Báo cáo toán học: "Some Examples of ACS-Rings" pdf

... idempotent of S is of form (e, 0), where e 2 = e ∈ R. Proposition 2.1. Let R be a commutative ring and I an ideal of R.LetS = R ∝ I be the trivial extension of R by I.IfS is an ACS-ring, so is R. Proof. ... Rr R (X)=l R (X) for any subset X of R and that any idempotent of R is central. (5) ⇔ (7). Note that l R (aR)=l R (RaR) for any a ∈ R. (5) ⇔ (6). The proof is similar to that...

Ngày tải lên: 06/08/2014, 05:20

... R: Properties of a class of functions with bounded boundary rotation. Ann. Polon. Math. 31, 311–323 (1975) [3]. Noor, KI: On radii of convexity and starlikeness of some classes of analytic functions. ... 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. Some properties...

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Ngày tải lên: 05/08/2014, 15:21

... Kayoko Shikishima-Tsuji 3. Set of Primitive Words In this section, we deal with the set of all primitive words. First we provide the following three lemmas . The proofs of the lemmas are based on ... denotes the empty word of X ∗ . For the sake of ∗ This work was supported by the grant of the Japan-Hungary Joint Research Project or- ganized by the Japan Society for the Promotion...

Ngày tải lên: 06/08/2014, 05:20

... effort has been devoted to the use of algebraic techniques in the study of graphs as, for instance, the achievement of bounds for (some of) their parameters in terms of their (adjacency or Laplacian) ... 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 combinatorics 4 (1997), #R21 3 In the rest...

Ngày tải lên: 07/08/2014, 06:20

... determinant, namely the matrices then consist of consecutive binomial coefficients of the form  2m+1 m  . Simultaneously, this yields another proof of the result of Desainte – Catherine and Viennot, which ... formula (yielding a “90 % bijective proof” for tableaux whose columns consist of an even number of elements and are bounded by height 2n) to Gordon’s result [36] in the proof...

Ngày tải lên: 07/08/2014, 06:22

... a sequence ˜ S of length m which consists of all nonzero eigen- values of X n such that the number of appearences of an eigenvalue is its multiplicity. the electronic journal of combinatorics ... journal of combinatorics 14 (2007), #R45 7 2. The multiplicity of zero as an eigenvalue of X n is n − m. 3. If α(λ) is the multiplicity of the eigenvalue λ of X n , then λα(λ) i...

Ngày tải lên: 07/08/2014, 15:22

... exist 1. a number r ∈ (0, 1); 2. a sequence of complex numbers z n , |z n | < r; Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Qi ... text (HTML) versions will be made available soon. Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Advan...

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... 2011:60 http://www.advancesindifferenceequations.com/content/2011/1/60 Page 8 of 14 comes down to zero. The greatest values of the considered functions are infinite, when k 0 = ∞. 2.7. The first derivatives of the ch1 function of HC in relation to the degree of freedom ... 2)ψ 2 (υ +1)+ψ 4 (k + n − 2)  . In general, the HC of the mth derivative of n can be defined on the basis...

Ngày tải lên: 20/06/2014, 21:20

... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof. With the aid of above preparations, now we will give the proof of Theorem 1.2. Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, so we omit the details of its proof. Lemma 3.4 Under the conditions of Theorem 1.2, F(x) satisfies the PS condition. Proof From the proof of Le...

Ngày tải lên: 20/06/2014, 21:20