Báo cáo toán học: "A Proof of the Two-path Conjecture" pps

... vertices. The cycle C 6 is the edge-disjoint union of two paths of length 3 with common endpoints. In the first case, the graph has twelve paths of length 3; in the second there are six such paths. The ... vertex, then the graph has a third subgraph that is also a path of length n. For example, the complete graph K 4 is an edge-disjoint union of two paths of length...

Ngày tải lên: 07/08/2014, 06:23

Ngày tải lên: 05/08/2014, 09:46

... 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

... non-analytic proof of this evaluation. This method of proof is inspired by D. Zeilberger’s creative application in [Z1]. AMS Subject Classification: Primary 05A, 11A, 15A One of the most famous ... essentially non-analytic proof of this evaluation. This method of proof is inspired by D. Zeilberger’s creative application in [Z1]. We begin by recalling some notations. Given...

Ngày tải lên: 07/08/2014, 06:20

... we show how the general case can be handled. In the first subsection we describe the solution g in the general case, while the second subsection is devoted to the proof of the main theorem. 4.1 ... (see Fig. 2 for the labeling of the chords). Now we can define g : R → {0, ±1} by g(R) = 1 − q(R) as before. Figure 12: The orientation in the general case. 4.2 Proof o...

Ngày tải lên: 08/08/2014, 01:20

... dim E, the multiplicity of the irreducible E λ in the c-eigenspace of Λ E r equals the multiplicity of S λ in the c- eigenspace of L |λ|,r . Proof. Suppose |λ| =dimE. Then the c-eigenspace of L |λ|,r is ... self-conjugate. Then a r λ =  1 if d(λ)=n − 2r 0 otherwise Proof. Straight forward observation. Propositions 3.1, 3.3 and 3.4 comprise the first steps of Bouc’s...

Ngày tải lên: 07/08/2014, 06:23

... the condition nP(|X 1 | > η n ) ≤ c(log n) ε 0 , 0 < ε 0 < 1 in theorem 1.1 of [12]. Remark 1.4. If EX 2 < ∞, then X is in the domain of attraction of the normal law. Therefore, the ... completes the proof of Theo- rem 1.1. Competing interests The author declares that she has no competing interests. Acknowledgments The author was very grateful to the refe...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:21

... D(n). Proof. Consider the table of the characters χ N ; we are interested in the dimension of the row-span of this table. Since the dimension of the row-span of a matrix is equal to the dimension of ... well study the dimension of the space spanned by the columns of the table. By the preceeding lemma, the N th entry of the column corresponding to...

Ngày tải lên: 07/08/2014, 06:20

... the product of the probabilities of each of the events as an upper bound. In our approach, a key step to further improving the upper bound obtained in [2] is the exact computation of the probability ... involving the conjunction of the events using the occupancy problem for random placements of balls into bins. We make use of the sharp estimates obtained by K...

Ngày tải lên: 07/08/2014, 06:20