Báo cáo toán học: "Rotor-router aggregation on the layered square lattice" pps

... times. Therefore, the final chip configuration does not depend on the initial rotor configuration, and the initial and final rotor configurations are equal. Following the proof of Theorem 1, the Strong ... reflection of the edges of the lattice carries over to the rotors. Thus, the rotor directions on the axes alternate between the directions of the two parallel edges of...

Ngày tải lên: 08/08/2014, 12:23

... 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 ... weights. On the other hand, by the Theorem 1 of Schatte [3], Equation (3) fails for weight d k = 1. The optimal weight sequence remains unknown. The purpose of this article is to...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

... p 1 (x, y)= x, p 2 (x, y)=y are the canonical projections. By the Proposition 3.2 the second Some Re sults on the Properties D 3 (f) and D 4 (f) 147 8. D.Vogt , On two clases of (F )-spaces,Arch. ... id, Hence, R is the right inverse of q and the proposition is proved.  4.ProofofMainTheorem (i) The sufficiency is obvious. Now we prove the necessity. Let E be a Frechet space...

Ngày tải lên: 06/08/2014, 05:20

... f z 1 =  f z 1 on D 2 . Thus f =  f on D 1 × D 2 and the proof for the case N = 2 is completed. Now we assume that the conclusion of the theorem holds for N − 1 ≥ 2. Put k = k 1 + ···+ k N . From the hypothesis ... Forelli type (see Theorems 3.2 and 4.1 below). The paper is organized as follows. Beside the introduction, the paper contains three sections. In the second...

Ngày tải lên: 06/08/2014, 05:20

... sug- gesting the problem and for many helpful discussion during the preparation of this work. References 1. P. ˚ Ahag, The Complex Monge–Ampere Operator on Bounded Hyperconvex Do- mains, Ph. D. Thesis, ... vanishes on pluripolar sets. The function U (μ, h) plays a crucial role in solving the Dirichlet problem. 3. The Comparison Principle for  E p + B a loc In order to prove...

Ngày tải lên: 06/08/2014, 05:20

... f λ (q) is the generating function for the entries of the column corresponding to the λ-cycles. The dimension of the column-span of our table is therefore equal to dim F n , and the proposition is ... preceeding lemma, the N th entry of the column corresponding to the λ-cycles is equal to the number of nonnegative integer solutions to the equation λ 1 x 1 + ···+ λ k x...

Ngày tải lên: 07/08/2014, 06:20

... information on Maple) implementation of the downhill simplex function optimization method (see [13] for a good description of the method and a C implementation) to the maximize the expression. This ... (3) When conditioning on the event C P 0 , the random graphs of the resulting probability space may contain edges only from within the edges that connect vertices of differen...

Ngày tải lên: 07/08/2014, 06:20

... k>,ifthere are no solutions to the equation x 1 + ···+ x k = y 1 + ···+ y  in A. Denote by SF n k, the number of (k, )-sum-free subsets of [1,n]. Since the set of 1 the electronic journal ... of [1,n] are contained in arithmetic progression r mod ρ, where (k − )r ≡ 0modρ. If d  >ρthen every progression r mod d  consists of at most n/(ρ +1) elements hence it contains no...

Ngày tải lên: 07/08/2014, 06:20