Báo cáo toán học: " Some Periodicity of Words and Marcus Contextual Grammars" ppsx

... quasi-periodic word and let any letter in u be covered by a word v. Then we denote u = v ⊗ v ⊗···⊗v. Some Periodicity of Words and Marcus Contextual Grammars 387 However, the other types of Marcus contextual ... set of all hyper primitive words. Remark 1.3. Fig. 1.3 indicates that u is a quasi-periodic word. Fig. 1.3. Vietnam Journal of Mathematics 34:4 (2006) 381–...

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. ... by Noor [3–5] and Padmanabhan and Parvatham [2]. Also it can easily be seen that ( ) * 2 0 R S = and ( ) 2 0 , T K = where * S and K are the well-known classes...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 15:21

... extension of ring R by Z. Let R be a ring and Z the ring of all integers. Let S = R ∗ Z be the Dorroh extension of R by Z. As sets, S = R × Z, the Cartesian product of R and Z. The addition and multiplication ... 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...

Ngày tải lên: 06/08/2014, 05:20

... particularization of these results to the case of regular graphs with four distinct eigenvalues proves some conjectures of Haemers and Van Dam [29] ,[12] ,[10] . Some Applications of the Proper and Adjacency Polynomials ... presence of high levels of structure in the considered graphs. See, for instance, the papers of Haemers and Van Dam, [12] , and Garriga, Yebra,...

Ngày tải lên: 07/08/2014, 06:20

... 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 was originally ... just characterizes the total number of permutations of n things, cf. [63], p. 16, and hence can derive det(A (2) n )fromdet(A (0) n ) and det(A (1) n )alsothisway. 4) From t...

Ngày tải lên: 07/08/2014, 06:22

... leaf, and we print it out. If q is weakly self-avoiding then we append q0andq1 to the end of the queue. the electronic journal of combinatorics 8 (2001), #N2 2 Weakly Self-Avoiding Words and a ... 0011110101010, 0011110101011 and the four words obtained by changing 0 to 1 and 1 to 0. (c) If k ≥ 3, there exists an infinite weakly self-avoiding word. Proof. (a) If a word x over Σ...

Ngày tải lên: 07/08/2014, 06:22

... of this journal for pointing out the second exception of the case n = 10 in the proof of Lemma 4. References [1] F. Blanchet-Sadri, E. Clader, and O. Simpson. Border correlations of partial words. Theory ... the rest of the paper. We refer to Lothaire’s book [6] for more basic and general definitions of combinatorics on words. We denote the length of a word w by |w|. A wo...

Ngày tải lên: 07/08/2014, 15:22

... number and the clique number of X n and of the com- plementary graph ¯ X n . We remark that ω( ¯ X n ) and χ( ¯ X n ) are also called the independence number and the clique covering number of X n . ... with multiplicity ϕ(n), if and only if n is squarefree and even. Theorem 15. Let m be the maximal squarefree divisor of n and let M be the set of positive divisors of...

Ngày tải lên: 07/08/2014, 15:22

... appear as prefix, central factor, and suffix of µ(b), and π 2 (f 1 ), π 2 (f 2 ), π 2 (f 3 ) as prefix, central factor, and suffix of µ(c). Definition 1. The words f 1 , f 2 , and f 3 (resp. π(f 1 ), π(f 2 ), ... 2, - There exist some unique x u , y u ∈ A 3 , and some unique m u , s u , p u ∈ A ∗ 3 , s u = ǫ suffix of µ(x u ), p u prefix of µ(y u ), such that u = s u µ(m u )p u...

Ngày tải lên: 08/08/2014, 14:23