Báo cáo toán học: "A Note on The Rogers-Fine Identity" pot

... 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 ... (1988) [3] Schatte, P: On strong versions of the central limit theorem. Mathematische Nachrichten. 137, 249–256 (1988) [4] Lacey, MT, Philipp, W: A note on the almost sure central...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:21

... 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 ... x) =4 1+ln +1 2 (k − )( +1) . Combining the above inequalities with (10), the result follows. Let us conclude this note with some further remarks on the range of k and  satis...

Ngày tải lên: 07/08/2014, 06:20

... bounded, then the height distribution concentrates on two consecutive points. 3 Derivation of Results We establish the five parts of Theorem 2. Since the analysis involves a routine use of the saddle ... 1wewrite  A/b 0 (···)=  ∞ 0 (···)−  ∞ A/b (···), evaluate the first integral exactly and use Laplace’s method on the second integral. Now f  (u) < 0 for u ≥ A/b and the...

Ngày tải lên: 07/08/2014, 06:20

... several directions. They conjectured that if |G| > |Aut(G)| and the action of Aut(G)onG has no singleton orbits, then (G) = 2. Though there are graphs for which this fails 1 , the idea that ... define the class Π P k to consist of all languages L for which L ∈ Σ P k .Above, the notation · , · refers to some canonical pairing function. With these definitions, NP = Σ P 1 ,coNP=Π P 1...

Ngày tải lên: 07/08/2014, 06:22

... A note on the ranks of set-inclusion matrices D. de Caen Department of Mathematics and Statistics Queen’s University Kingston, Ontario, Canada K7L 3N6 decaen@mast.queensu.ca Submitted: ... relation is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t,k (v) be the (0,1)-matrix of inclusio...

Ngày tải lên: 07/08/2014, 06:22

... stationary dis- tribution is the desired distribution. The transitions of the chain consist of selecting a vertex uniformly at random and modifying the configuration only at the chosen vertex. The ... Background Consider a Markov chain (P, Ω,π)whereP denotes the transition matrix, Ω denotes the state space, and π denotes the unique stationary distribution. Recall that the v...

Ngày tải lên: 07/08/2014, 06:22

... columns j =1, ,ρn.DenotebyM 4 the block consisting of the rows i = |A + |+1, ,mand the columns j =2ρn+1, ,n.DenotebyM 5 the block consisting of the rows i =1, ,|A + | and the columns j =2ρn +1, ,n. ... this conjecture, and together with a well-known construction obtain that it is sharp. Furthermore, we obtain that the extremal graphs must be biregular. Our main theorem is the...

Ngày tải lên: 07/08/2014, 06:23