Báo cáo toán học: " Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type" pdf

... 1994. Abstract New short and easy computer proofs of finite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the first Rogers-Ramanujan identity ... Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type Peter Paule ∗ Research I...

Ngày tải lên: 07/08/2014, 06:20

... characterised by vertical and horizontal wind speed) and gas (water vapour, CO 2 and other bio- genic gases) content of the air. Heat and gas contents of the air are called “scalars” because they are characterised by ... interception and sources in case of the emission of thermal infra red radiation. Scattering processes at the surface of the organs depends on wa...

Ngày tải lên: 08/08/2014, 14:22

... linear space of the set of all fuzzy sets of a non-empty set. We define the concepts of n-isometry, n-collinearity, n-Lipschitz mapping in this space. Also, we generalize the Mazur– Ulam theorem, ... when the n-isometry mapped to a linear n-normed space is affine. They also obtain extensions of Rassias and ˇ Semrl’s theorem [18]. Moslehian and Sadeghi [19] investigated the...

Ngày tải lên: 20/06/2014, 21:20

... important effect on the performa nce of the proposed method and the computational cost. As shown in Figure 6, the performances of the VAD in various K are mea- sured in terms of the the the receiver ... any hang over during the detection, as these can be added in a heuristic way after the design of the decision rule. Figures8,9 ,and1 0showstheROCcurvesofthese VAD...

Ngày tải lên: 20/06/2014, 21:20

... the other hand, the possibility of occlusion with the border of the image just depends on the proxi- mity of a moving object to the border of the image. Then, the possibility o f occurrence of ... dY a represent the length in pixels of the projection of the dimension a on the X and Y reference axes of the image plane, respectively. H and W are th...

Ngày tải lên: 20/06/2014, 21:20

... ,a m } andB={b 1 , ,b m }ofthevertexsetofD,andforeachdirectededgeijofD,addtheedgea i b j to H.BytheHall-K¨onigTheoremtheedgesofofHcanbepartitionedintoatmosthmatchings,which givethedesiredpartitionoftheedgesofD.)Therefore,bythepigeon-holeprincipletherearesome 8nclasseswhichcontaintogetheratleast n 2 16 · 8n n/2−1 ≥n 2 non-backedgesamongthoseoflengthatleast17nonV  .LetE  denotethesetofthe...

Ngày tải lên: 07/08/2014, 06:20

... (v i ,v j ). Then neither of the bottom vertices of T is on v i Hv k . Proof. Neither v i nor v k is a bottom vertex, since each is the initial vertex of an arc in H andanarcnotinH. Similarly, neither ... that the bound in Theorem 2.2 is not sharp in general. The construction of score certificates for upset tournaments given in the proof of Theorem 2.2 makes little use of...

Ngày tải lên: 07/08/2014, 06:22

... one cycle, the minimum length of a cycle in G is called the girth of G, denoted g(G). On the other hand, if G contains no cycles, the girth of G is defined to be infinity. The number of arcs leaving ... the terminus of (u, v). Since the number of special arcs is less than the number of vertices with outdegree exactly 1 in any digraph, the following Corollary 1 a...

Ngày tải lên: 07/08/2014, 07:21

... exercise of linear algebra, the kernel of right-multiplication by N is generated by (1, 1, 1).  We may now complete the proof of Theorem 1. Proof: [Proof of case (N)] Now let (a 1 ,a 2 ,a 3 )beoftype(N). ... =  x s 23 3 x s 31 1 x s 12 2 x s 32 2 x s 13 3 x s 21 1  . Proof: The idea is to verify that the 2 × 2minorsofM are p 1 , p 2 ,andp 3 . Then, by the Hilbert-Burch Th...

Ngày tải lên: 07/08/2014, 08:20

... vertices and r +s−j edges. Number and orient the components of H  in order of their appearance in C 1 . The sizes of these components can be chosen in  p+j−1 p−1  ways (the number of ordered ... the sharpness of (3.2), consider the following conditions for all i, i  . When we speak of the distance between two edges, we mean the length of the shortest path...

Ngày tải lên: 07/08/2014, 08:20