Báo cáo toán học: "Hybrid Proofs of the q-Binomial Theorem and other identities" ppsx

... theorem and other identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the ... 2}, {15}, the electronic journal of combinatorics 18 (2011), #P60 15 Hybrid Proofs of the q-Binomial Theorem and other identities Dennis Eichhorn Departm...

Ngày tải lên: 08/08/2014, 14:22

... q-analogue of the hook formula (see the Theorem in section 4) which all the other proofs do not. Secondly, the same idea also works to provide a bijective proof of the hook formula for the number of ... 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)....

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 05/08/2014, 15:20

... 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 = ... YL and WY participated dis- cussion and corrected the main theorem. All authors read...

Ngày tải lên: 20/06/2014, 20:20

... uniform. 2. New proofs three theorems To prove the above three theorems, we need the following lemmas. Lemma 1. [1, p. 67],[2] If ϕ is symmetric and convex (concave) on symmetric convex set Ω, then ϕ ... t)y j ) 2   2 ≤ 0, and then h  (t) ≤ 0, so f (t) is concave on (0, 1). NEW PROOFS OF SCHUR-CONCAVITY FOR A CLASS OF SYMMETRIC FUNCTIONS HUAN-NAN SHI ∗ , JIAN ZHANG AND C...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

... simplicity, we will solve this problem in the case of r =1andr = 2. Then the other cases follow by the same method. 2. Notations and Premilinaries Throughout this paper, the following notations will be ... 0. 1. Introduction The notion of variational bicomplexes was introduced in studying the problem of characterizing the kernel and image of Euler-Lagrange mapping...

Ngày tải lên: 06/08/2014, 05:20

... ,x n }⊂ Tx 0 . The theorem is proved.  Before proving a minimax theorem we establish a coincidence theorem which is analogous to a modified version of a theorem of Ben-El-Mekhaiekh et al. in [2]. Theorem ... 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 h...

Ngày tải lên: 06/08/2014, 05:20

... proved that the assertion of Theorem 2.2 remains valid if instead of (c1)–(c4) we use (c1)–(c5). The method of dealing with (c5) is similar to that of dealing with (c4) in the proof of Theorem 2.2. ... R n : ∇f(x)v =0}. The ideas of the proof of Theorem 2.2 are adapted from [8, Theorem 4.1] and [12, Theorem 6]. In [8], some results involving Schur complemen...

Ngày tải lên: 06/08/2014, 05:20