Báo cáo toán học: "n Praise of an Elementary Identity of Euler" pot

... (7.4) Remark. Identity (7.4) is one of the two q-analogs of the Chu–Vandermonde identity (6.6). See Gasper and Rahman [21, eq. (1.5.2)]. Proof. By dividing by the RHS, we form an equivalent identity of ... next identity, due to Ramanujan, appeared in van der Poorten’s charming exposition [38] of Ap´ery’s proof of the irrationality of ζ(3). Example 4.6 (Ramanujan). Let n b...

Ngày tải lên: 08/08/2014, 14:23

... lattices of height n and size k by certain integer sequences 0 = z 1 ··· z n k − 2, and (ii) a “canonical 2-decomposition” of ordinally indecomposable posets into “2- indecomposable” canonical summands. 1 ... former is that now the top element  1 of the lower summand and the bottom element ⊥ 2 of the upper summand are identified instead of the electronic journal of combinatorics 9...

Ngày tải lên: 07/08/2014, 06:23

... as: Guess (6, 3): 6 copies of (04)(13)(25) and the identity. Guess (7, 3): 7 copies of (04)(13)(25). Guess (8, 3): 2 copies of (04)(15)(26)(37) and of (02)(13)(46)(57) and of (03)(14)(25) together ... an ad hoc solution: two copies of (05)(16)(27)(38)(49) and of (04)(15)(26)(37)(8 10), 3 copies of (03)(14)(25)(68)(79), and one copy of (04)(13)(26)(59)(8 10) and of (05)...

Ngày tải lên: 07/08/2014, 08:20

... n-color partitions of 8 but only one partition viz., 6 2 +2 2 is relevant for Theorem 3 and none is relevant for Theorem 4. Out of 859 n-color partitions of 11, none is relevant for Theorems 3-4. ... containing 4 functions of order 3, second containing 10 functions of order 5 and the third containg 3 functions of order 7. Watson [8] found three more functions of order 3 and two...

Ngày tải lên: 07/08/2014, 08:20

... in: B. E. Sagan, R. P. Stanley (Eds.), Mathematical Essays in honor of Gian-Carlo Rota, Birkauser, Basel. 1998, pp. 111-129 [3] Z. G. Liu, Some operator identities and q-series transformation ... 2 The proof of the Theorem The q-difference operator and the q-shift operator η are defined by D q {f(a)} = 1 a (f(a) − f(aq)) and η{f (a)} = f (aq), respectively. In [2] Chen and Liu construct ......

Ngày tải lên: 07/08/2014, 08:22

... consists of a single element of GF(q 2 ) the translation plane is the affine Hall plane of order q 2 and its dual plane is the affine Moulton plane of order q 2 . For details on these planes see ... Every pre- quasifield coordinatizes a translation plane; see [4, Section 5.6]. In our case this translation plane is an affine Andr´e plane A(q 2 ) of order q 2 and dimension 2 over its kerne...

Ngày tải lên: 07/08/2014, 15:22

... subgroup of the normalizer of Γ 0 (N). Moreover, any element of Γ + 0 (N) is an Atkin-Lehner involution of Γ 0 (N). Recall that an Atkin-Lehner involution w q of Γ 0 (N) is an element of determinant ... (mod n), a rectangle if and only if 2|m, m|2n, and 2u 2 ∓ 2u + 1 ≡ 0 (mod n), and a hexagon if and only if 3|m, m|3n and 3u 2 ∓ 3u + 1 ≡ 0 (mo d n). Proof. If n = 1, then the...

Ngày tải lên: 08/08/2014, 01:20

... Beyond AER: An Extensive Analysis of Word Alignments and Their Impact on MT Necip Fazil Ayan and Bonnie J. Dorr Institute of Advanced Computer Studies (UMIACS) University of Maryland College ... of EMNLP’2005. Franz J. Och and Hermann Ney. 2000. A comparison of alignment models for statistical machine translation. In Proceedings of COLING’2000. Franz J. Och. 2000b. GIZA++: Train...

Ngày tải lên: 20/02/2014, 11:21

... field distribution as a function of the size of the NPs. Figure 7. Energy band diagram profile and electric field distribution. (a) Energy band diagram profile and (b) electric field distribution ... Trans Nanotechnology 2010, 9:414-421. 8. Langhuth H, Frédérick S, Kaniber M, Finley J, Rührmair U: Strong photoluminescence enhancement from colloidal quantum dot near silver nano-is...

Ngày tải lên: 20/06/2014, 20:20

... emergence of drug-resistant HSV strains [5]. The discovery of new non-nucleoside anti-HSV-1 agents with different mechanisms of action could offer an additional strategy against drug resistance of ... primary cause of facial lesions (mouth, lips, and eyes) in humans. The widespread use of acyclovir and nucleoside analogues has led to emergence of HSV strains that are resis...

Ngày tải lên: 20/06/2014, 20:20