Báo cáo toán học: "Improving Dense Packings of Equal Disks in a Square" ppsx

... packing disks in squares. Improving Dense Packings of Equal Disks in a Square David W. Boll Jerry Donovan Ronald L. Graham Boris D. Lubachevsky Hewlett-Packard Hewlett-Packard University of California ... 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 exponenti...

Ngày tải lên: 07/08/2014, 06:20

... of repeating “patterns” of dense (and presumably optimal) packings of n equal non-overlapping disks in- side an equilateral triangle (see Fig. 1.1 for and example). It is natural to investigate ... disks RepeatedPatternsofDensePackings of Equal Disks in a Square R. L. Graham, rlg@research.att.com B. D. Lubachevsky, bdl@research.att.com AT&T Bell Laboratories Mu...

Ngày tải lên: 07/08/2014, 06:20

... many of the packings displayed in [2] show, by rotating by half a right-angle certain squares from the trivial method of packing squares, we may be able to pack one extra square, or even many ... unit squares in a square by demon- strating that non-trivial packings can result in a wasted area that is surprisingly small. For a square with side length n + δ,wheren is an in...

Ngày tải lên: 07/08/2014, 06:23

... The number of matchings in a tree In t his section, we turn to the number of matchings in a graph. This is a lso known as the Hosoya index, or the Z-index in mathematical chemistry. For a rooted ... shows that for all a, (a, k) ∈ B which, by Proposition 7, implies that (k, a) ∈ B. Repeating the argument by increasing k, we conclude that B = Z 2 m . the electronic journal...

Ngày tải lên: 08/08/2014, 11:20

... stronger forms of some of our lemmas. In particular: Lemma 7 Let T be a triangle, and suppose that the component of any side of T in the direction of any unit vector making an angle of 0 ◦ or 45 ◦ with ... 1.7). Again these 12 points form an unavoidable set in the context of 45 ◦ packings, and since three of them are in one box, there cannot be 11 nonintersecting bo...

Ngày tải lên: 07/08/2014, 07:21

... also obtained in which all disks are Dense Packings of Equal Disks in an Equilateral Triangle: From 22 to 34 and Beyond R. L. Graham B. D. Lubachevsky AT&T Bell Laboratories, Murray Hill, ... best packings of 58 disks (t5 8a) , 95 disks (t9 5a) , 108 disks (t10 8a) , and 175 disks (t17 5a) . the electronic journal of combinatorics 2 (1995), #A1 4 Small black...

Ngày tải lên: 07/08/2014, 06:20

... 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, Repeated patterns of dense packings ... of packing n congruent spheres in a unit cube C was raised apparently in 1966 in [S1]. It is shown in that paper that any optimal configuration contains at least...

Ngày tải lên: 07/08/2014, 08:20

... (LREC), Valletta, Malta. European Language Resources Association (ELRA). Fatiha Sadat and Nizar Habash. 2006. Combination of Arabic Preprocessing Schemes for Statistical Ma- chine Translation. In Proceedings ... corpus of anaphora and deixis in spoken and written Italian. In Manuscript. Marta Recasens and M. Ant ` onia Mart ´ ı. 2010. AnCora-CO: Coreferentially Annotated Corpora for...

Ngày tải lên: 24/03/2014, 03:20

... discrete Volterra difference equations Istv´an Gy˝ori ∗1 and Essam Awwad 1,2 1 Department of Mathematics, Faculty of Information Technology, University of Pannonia, Hungary 2 Department of Mathematics, Faculty ... κ. Competing interests The authors declare that they have no competing interests. Authors’ contributions This was a joint work in every aspect. All the authors have read...

Ngày tải lên: 20/06/2014, 20:20

... as nanowires and nanorods has gained much attention because this constitutes an important building block of nanodevices and integrated nanosystems [1-5]. Among the available transition metal ... (N 2 O, NO, and NO 2 ). Appl Catal B 2006, 62:336-344. 12. Ghosh S, Avasthi DK, Shah P, Ganesan V, Gupta A, Sarangi D, Bhattacharya R, Assmann W: Deposition of thin films of different oxide...

Ngày tải lên: 20/06/2014, 21:20