Báo cáo toán học: "On highly closed cellular algebras and highly closed isomorphisms" pot

... of X and the lower semicontinuity of f and p(u, ·), we know that (Y, d) is a nonempty complete metric space. Applying a generalization version of Ekeland’s variational principle due to Lin and ... class of all nonempty subsets of X, C(X) the family of all nonempty closed subsets of X and CB(X) the family of all nonempty closed and bounded subsets of X. A function H : CB(X) × CB(...

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... search tree T of size n ≥ 3, with left and right subtrees T 1 and T 2 , is a random LBST if and only if, both T 1 and T 2 are random independent LBSTs, and π n,k =  |T 1 | = k − 1    |T | ... other interesting relationships that hold for both random BSTs and random LBSTs. Proposition 1.2. Consider a random search tree of size n and let S n,j = # of comparisons in a successfu...

Ngày tải lên: 07/08/2014, 06:22

... v-equivalence ≡ v and the set V λ := T λ / ≡ v of vertical tableaux of shape λ. Consider a horizontal tableau Γ with rows r 1 , ,r p and a vertical tableau ∆ with columns c 1 , ,c q . Call Γ and ∆ orthogonal, ... inequality |r i ∩ c j |≤1 holds for all i, j . Equivalently, Γ and ∆ are orthogonal if and only if there exists a tableau ρ consistent with both Γ and ∆. Define the matrix...

Ngày tải lên: 07/08/2014, 08:22

... group of order n and exponent m, and let S be a sequence of elements in G with |S| = n + m − 1. Then, either 0 ∈  n (S) or |  n (S)| ≥ 2m − 1. Proof. It follows from Theorem A and Theorem 1 immediately. ... terms of S 1 are in H and no term of S 2 is in H. Hence S 1  = g = H and |S 1 | ≥ v g (S) ≥ m+1 3 . Let φ be the projection from G to G/H. Let S 2 = (b 1 , . . . , b w ),...

Ngày tải lên: 07/08/2014, 15:22

... integer and (u, n) = 1. Then G(∞, u/n) contains a triangle if and only if m | n, u 2 ∓ u + 1 ≡ 0 (mod n), a rectangle if and only if 2|m, m|2n, and 2u 2 ∓ 2u + 1 ≡ 0 (mod n), and a hexagon if and ... q = a ∗ (c ∗ N/ h)/q ∗ and therefore a cN/ h 2 q = a ∗ c ∗ N/ h 2 q ∗ . A simple calculation shows that q = q ∗ . Then it follows that A −1 T A and B −1 SB have the same order an...

Ngày tải lên: 08/08/2014, 01:20

... vertex and edge connectivity, and vertex and ed ge chromatic number. We also compute its automorphism group, settling a question of Klotz and Sander. In addition, we classify all planar graphs and ... a common neighbor of a and b and so diam G R  2. Obviously G R is not complete in this case, so diam G R = 2. If t  2 and f 1 = 2, observe that the vertices (0, 0, . . . , 0)...

Ngày tải lên: 08/08/2014, 01:20

... ατ r 1 τ r 2 −1 α ′ −1 ∈ U and hence there are exactly λ these [j, β]’s by the assumption. Let 0  i = i ′  t−1 and α, α ′ ∈ G. Supp ose that (i, α)I[j, β] and (i ′ , α ′ )I[j, β]. Then since αβ −1 ∈ D ij and α ′ β −1 ∈ ... ·∪B k−1 and B i ∩ B j = ∅ for 0  i = j  k − 1. Let 0  j  t −1, 0  r  s−1, and ϕ, ϕ ′ (=) ∈ U. Suppose that (i, α)I[j, ϕτ r ] and (i, α)I[j, ϕ ′ τ...

Ngày tải lên: 08/08/2014, 01:20

... Firing Game and Matroid Complexes, in Discrete Models: Combinatorics, Computation, and Geometry, DM-CCG 2 001, R. Cori, J. Mazoyer, M. Morvan, and R. Mosseri, eds., Discrete Mathematics and Theoretical ... m(σ) : σ is a path between σ A + and σ C }. We show that these monomials satisfy the condition of Proposition 4.2. Let σ and σ ′ be two paths in between σ A + and σ C , with m...

Ngày tải lên: 08/08/2014, 01:20