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... This approach leads in a natural way to a class of abstract spaces called the Banach spaces. Interlude – Banach spaces and linear operators In what follows we shall restrict our attention to the state spaces which are Banach spaces. To recall, a Banach space is a vector space X, equipped with a finit ...
... This approach leads in a natural way to a class of abstract spaces called the Banach spaces. Interlude – Banach spaces and linear operators In what follows we shall restrict our attention to the state spaces which are Banach spaces. To recall, a Banach space is a vector space X, equipped with a finit ...
On the number of rich lines in truly high
... also that for d = 2, 3 and r sufficiently small, the condition of the theorem also cannot hold, by the Szemeredi-Trotter theorem. However, when d becomes larger, our theorem gives non trivial results (and becomes closer to optimal for large d). The proof of Theorem 1 actually shows (Lemma 3.1) that, ...
... also that for d = 2, 3 and r sufficiently small, the condition of the theorem also cannot hold, by the Szemeredi-Trotter theorem. However, when d becomes larger, our theorem gives non trivial results (and becomes closer to optimal for large d). The proof of Theorem 1 actually shows (Lemma 3.1) that, ...
Interlacement of double curves of immersed spheres
... Recall that the linking graph G of a paired tree T is an undirected graph defined in [Li04] whose vertices correspond to the pairs of edges of the paired tree and two vertices of G are connected by an edge if and only if the two corresponding pairs of edges {a1 , b1 } and {a2 , b2 } of the tree T ar ...
... Recall that the linking graph G of a paired tree T is an undirected graph defined in [Li04] whose vertices correspond to the pairs of edges of the paired tree and two vertices of G are connected by an edge if and only if the two corresponding pairs of edges {a1 , b1 } and {a2 , b2 } of the tree T ar ...
