Báo cáo toán học: "Ramanujan Type Congruences for a Partition Function" docx

... Ramanujan Type Congruences for a Partition Function Haijian Zhao and Zheyuan Zhong Center for Combinatorics, LPMC-TJKLC Nankai University, Tianjin, P.R. China haijian.nankai@gmail.com, ... and a generalization of his “ most beautiful identity”, Int. J. Number Theory, 6 (2010), 673–680. [6] H C. Chan, Ramanujan’s cubic continued fraction and Ramanujan type congruences for...

Ngày tải lên: 08/08/2014, 14:22

... the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Lyapunov -type inequalities for a class of even-order differential equations Journal ... Lyapunov-typ e inequalities for certain higher order differential equations. J. Math. Anal. Appl. 195 , 527–536 (1995) [9] Tang, XH, Zhang, M: Lyapunov inequalities and stabilit...

Ngày tải lên: 20/06/2014, 21:20

... define R L j :=R A j ∪ {a j a j−1 ·· a 2 a −1 1 a 0 ,a j a j−1 ·· a 2 a −1 1 a 0 a −1 1 } ∪ {a j a j−1 ·· a 2 a −1 1 a 0 a 1 , , a j a j−1 ·· a 2 a −1 1 a 0 a 1 a 2 ·· a j }. For example, R L 2 = {1 ,a 2 ,a 2 a 1 ,a 2 a −1 1 ,a 2 a −1 1 a 0 ,a 2 a −1 1 a 0 a −1 1 ,a 2 a −1 1 a 0 a 1 ,a 2 a −1 1 a 0 a 1 a 2...

Ngày tải lên: 07/08/2014, 08:22

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Ngày tải lên: 05/08/2014, 10:20

... ≥ max {a 1 , ,a r }. Folkman [3] proved that there exists a graph G such that G → (a 1 , ,a r )andcl(G)=max {a 1 , ,a r }. Therefore F (a 1 , ,a r ; q) exists if and only if q>max {a 1 , ,a r }. ... (a ϕ(1) , ,a ϕ(r) ) for any permutation ϕ ∈ S r . That is why we may assume that a 1 ≤ ≤ a r ≤ p. (25) We shall prove that a 1 + a 2 − 1 ≤ p.Ifa 2 ≤ 2thisistrivial :a 1...

Ngày tải lên: 07/08/2014, 13:21

... 125, Almaty, Kazakhstan askar56@hotmail.com Submitted: Mar 29, 2009; Accepted: Feb 18, 2010; Published: Feb 28, 2010 Mathematics Subject Classification: 0 5A0 5, 0 5A1 5 Abstract We show that the major ... w 1 and w 2 is defined recursively by w 1 ⊔⊔ǫ = w 1 , ǫ⊔⊔w 2 = w 2 and au⊔⊔bv = a( u⊔⊔bv) + b(au⊔⊔v), a, b ∈ A, u, v ∈ A ∗ . For example, ab⊔⊔cd = abcd + acbd + acdb + cabd + cadb + cd...

Ngày tải lên: 08/08/2014, 12:22

... two patterns 321 and 3412. For more examples, a searchable database listing which classes of permutations avoid certain patterns can be found at Tenner [2009]. Since we know pattern avoidance can be used ... journal of combinatorics v17 (2010), #R127 10 Enumerating Pattern Avoidance for A ne Permutatio ns Andrew Crites ∗ Department of Mathematics University of Washington, Seattle, WA,...

Ngày tải lên: 08/08/2014, 12:22

... information on the parental (paternal or maternal) origin of marker alleles, in addition to information on marker genotypes. The parental origin of marker alleles in an ... marker alleles for individual i are known, then they will be arbitrarily labelled as Mi and M2. For example, suppose individual i has marker alleles A3 and Al, then A3 ....

Ngày tải lên: 09/08/2014, 18:21

... +1)q j(j+1)/2 , where (1.4) (A) N = (A; q) N = N−1  j=0 (1 − Aq j ). (1) Partially supported by National Science Foundation Grant DMS-8702695-04 Typeset by A M S-T E X Finally, it may well be asked what happens when a is ... (14.31)] ∞  n=0 (z) n+1 z n (−zq) n =1+2  n≥1 (−z 2 ) n q n 2 . Now apply Theorem 1 with a =2,b = 1 noting that for p ≡ 5(mod8)2isa non-quadratic residue, and...

Ngày tải lên: 07/08/2014, 06:22

... Bryant Department of Mathematics University of Queensland Qld 4072 Australia Heather Gavlas Department of Mathematics Illinois State University Campus Box 4520 Normal, IL 61790-4520 USA Alan ... first author is supported by the Australian Research Council. The research of the third author is sponsored by ARO grant DAAD19-01-1-0406 and by DOE EPSCoR. References [1] B. Alspach and H. Gavlas, ......

Ngày tải lên: 07/08/2014, 08:20