Palliation
发表于 2025-3-23 11:56:12
Spline: Variational Model in 3-DBy now, our finite-element mesh is quite regular and accurate. It is now time to define basis functions (B-splines) on it. What is a basis function? It has the following properties:
MAPLE
发表于 2025-3-23 17:00:47
Permutation Group and the DeterminantLet us design a new group: the group of permutations. It will help define the determinant in a new way. This will give us a few attractive properties. Later on, in quantum chemistry, this will help analyze the electronic structure in the atom.
stratum-corneum
发表于 2025-3-23 20:23:51
https://doi.org/10.1007/978-3-031-22422-5Group theory; Linear algebra; High dimensional vectors; Fourier matrices; Markov chain; Quantum mechanics
安慰
发表于 2025-3-23 23:56:24
Numerical Integrationur numerical results are encouraging: as the mesh refines, the numerical integral gets more and more accurate. This indicates that our original algorithm is indeed robust and could be used in even more complicated domains.
尽管
发表于 2025-3-24 05:36:13
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欺骗世家
发表于 2025-3-24 09:46:11
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Erythropoietin
发表于 2025-3-24 11:50:16
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STERN
发表于 2025-3-24 16:34:48
Markov Matrix and Its Spectrum: Toward Search Enginesheory, they may help design a weighted graph and model a stochastic flow in it. This makes a Markov chain, converging to a unique steady state. This has a practical application in modern search engines in the Internet.
Detonate
发表于 2025-3-24 21:20:38
Mesh Regularityomised. After all, to approximate the curved boundary well, the tetrahedra must be a little thin. Still, thanks to our tricks, regularity decreases only moderately and linearly from level to level. This is not too bad: it is unavoidable and indeed worthwhile to compromise some regularity for the sake of high accuracy.
constellation
发表于 2025-3-24 23:53:31
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