Báo cáo toán học: "A Toeplitz-Hausdorff theorem for matrix ranges " pdf

... values T(m, n) form the Fibonacci sequence; more generally, for each fixed m, the values of T( m, n) form a sequence satisfying a higher-order linear recurrence relation (see section 4 for an explanation ... n)=T( m, n) for all n. When m is congruent to 2 (mod 4), a modified version of this holds: T(m,−2− n)=(−1) n T(m,n) for all n. That is, one observes (and we will in fact show): T HE...

Ngày tải lên: 07/08/2014, 06:22

... record, then  σ∈S n x f(σ) y majcode(σ) =  σ∈S n x f(σ) y invcode(σ (−1) ) for n = 2, 3, 4 but not for n = 5. For the other six kinds of records, f = r[max, i], r[min, i], l[max, v], l[max, i], l[min, v], l[min, i] and for the bi-statistics (f, ... are equidistributed and the g enerating functions are given by (1). 5 Proof of Theorem 1.3 Theorem 1.3 can be reformulated as follow...

Ngày tải lên: 08/08/2014, 12:22

... This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. A novel method for crystalline silicon ... and distributed freely for any purposes (see copyright notice below). Articles in Nanoscale Research Letters are listed in PubMed and archived at PubMed Central. For information abou...

Ngày tải lên: 20/06/2014, 21:20

... required to be uniformly continuous. In this article, we assume the continuity of T instead of un iform continuity. Chidume et al. [ 20] gave the w eak convergence theorem for u niforml y continuous ... scheme for the mappings which are asymptotically nonexpansive in the intermediate sense in Banach spaces. Weak convergence theorem is established for this three-step iterative scheme...

Ngày tải lên: 20/06/2014, 21:20

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... establish the conditions for n −1/2 n  k=1 ϕ(X k ) L −→ N(μ, σ 2 ). We need a central limit theorem for martingale differences as follows Theorem 2.3. (Central limit theorem for martingale differences) ... respec- tively. 3.2. Functional Central Limit Theorem We have the following ergodic theorem for the imbedded chain Theorem 3.1. (Ergodic theorem for the imbedded proc...

Ngày tải lên: 06/08/2014, 05:20

... REFERENCES 3 For appropriate positive constants c 1 and c 2 , f (P ) is the objective function for our maximization problem. In practice, we make c 1 relatively ... 1994; Accepted: September 18, 1994 Abstract For k ≥ 5, we establish new lower bounds on the Schur numbers S(k) and on the k-color Ramsey numbers of K 3 . For integers m and n ,let[ m, n ]denotetheset{ i | m ≤ i ≤ n }.AsetS...

Ngày tải lên: 07/08/2014, 06:20