Báo cáo toán học: "The solution of the Ar T-system for arbitrary boundary" potx

... 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 = ... ∆, then for 0 ≤ α ≤ k, there exist 1. a number r ∈ (0, 1); 2. a sequence of complex numbe...

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

... Introduction The notion of variational bicomplexes was introduced in studying the problem of characterizing the kernel and image of Euler-Lagrange mapping in the calcu- lus of variations. This ... 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 constru...

Ngày tải lên: 06/08/2014, 05:20

... point theory”, organized jointly by the Hanoi Institute of Mathematics and Hanoi University of Education. The author would like to thank the members of this Seminar for their useful comments. The ... Bx 0 . ThecasewhenC is compact can be proved similarly. The proof is complete.  Now we are in a position to proof a version of the well known minimax theorem due to Neumann...

Ngày tải lên: 06/08/2014, 05:20

... (c1)–(c5). The method of dealing with (c5) is similar to that of dealing with (c4) in the proof of Theorem 2.2. Up to now we have not found any example of quadratic programs of the form (1) for which there ... (c5) in the formulation of Theorem 2.2. 3. Examples The following example shows that the conditions stated in Theorem 2.1 are not sufficient for having the l...

Ngày tải lên: 06/08/2014, 05:20

... λ r > 0, for some r .The components of λ are called the parts of λ. The integer n, the sum of all the parts of λ, is called the norm of λ and is denoted by n(λ). The (ordinary) Ferrers diagram of λ ... 1995 Bijective proofs of the hook formulas for the number of ordinary standard Young tableaux and for the number of shifted standard Young tableaux...

Ngày tải lên: 07/08/2014, 06:20

... general, the vertex u depends on the value of k. Two straightforward consequences of the above theorem are the following. Corollary 2.9 Let Γ be a graph as above. Then, for each given 0 ≤ k ≤ d, there exists ... trivial.) Then, by the converse of Theorem 2.5 , it must be Q k  u ≥ 1. On the other hand, in the proof of Theorem the electronic journal of combinatoric...

Ngày tải lên: 07/08/2014, 06:20

... v j ) e γ 1 u i +γ 2 v j , where u i ,v j and e are arbitrary parameters on the elliptic curve. First, we prove a lemma (set a = b = 0 to get the result of the theorem). Lemma: With the additional parameters a and b,wehave det  σ(u i+a + ... y j ) . This expression lends itself to explicit formulas in Pad´e approximation theory and further applications in transcendental theory. O...

Ngày tải lên: 07/08/2014, 06:20