Báo cáo toán học: "On the Dimer Problem and the Ising Problem in Finite 3-dimensional Lattices" pps

... amazing that these ideas extend nicely to the case of partially ordered sets. The ideas in Abu-Sbeih and Khamsi Fixed Point Theory and Applications 2011, 2011:97 http://www.fixedpointtheoryandapplications.com/content/2011/1/97 Page ... X. Define the lower and upper cones by C l ( M ) = {x ∈ X; there exists m ∈ M such that x ≺ m } Abu-Sbeih and Khamsi Fixed Point Theory and A...

Ngày tải lên: 20/06/2014, 21:20

... ( G ) of the graph G is defined as the sum of singular values of the incidence matrix [9]. The directed incidence energy DIE(G) is defined as the sum of singular values of the directed incidence ... LEL(G) in [10]. The connection between IE and Laplacian eigenvalues (for bipartite graphs) was first pointed out in [6]. For more information on IE and DIE/LEL, see [7, 14] and...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 15:20

... easily to binary trees : the BFS random walk for a binary tree is a ruin sequence, and in the correspondence between ruin sequences and general trees, the maximum of the ruin sequence is within O(1) ... at each of the n following stages of the BFS, the vertex x at the head of the queue is removed from the queue, and all “new” neighbors of x areaddedattheendof the...

Ngày tải lên: 07/08/2014, 06:22

... multicolorings. Among many other interesting results and problems in [3] Erd˝os and Gy´arf´as deter- mined for every p the smallest q (q lin =  p 2  − p + 3) for which f (n, p, q) is linear in n and ... to the case when p and q are fixed and n tends to in nity. The study of f(n, p, q) leads to many interesting and difficult problems. For example determining f(n, p, 2) is...

Ngày tải lên: 07/08/2014, 07:21

... with integers. Given a matching m of the Aztec diamond graph A, define the weight of the matching (m) to be the product of the weights of all the edges in the matching. Then the weight of the ... to the Aztec diamond of order n in which the vertices are the squares and an edge joins two vertices if and only if the corresponding squares are adjacent in the...

Ngày tải lên: 07/08/2014, 08:20

... concave down. By finding the zeros of this polynomial in terms of n and then maximizing (over n) the greatest of them, we can find the c which will guarantee the inequality in (6). For n ≥ 2, it ... B m+ for m ≤ . Then by making superficial changes to the remainder of the proof we establish the result for the nonsymmetric case. Thus we have the following: the electron...

Ngày tải lên: 07/08/2014, 15:23

... isomorphism, the roots decorating the vertices will have changed. Furthermore, the construction of ˜ D respects the fact that the edges in the Dynkin diagram represent the inner products of the the electronic ... non-orthogonal if there is some i such that crossing out the i th row and the i th column succeeds in crossing out both α and β. Figure 1 shows the root...

Ngày tải lên: 07/08/2014, 21:20

... cycle, such that there are f i i-gons in the exterior of the Hamiltonian cycle and f ′ i i-gons in the interior of the Hamiltonian cycle. Then  i (i − 2)(f i − f ′ i ) = 0. (1) The theorem can be ... additional edges incident to x ′ and y ′ . By Theorem 2.3 and Propo sition 3.3 there is a cycle of length 4692 in the remaining graph, which proves the coro llar y. ✷...

Ngày tải lên: 08/08/2014, 14:23

... interpretation of the corresponding recursion under sets of initial conditions that are forced on by the interpretation itself (see [4] and t he references cited therein). The combinatorial inter- pretation ... = E k and A(E k+1 + 1) = A(3) = 2 = E k + 1. Assume that the three hypotheses hold up to n, and note since A(i) is slow and unbounded, A −1 ({E n }) = [α, β]. In the...

Ngày tải lên: 08/08/2014, 14:23