Poincaré half-space model. Take the open upper half-space \[\mathbb{H}^n := \{(x_1,\dots,x_n)\in\mathbb{R}^n \mid x_n 0\}\] equipped with the Riemannian metric whose components on the coordinate tangent vectors are \[g_{ij}(p) \;=\; g_p\!\left(\frac{\partial}{\partial x_i}\bigg|_p,\; \frac{\partial}{\partial x_j}\bigg|_p\right) \;=\; \frac{1}{p_n^2}\,\delta_{ij}.\] Geodesics are semicircles (or rays) orthogonal to the boundary hyperplane \(\{x_n = 0\}\).
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Geometry — Circle, Rectangle, Polygon, Arrow, Arc, Star, Brace, and more
A recent article published by the BBC explored how generative AI tools could be “hacked” within minutes by introducing newly published online content. In the example presented, a blog post claiming expertise in a highly niche category was later echoed in responses from systems such as OpenAI’s ChatGPT and Google’s AI outputs when prompted with […]
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Before diving into API design, it's worth asking: what is a stream?，详情可参考旺商聊官方下载
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