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“Tong Guan Li Qiao” Acupuncture Therapy on Post-Stroke Dysphagia
Published 2022-12-01Subjects: Get full text
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Michael-Simon type inequalities in hyperbolic space Hn+1 ${\mathbb{H}}^{n+1}$ via Brendle-Guan-Li’s flows
Published 2024-04-01“…Further, we also establish and confirm a new sharp Michael-Simon inequality for the kth mean curvatures in Hn+1 ${\mathbb{H}}^{n+1}$ by virtue of the Brendle-Guan-Li’s flow (“An inverse curvature type hypersurface flow in Hn+1 ${\mathbb{H}}^{n+1}$ ,” (Preprint)) as below(0.2)∫Mλ′f2Ek2+|∇Mf|2Ek−12−∫M∇̄fλ′,ν⋅Ek−1+∫∂Mf⋅Ek−1≥pk◦q1−1(W1(Ω))1n−k+1∫Mfn−k+1n−k⋅Ek−1n−kn−k+1 \begin{align}\hfill & \underset{M}{\int }{\lambda }^{\prime }\sqrt{{f}^{2}{E}_{k}^{2}+\vert {\nabla }^{M}f{\vert }^{2}{E}_{k-1}^{2}}-\underset{M}{\int }\langle \bar{\nabla }\left(f{\lambda }^{\prime }\right),\nu \rangle \cdot {E}_{k-1}+\underset{\partial M}{\int }f\cdot {E}_{k-1}\hfill \\ \hfill & \quad \ge {\left({p}_{k}{\circ}{q}_{1}^{-1}\left({W}_{1}\left({\Omega}\right)\right)\right)}^{\frac{1}{n-k+1}}{\left(\underset{M}{\int }{f}^{\frac{n-k+1}{n-k}}\cdot {E}_{k-1}\right)}^{\frac{n-k}{n-k+1}}\hfill \end{align} provided that M is h-convex and Ω is the domain enclosed by M, p k(r) = ω n(λ′)k−1, W1(Ω)=1n|M| ${W}_{1}\left({\Omega}\right)=\frac{1}{n}\vert M\vert $ , λ′(r) = coshr, q1(r)=W1Srn+1 ${q}_{1}\left(r\right)={W}_{1}\left({S}_{r}^{n+1}\right)$ , the area for a geodesic sphere of radius r, and q1−1 ${q}_{1}^{-1}$ is the inverse function of q 1. …”
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Quantum public-key encryption protocol based on single-photon
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Quantum public-key encryption protocol based on single-photon
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Time analysis of regional structure of large-scale particle using an interactive visual system
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Prediction of Individual Halo Concentrations Across Cosmic Time Using Neural Networks
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Clinical application of E ⁃MAX glass ceramic onlays in the restorations of the nonvital posterior teeth
Published 2017-09-01Get full text
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Application of QVP Method to Winter Precipitation Observation Based on Polarimetric Radar
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Thermal stability of permafrost under U-shaped crushed rock embankment of the Qinghai‒Tibet Railway
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Nature’s Neighborhood: The Housing Premium of Urban Parks in Dense Cities
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Variation and Vertical Structure of Clear-air Echo by Ka-band Cloud Radar
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Spatial Planning Implementation Effectiveness: Review and Research Prospects
Published 2022-08-01Get full text
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