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[ algebra ] function field theorem conjecture finite map math element module prime rank degree operator polynomial proof algebra extension integer point adic root abelian elliptic subgroup rational curves isomorphism formula defined proposition algebraic ring power mod lemma definition modules zeta curve sum order space characteristic complet
[ algebraic geometry ] manifold map space theorem metric curvature function invariant equation action defined compact system math constant holomorphic flow orbit submanifold bundle proposition complete lie flat complex kahler smooth suppose symmetric point ricci follow harmonic exist denote exp satisfies implies geometry normal spaces proof riemannian d
[ mathematical theory ] theorem lemma proof follow constant bound exist definition hold prove assume positive bounded inequality implies denote condition fact integer define suppose function assumption corollary satisfies subset element defined property upper_bound lower_bound proof_theorem sum independent argument sequence satisfying proved proposition
[ finite element and grid-based modeling ] mesh equation domain finite_element numerical element refinement adaptive algorithm convergence linear function approximation basis operator order grid iteration local nonlinear computational multigrid coarse space boundary system estimates meshes global scheme discretization estimate norm decomposition elliptic solve boundary_con
[ graph theory and algorithms ] graph edges edge vertices vertex path degree log connected random subgraph cycle pair drawing weight complete matching disjoint directed embedding theory distance chung adjacent maximum coloring cycles planar_graph connectivity regular bipartite odd connected_component power_law shortest_path diameter