of these systems. Simultaneously, arbitrary switched linear system can be expressed as a problem of uncertain liner system, so some delaydependent stability criterions are obtained with the result of uncertain liner system. Two examples illustrate the exactness of the proposed criterions

Delay-Dependent Stability Criterion of Arbitrary Switched Linear Systems with Time-Varying Delay

This paper deals with the problem of delay-dependent stability criterion of arbitrary switched linear systems with time-varying delay. Based on switched quadratic Lyapunov functional approach and free-weighting matrix approach, some linear matrix inequality criterions are found to guarantee delay-dependent asymptotically stability of these systems. Simultaneously, arbitrary switched linear system can be expressed as a problem of uncertain liner system, so some delay-dependent stability criterions are obtained with the result of uncertain liner system. Two examples illustrate the exactness of the proposed criterions