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Let r ⩾ 3 r\geqslant 3 be an integer and 푄 any positive definite quadratic form in 푟 variables. We establish asymptotic formulae with power-saving error terms for the number of rational points of bounded height on singular hypersurfaces S Q S_{Q} defined by x 3 = Q ⁢ ( y 1 , … , y r ) ⁢ z x^{3}=Q(y_{1},\dots,y_{r})z . This confirms Manin’s conjecture for any S Q S_{Q} . Our proof is based on analytic methods, and uses some estimates for character sums and moments of 퐿-functions. In particular, one of the ingredients is Siegel’s mass formula in the argument for the case r = 3 r=3 . [ABSTRACT FROM AUTHOR]

The study of Land Use and Landscape Patterns (LULPs) changes and their ecological quality effects in Haikou city under the background of the Hainan Free Trade Port Plan (HFTPP) helps to promote coordinated development between cities and the environment. To date, most research on ecological quality has focused on areas with extremely fragile ecology and/or is related to LULP analysis. There are few studies in the literature focusing on the impact of high-intensity human activities caused by relevant policies on urban LULPs. The purpose of this research was to design a framework that monitors urban ecological security by considering the effect of the developing free trade port. The proposed framework was constructed by integrating multi-temporal Sentinel-2 remote sensing images, night light remote sensing data, digital elevation model (DEM) data, and spectral index features such as the normalized difference vegetation index (NDVI), enhanced vegetation index (EVI), bare soil index (BSI), and normalized intertidal mangrove index (NIMI), as well as analytical approaches such as the land use transfer matrix, land use dynamic degree, land use degree and transfer matrix, land use gravity center measurement, and landscape pattern index. The framework takes advantage of the Google Earth Engine (GEE) cloud platform and was applied to a highly developed Haikou city, the capital of Hainan province. Maps of brightness (SBI), greenness (GVI), and humidity (WET) were created annually from 2016 to 2021, enabling detailed ecological environment quality evaluation and analysis. The advantages of this study are (1) reliable land cover results obtained automatically and quickly; (2) the strong objectivity of the quantitative research on landscape patterns and land use; and (3) deep integration with free trade port policies. Through the research on the ecological quality problems caused by the change in LULP in the study area, the research results show that, from 2016 to 2021, the spatial distribution of land use and landscape pattern in Haikou city had been constantly changing; the area of construction land has decreased, with most of it having been converted into forest land and farmland; the gravity center of the building land has moved to the northwest; the degree of landscape fragmentation has decreased and the heterogeneity of landscape distribution has increased; the free trade port policies have promoted Haikou's economic development and ecological civilization construction; and finally, Haikou's ecological environmental quality has improved significantly. [ABSTRACT FROM AUTHOR]

Oil spills have always been a threat to the marine ecological environment; thus, it is important to identify and divide oil spill areas on the ocean surface into segments after an oil spill accident occurs to protect the marine ecological environment. However, oil spill area segmentation using ordinary optical images is greatly interfered with by the absorption of light by the deep sea and the distribution of algal organisms on the ocean surface, and it is difficult to improve segmentation accuracy. To address the above problems, a hyperspectral ocean oil spill image segmentation model with multiscale feature fusion (MFFHOSS-Net) is proposed. Specifically, the oil spill segmentation dataset was created using hyperspectral image data from NASA for the Gulf of Mexico oil spill, small-size images after the waveband filtering of the hyperspectral images were generated and the oil spill images were annotated. The model makes full use of having different layers with different characteristics by fusing feature maps of different scales. In addition, an attention mechanism was used to effectively fuse these features to improve the oil spill region segmentation accuracy. A case study, ablation experiments and model evaluation were also carried out in this work. Compared with other models, our proposed method achieved good results according to various evaluation metrics. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a two-species reaction-diffusion-advection competitive model with nonlocal delay subject to the homogeneous Dirichlet boundary conditions. The existence of the spatially inhomogeneous steady state is studied by using the implicit function theorem. The stability of the inhomogeneous steady state and the associated Hopf bifurcation are investigated by analyzing a non-self-adjoint linear operator. Taking the time delay as the bifurcation parameter, we obtain the critical value of time delay for the Hopf bifurcation and the stability switch phenomenon. [ABSTRACT FROM AUTHOR]

Background: Anwuligan (ANW) isolated from nutmeg, also known as myristyl lignan, has attracted attention due to its therapeutic potential in diseases. However, its effect on lung cancer is still unclear. Methods: In this study, the cytotoxicity of ANW on non‐small cell lung cancer (NSCLC) cells was detected using a Cell Counting Kit‐8 (CCK‐8) assay. In vitro, clone formation, wound healing, and Transwell assays were used to investigate the migratory and invasive abilities of NSCLC cells after ANW treatment. The expression levels of the associated proteins were detected using Western blotting. A luciferase assay was used to validate the binding of let‐7c‐3p to the 3′‐untranslated region (UTR) of PIK3CA. In vivo, an A549 cell xenograft mouse model was used to verify the effect of ANW on tumor growth. Results: The results showed that ANW treatment (20 or 50 μM) had obvious cytotoxicity against A549 and H460 cells, suppressing cell proliferation and migration in vitro. In vivo, the growth of the implanted tumor was inhibited by ANW in a nude mouse model. The growth of NSCLC cells was also inhibited by let‐7c‐3p overexpression in vitro and in vivo. The inhibitory effect of ANW on the proliferation and metastasis of NSCLC cells was weakened by the downregulation of let‐7c‐3p, whereas it was enhanced by the overexpression of let‐7c‐3p; PIK3CA was the main target of let‐7c‐3p. Conclusions: In summary, ANW inhibits the growth and metastasis of NSCLC cells in vivo and in vitro by upregulating the expression of let‐7c‐3p, which can regulate the PI3K/AKT/mTOR signaling pathway. PIK3CA is the main target of let‐7c‐3p. [ABSTRACT FROM AUTHOR]