Báo cáo toán học: "Dense Packings of Equal Disks in an Equilateral Triangle: From 22 to 34 and Beyond" pptx

... published packings of equal disks in an equilateral triangle have dealt with up to 21 disks. We use a new discrete-event simulation algorithm to produce packings for up to 34 disks. For each n in the ... packings, the distance of the disk center to the boundary of this enclosing triangle is the distance to the line between bonds with the left side of the...

Ngày tải lên: 07/08/2014, 06:20

... 198–208. [GL1] R. L. Graham and B. D. Lubachevsky, Dense packings of equal disks in an equilateral triangle: from 22 to 34 and beyond, Electron. J. Combin. 2 (1995), #A1. [GL2] R. L. Graham and B. D. Lubachevsky, ... 32 1 5 1 20 1 25 1 50 1 25 1 10 1 2 1min 5min 3min 40 min 12 min 5min 1min Table 1: Frequency of obtaining f(P (n) ) with Algorithm 2 and averag...

Ngày tải lên: 07/08/2014, 08:20

... packing 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 Figure 2.8: The densest packings found of 60 and 61 disks and inferior packings of 62, 72, and 78 disks the electronic journal of combinat...

Ngày tải lên: 07/08/2014, 06:20

... journal of combinatorics (2000),#R46 5 are n ≤ 27, and these proofs involve substantial computation as the value of n increases, and the examination of an exponentially increasing number of cases. Before ... 0.130805E-01 Another example is the pair of disks 30 and 38 in the improved packing of 50 disks shown at the bottom left in Fig. 2.2. The distance between thes...

Ngày tải lên: 07/08/2014, 06:20

... 10 points and 4 pairs of alternative points. Three points are placed at (1, 1.74), (2, 1.74), and (1.6, 1), while one pair consists of the points A and B from above. The remaining points and pairs ... − 1 2 + 6 · √ 3 2 > 6.11, and are less than √ 2− 1 2 from the upper edge of S. Lemma 2 is applicable to the triangles, Lemma 4 to the rectangles, and Lemma 5 to th...

Ngày tải lên: 08/08/2014, 12:22

... [ICs], analog ICs, memory modules, and MEMS) and the embedded passive components (capacitors, resistors, and inductors) into a multilayer-integrated substrate and provides an improved miniaturization ... existence of α-Al 2 O 3 in the composite thick films and to examine the variations in crystallinity according to the changes in the mixing ratio. The crystallite...

Ngày tải lên: 20/06/2014, 20:20

... precursors 1 to 3. SMJ and SY carried out the laboratory experiments and analyzed the data. YK, and SJ analyzed the data and discussed the analysis. YK, and SJ designed the experiments. YK and SJ ... cooled to room temperature and the solutions were precipitated with an excess of methanol and 1-butanol and dried in air. Optical and structural characterizati...

Ngày tải lên: 20/06/2014, 20:20

... connecting (u, v )to( u, v +1)andto(u +1,v) (if this is in V,ofcourse). Further let A = {a 0 , a n−1 } and B = {b 0 , b n−1 } be two sets disjoint to each other and to V. Then we connect A and B to ... (1.4) Desainte–Catherine and Viennot [24] also gave a combinatorial interpretation of this de- terminant in terms of special disjoint lattice paths and applications to...

Ngày tải lên: 07/08/2014, 06:22

... on [n] and let X be the random variable counting the number of directed edges (u, v) in  G f such that u, v and the ancestors of v in  G f do not belong to any cycle in  G f , and in addition, v ... a single vertex then an induced F -matching is an independent set. The notion of F -ma t ching, which is sometimes called F -packing (and in the spanning case F -fa...

Ngày tải lên: 08/08/2014, 12:23

... as in Fig. 1. Total proteins including histones were also detected by Coomassie Brilliant Blue staining. Table 2. Quantitation and comparison of proteins in GM and WI-38 cells. From the data in ... proteins in SV40-transformed human fibroblast (GM00637) and WI-38 cells. Mcm2–7 proteins, ORC2 and PCNA were detected in total cellular proteins (A) and the chromatin-bound f...

Ngày tải lên: 20/02/2014, 23:20