Topological and differentiable rigidity of submanifolds in space forms

Let $F^{n+p}(c)$ be an $(n+p)$-dimensional simply connected space form with nonnegative constant curvature $c$. We prove that if $M^n(n\geq4)$ is a compact submanifold in $F^{n+p}(c)$, and if $Ric_M>(n-2)(c+H^2),$ where $H$ is the mean curvature of $M$, then $M$ is homeomorphic to a sphere. We also show that the pinching condition above is sharp. Moreover, we obtain a new differentiable sphere theorem for submanifolds with positive Ricci curvature.Comment: 12 page

Landscape Planning and Public Space Optimization of Grand Canal Cultural Park based on Computer-aided Design

Collaborative As the rate of urbanisation is increasing at a very fast pace, there is a huge demand for Landscape planning with proper public space optimisation. China, a country which has witnessed rapid growth in population and economics, has become a target of urbanisation. The country is known for its aesthetic appeal in the Grand Canal cultural park, which has been a primary factor in the country's development since ancient times. However, landscape planning with efficient utilization of available public space in the region using contemporary computing technologies is the need of the hour. This work focuses on deploying Computer-Aided Design in landscape planning using the Artisan plugin, specifically meant for environment planning. The special tools available in this plugin help landscape planning architects to accurately study the characteristics of the landscape, like terrain, water bodies, planar regions, etc. Also, this work proposed a four-phased model that aids the development process of landscape planning activity by including micro-level factors that directly interact with the environment. In future, this model could be extended to include AR, VR, AI and ML technologies

Efficient Volumetric Method of Moments for Modeling Plasmonic Thin-Film Solar Cells with Periodic Structures

Metallic nanoparticles (NPs) support localized surface plasmon resonances (LSPRs), which enable to concentrate sunlight at the active layer of solar cells. However, full-wave modeling of the plasmonic solar cells faces great challenges in terms of huge computational workload and bad matrix condition. It is tremendously difficult to accurately and efficiently simulate near-field multiple scattering effects from plasmonic NPs embedded into solar cells. In this work, a preconditioned volume integral equation (VIE) is proposed to model plasmonic organic solar cells (OSCs). The diagonal block preconditioner is applied to different material domains of the device structure. As a result, better convergence and higher computing efficiency are achieved. Moreover, the calculation is further accelerated by two-dimensional periodic Green's functions. Using the proposed method, the dependences of optical absorption on the wavelengths and incident angles are investigated. Angular responses of the plasmonic OSCs show the super-Lambertian absorption on the plasmon resonance but near-Lambertian absorption off the plasmon resonance. The volumetric method of moments and explored physical understanding are of great help to investigate the optical responses of OSCs.Comment: 11 pages, 6 figure

The sphere theorems for manifolds with positive scalar curvature

Some new differentiable sphere theorems are obtained via the Ricci flow and stable currents. We prove that if $M^n$ is a compact manifold whose normalized scalar curvature and sectional curvature satisfy the pointwise pinching condition $R_0>\sigma_{n}K_{\max}$, where $\sigma_n\in (\frac{1}{4},1)$ is an explicit positive constant, then $M$ is diffeomorphic to a spherical space form. This gives a partial answer to Yau's conjecture on pinching theorem. Moreover, we prove that if $M^n(n\geq3)$ is a compact manifold whose $(n-2)$-th Ricci curvature and normalized scalar curvature satisfy the pointwise condition $Ric^{(n-2)}_{\min}>\tau_n(n-2)R_0,$ where $\tau_n\in (\frac{1}{4},1)$ is an explicit positive constant, then $M$ is diffeomorphic to a spherical space form. We then extend the sphere theorems above to submanifolds in a Riemannian manifold. Finally we give a classification of submanifolds with weakly pinched curvatures, which improves the differentiable pinching theorems due to Andrews, Baker and the authors.Comment: 35 page

Florofangchinoline inhibits proliferation of osteosarcoma cells via targeting of histone H3 lysine 27 trimethylation and AMPK activation

Purpose: To investigate the effect of florofangchinoline on osteosarcoma cell growth in vitro, and the underlying mechanism of action.Methods: Changes in the viability of KHOS and Saos-2 cells were measured using water soluble tetrazolium salt (WST) assay, while apoptosis was determined using Annexin V/PI staining and flow cytometry. Increases in mtDNA, and expressions of PGC-1α and TFAM were assayed with immunoblot analysis and quantitative real-time polymerase chain reaction (qPCR), respectively.Results: Microscopic examination of florofangchinoline-treated cells showed significant decrease in cell density, relative to control cells (p < 0.05). Treatment with 10 μM florofangchinoline increased apoptosis in KHOS and Saos-2 cells to 56.32 and 63.75 %, respectively (p < 0.05). Florofangchinoline treatment markedly enhanced cleavage of caspase-3, caspase-8, caspase-9 and PARP. It elevated Bax level and reduced Bcl-2 in KHOS and Saos-2 cells. Moreover, florofangchinoline increased p21 and p-AMPKα levels, and mtDNA counts in KHOS and Saos-2 cells (p < 0.05). Moreover, in florofangchinoline-treated KHOS cells, the expressions of EED, EZH2 and SUZ12 were significantly suppressed (p < 0.05).Conclusion: Florofangchinoline inhibits osteosarcoma cell viability by activation of apoptosis. Moreover, it activates AMPK and down-regulates  histone H3 lysine 27 trimethylation in osteosarcoma cells. Therefore, florofangchinoline has potentials for development as a therapeutic drug forosteosarcoma. Keywords: Osteosarcoma, Histone H3, Florofangchinoline, Apoptosis, Chemotherapeuti