Báo cáo toán học: "lattice tilings by cubes: whole, notched and extended" potx

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Ngày tải lên: 20/06/2014, 21:20

... be made available soon. An endogenous factor enhances ferulic acid decarboxylation catalyzed by phenolic acid decarboxylase from Candida guilliermondii AMB Express 2012, 2:4 doi:10.1186/2191-0855-2-4 Hui-Kai ... and oat (Mathew and Abraham 2004). Bacterial phenolic acid decarboxylases (PADs), which decarboxylate FA, p-coumaric acid (PCA), and/or caffeic acid (CA) wi...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 15:20

... (16) where dω m and dω k denote the Lebesgue measures on S m−1 in R m and S k−1 in R k , respectively. From (14) and (15), we have Polar Coordinates on H-type Groups and Applications 309 Let d(x, ... polar coordinates on H-type groups. In [1], the polar coordinates were given in Carnot groups and groups of H-type, but the expression here is slightly different...

Ngày tải lên: 06/08/2014, 05:20

... 3). We use the fact that there is a bijection between rhombus tilings of the hexagon and perfect matchings of the hexagon s ‘dual’ graph G (see Figure 2 for the construction of the dual graph and Figure ... are missing. In particular, Problem 4 of [8] asks for a formula for the number of rhombus tilings of a regular hexagon, where two of the six ce...

Ngày tải lên: 07/08/2014, 06:20

... parity-reversing. It follows that in the signed sum of walks in W all terms corresponding to walks in N cancel, leaving only the walks that correspond to permutations of {1, 2, ,n/2} with no ascending ... correspondence with lattice walks. Interestingly, however, by providing a combinatorial proof of this correspondence, in section 3 below, we will be giving an indepe...

Ngày tải lên: 07/08/2014, 06:22

... obtain  1 N (ξ)= d  j=1 sin πξ j πξ j − F(ξ) d  j=1 sin πδ j ξ j πξ j , (11) lattice tilings by cubes: whole, notched and extended Mihail Kolountzakis Department of Mathematics 1409 W. Green St., University ... (11)). We find all the tilings discovered by Stein, which, by a deeper theorem of Schmerl [Sch], is the complete list of possible translational tilings (lattice...

Ngày tải lên: 07/08/2014, 06:22

... lattice paths, d[m, n]=d[m−1,n]+d[m, n − 1] + γd[m − 1,n−1]. The paths take horizontal, vertical, and diagonal steps (a king). If we write = à − 1, then this recurrence enumerates lattice paths ... Brownian motion between parallel reflecting walls, a continuous version equivalent to the asymptotic distribution of the Kolmogorov-Smirnov test. The exact number of ordinary paths betwe...

Ngày tải lên: 07/08/2014, 06:22

... and that there is a natural bijection between these permutations and lattice paths from (0, 0) to (j, j) using steps (0, 1) and (1, 0) which never go above the main diagonal. Also, let C(x)=  n≥0 c n x n = 1− √ 1−4x 2x . ... diagonal (say it stays below). Suppose it touches the diagonal first at the point (i, i). If there is an entry of rank more than 1 inserted between the ith an...

Ngày tải lên: 07/08/2014, 06:22

... (10) Sylvester treated the Euclidean division by a different method, using summations on subsets of roots (cf. [LP]). We shall for our part interpret now the Euclidean division as producing a sequence ... )=det  S λ i +j−i ( − )  1≤i,j≤ . Then Theorem 1 The k-th remainder in the Euclidean division of σ z ( ) by 1 is f k (z)=S (k+1) k ( ) −1 ∞  i=0 z i S k+1+i,(k+1) k−1 ( ) . (6)...

Ngày tải lên: 07/08/2014, 06:22

... of cliques from an irreducible covering by cliques of the complementary graph G. 2 Main result We will evaluate the clique number ω(G)whenG of order n has an irreducible covering by n − k cliques. Theorem ... irreducible coverings by cliques of complete multi- partite graphs, J. of Combinatorial Theory, Series B, 2, 28(1980), 127-141. [9] I. Tomescu, On the number of irreducib...

Ngày tải lên: 07/08/2014, 06:23

... 33111 322 24 → 331 322 2411 → 331 324 221 1 → 3431 322 211 → 3431 322 211 ∈ [4] 10 (1 12) . (7) the electronic journal of combinatorics 9 (2) (20 02) , #R3 15 Corollary 16 For any p ≥ 0 F v p,0 (x; 2) = e x p  j=0 x j j! . Proof. ... 121 }, {1 12, 121 }, {1 12, 122 }, {1 12, 21 1}, {1 12, 21 2}, {1 12, 22 1}, { 121 , 21 2}. Theorem 5 The pairs {111, 1 12} and {111, 121 } are Wilf e...

Ngày tải lên: 07/08/2014, 07:21

... our construction for the proof of Theorem 2 the tile X has constant cardinality 15. 2. There is nothing magical about the choice of the primes 2, 3 and 5 in the proof of Theorem 2. Any three ... y z Q 3p 5q 2 A x Figure 1: The group Z 3p ì Z 5q ì Z 2 and (0, 0, 1). Then, in the bottom level of the tiling shift one of the columns along the x direction, say the s...

Ngày tải lên: 07/08/2014, 07:21

... the lattice structure comes from orientations of the completion. 2 Lattices of Fixed Degree Orientations A plane graph is a planar graph G =(V, E) together with a fixed planar embedding. In particular ... there may exist rigid the electronic journal of combinatorics 11 (2004), #R15 15 Lattice Structures from Planar Graphs Stefan Felsner Technische Universităat Berlin, Institut fău...

Ngày tải lên: 07/08/2014, 08:20