Báo cáo toán học: " Combinatorial Laplacian of the Matching Complex" pps

... involves the combinatorial Laplacian which is an analogue of the Laplacian on differential forms for a Riemannian manifold. The analogue of Hodge theory states that the kernel of the combinatorial Laplacian ... to decompose all the eigenspaces of the Laplacian into irreducibles and thereby decompose the homology. They also show that the spectrum of the...

Ngày tải lên: 07/08/2014, 06:23

... interpretation for these numbers. We can easily find it from combinatorial theory of generating functions. Theorem 8. The integer V (n, k) is the number of partitions of [2n+1] into 2k +1 blocks of odd cardinality. Proof. ... 1. The integer LS(n, k) is the number o f signed k-partitions of [±n] 0 . By Theorems 1 and 2, we derive that the integer S(n, k) is the number o...

Ngày tải lên: 08/08/2014, 12:22

... T 2n,n which is indeed the right-hand side of (4), and the proof is finished. the electronic journal of combinatorics 5 (1998), #R38 9 Indeed, the first term in the parentheses on the right-hand side of (6) translates to  n r=0 ζ({3, ... include the occurrence of binomial coefficients (e.g., in (10)). In the present paper we follow the combinatorial approach by ex- pl...

Ngày tải lên: 07/08/2014, 06:22

... orbits. In the present case a family is completely specified by the integer q ≡ q 1 which counts the traversals of the loop 1, i.e., the number of letters 1 in the code word. Each of these q letters ... operator u n =trU n (19) as sums of periodic orbits of the graph. The two-point correlations in the spectrum of S (16) can be expressed in terms of the average...

Ngày tải lên: 07/08/2014, 06:23

... g m (ζ)) b a+deg z,∞ a r m {b a+deg z,∞ a r m 1 m 2 qk−p(r) m ρ m } m 1 m 2 qk−p(r) M r [g m ](ζ). (3.11) 11 3. Proof of the results Proof of Theorem 1.4 Suppose that the conclusion of theorem is not true, then there exists an entire solution w(z) satisfies the equation [Q(w(z))] n = ... C, if ζ is not the zero of g(ζ), by (3.4) then we can get g (k) (ζ) = 0 from (3.5). By the...

Ngày tải lên: 20/06/2014, 20:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:21

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Ngày tải lên: 05/08/2014, 15:21

... in the theory of differential equations and in mathematical physics. Krupka [5] studied the sheaves of differential forms on finite r-jet prolonga- tions J r Y . Then he constructed the sequence of ... 0. 1. Introduction The notion of variational bicomplexes was introduced in studying the problem of characterizing the kernel and image of Euler-Lagrange mapping in the ca...

Ngày tải lên: 06/08/2014, 05:20

... similarly. The proof is complete.  Now we are in a position to proof a version of the well known minimax theorem due to Neumann-Sion [11, 15] in the case of hyperconvex metric spaces. Theorem 3.5. ... Seminar ”Geometry of Banach spaces and Fixed point theory”, organized jointly by the Hanoi Institute of Mathematics and Hanoi University of Education. The author would like...

Ngày tải lên: 06/08/2014, 05:20