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Let $ U$ be a connected unipotent algebraic group over a field of characteristic $ p>0$ . Assume $ U$ acts on an affine variety $ X$ by regular maps. Is it true that the stabilizers of rational points $ x\in X$ under this action are connected? Edit as the comments below point out, theRead more

Let $ \mathbb{A}^{n}$ be the $ n$ -dimension affine space over a field $ k$ and $ H$ an arbitrary hypersurface of $ \mathbb{A}^{n}$ . Does there exist a hyperplane $ P$ such that $ P \cap H =\emptyset$ ?Read more

I wrote a function to batch-transform 3D vectors by a single 3×4 matrix using SSE2: struct alignas(16) Matrix3x4f { union { Vector4 r[3]; // (r[0].w, r[1].w, r[2].w) contains the translation float m[3][4]; }; // (0, 0, 0, 1) is the forth row of the full 4×4 matrix }; struct Positions_SoA { Vector4 * xs; Vector4Read more