Báo cáo tin học: "The 99th Fibonacci Identity" pdf

... 2003 [2] S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section: Theory and Applica- tions, Wiley & Sons, Inc., New York, 1989. [3] D. Zeilberger, A Fibonacci- Counting Proof Begged ... setting p = 0, the following corollary is just as strong as Identity 6. Corollary 7. For n ≥ 1, q ≥ 0,  k≥0  n k  G qk (f q−3 ) n−k = (f q−1 ) n G 2n or, equivalently, using the classical F...

Ngày tải lên: 07/08/2014, 15:23

... largest possible. We distinguish three subcases. See Figure 8 for the first two of these subcases. 2.1. r U ≥ l V . Let x 1 = (r U , 0). If S ∈ S is a triangle intersecting T , then r S ≥ r U and l S ≤ ... [13], 4 for the collections of pairwise intersecting discs (i.e., with (2, 2)-property) [3], and at most 3 for the collections of pairwise intersecting translates of a convex set [10]. See t...

Ngày tải lên: 07/08/2014, 15:23

... a High Distinction for guessing 75% of the time and putting the right answer for the other 25%, a Distinction for 100% guessing, and a Credit for guessing 75% of the time and putting a wrong ... punctuating our theoretical discussions and explanations with empirical demonstrations where we use 1:1 and 4:1 prevalence versus matching and mismatching bias to generate the chance level con...

Ngày tải lên: 22/02/2014, 02:20

... pyridine nucleotides, which also bind to calvectin; bound NAD+ decreased the association of calvectin with the membrane [28]. Mitochondria could be depleted of cal- vectin by treating them with uncoupling concentrations of ... different from that transporting Sr 2+ ). The authors suggested an interesting but rather simple ‘two-step’ model of calvectin involvement in Ca 2+ transport: first, sol...

Ngày tải lên: 23/03/2014, 03:20

... “Properties of codes in rank metric,” http://arxiv .org /pdf/ cs.DM/0610057/. [21] M. Schwartz and T. Etzion, “Two-dimensional cluster- correcting codes,” IEEE Transactions on Information Theory, vol. ... The Theory of Error-Correcting Codes, North-Holland, Amsterdam, The Netherlands, 1977. [2] V. Pless, “Power moment identities on weight distributions in error correcting codes,” Information...

Ngày tải lên: 21/06/2014, 22:20

... Collecting the results of the preceding lemmas gives the next result. Lemma 3.5. Let H be the automorphisms ... swaps 14 lines and fixes the remaining four. We leave the remaining details (which are entirely routine) to the reader. Before we determine the structure of the automorphism group Aut(M(F 4 )), we ... graphically by sending the E component of Γ to one of the six components of Γ ∪ Γ ...

Ngày tải lên: 07/08/2014, 15:23

... generating upper bounds for the probability of the union of events when the individual probabilities of the events as well as the proba- bilities of pairs of these events are known. By formulating ... then assigning nonnegative weights to each component and nonpositive weights to the edges connecting them. Proposition 3 Assume n ≥ 5. Let V = A ∪ B be a partition of the vertex set V and k = .....

Ngày tải lên: 07/08/2014, 15:23

... and label them by the same letter as a i where β is the betti number of G. The resulting graph is a tree consisting of tree edges in T and 2β semi-edges. We denote this new tree by ˆ T . Then indexing ... orders of letters and permitted to be empty. Parentheses are always omitted when unnecessary to distinguish cyclic or linear order. An embedding of a graph G into a surface S is a homeomorph...

Ngày tải lên: 07/08/2014, 15:23

... that case, it would make sense to ask about the complexity of computing χ q (G), in particular whether it is NP-hard, as is computing the chromatic number χ(G). Similarly, we found an exponential ... dimension for which the graph has an orthogonal representation. An interesting question arises in the random graph setting: what is the likely quantum chromatic number of G ∈ G(n, p)? Conjecture:...

Ngày tải lên: 07/08/2014, 15:23

... number of neighbors in the other class is at most  1 2 + β  deg(v). By deleting all edges with endpoints in distinct partition classes, we destroy all cycles of length at least 1 2 n + ∆ + ... 8ν 2 dn  1 + A 2ν √ d  and, setting d 0 ≥ (A/(2ν)) 2 and ν β := β/32, ≤ 16ν 2 dn ≤ 16ν β νdn = β 2 νdn. This yields a contradiction and completes the proof of Claim 15. Continuing the proof of the ....

Ngày tải lên: 07/08/2014, 15:23