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  1. Há 1 dia · Moreover, in 1936, Prof. Magnus Hestenes and Prof. Garrett Birkhoff presented the concept of conjugacy within the context of variational theory. The source of the conjugate direction algorithms was (Fox et al. 1948). Algorithms for computing a matrix’s eigenvalues were developed by Lanczos .

  2. Há 1 dia · The BirkhoffKakutani theorem (named after mathematicians Garrett Birkhoff and Shizuo Kakutani) states that the following three conditions on a topological group G are equivalent: G is (Hausdorff and) first countable (equivalently: the identity element 1 is closed in G, and there is a countable basis of neighborhoods for 1 in G).

  3. Há 5 dias · Abstract. We numerically calculate the spacetime describing the formation and evaporation of a regular black hole in 2D dilaton gravity. The apparent horizons evaporate smoothly in finite time to form a compact trapped region. The spacetime is asymptotically flat at future null infinity and is free of singularities and global horizons.

  4. Even logical laws can be revised according to Quine. Quantum logic, introduced by Garrett Birkhoff and John von Neumann, abandons the law of distributivity from classical logic in order to reconcile some of the apparent inconsistencies of classical Boolean logic with the facts related to measurement and observation in quantum mechanics.

  5. Há 5 dias · Koszul duality and the Poincaré-Birkhoff-Witt theorem. Using a homotopy introduced by de Wilde and Lecomte and homological perturbation theory for A_\infty -algebras, we give an explicit proof that the universal enveloping algebra UL of a differential graded Lie algebra L is Koszul, via an explicit contracting homotopy from the ...

  6. Há 4 dias · Saunders Mac Lane and Garrett Birkhoff; A definitive introductory text for abstract algebra using a category theoretic approach. Both a rigorous introduction from first principles, and a reasonably comprehensive survey of the field. Calculus, Vol. 1. Tom M. Apostol; Algebraic Geometry. Robin Hartshorne

  7. Há 6 dias · Abstract. We consider smooth area-preserving flows (also known as locally Hamiltonian flows) on surfaces of genus g≥1 and study ergodic integrals of smooth observables along the flow trajectories. We show that these integrals display a power deviation spectrum and describe the cocycles that lead the pure power behaviour, giving a ...