Báo cáo toán học: "Packing Unit Squares in a Rectangle" potx

... length of the minimum square that can contain N unit squares in the plane whose interiors do not overlap. The problem of packing unit squares into a square was initiated by Erd˝os and Graham [2]. They ... the minimum square into which N unit squares can be packed. This paper shows that, for given real numbers a, b ≥ 2, no more than ab − (a +1− a ) −(b +1−b) unit squares...

Ngày tải lên: 07/08/2014, 13:21

... q. a 1 a 2 a 1 a 2 a 1 a 2 a 3 a 1 a 2 a 4 a 3 a 1 a 1 a 2 a 4 a 2 a 1 a 3 a 3 a 1 a 3 a 5 a 2 a 1 a 1 a 3 a 5 a 2 a 4 a 3 a 3 a 5 a 2 a 5 a 2 a 4 (3) Define C(q)by C (a 1 ) = 011 000 111 001 C (a 2 ) = 011 100 011 001 C (a 3 ) ... Australia. Email: tsimpsonr@cc.curtin.edu.au Table 1. Possible pairs of q. a 1 a 2 a...

Ngày tải lên: 07/08/2014, 06:20

... done recently in [12] for bivariate functions whose coefficients are related to combinatorial random variables. The univariate case was treated in [41]. In order to achieve our goal we will stay as close as ... Asymptotic expansions for the coefficients of analytic generating functions. Aequationes Math., 28(1-2):50–63, 1985. [38] Alon Orlitsky, Narayana P. Santhanam, and Junan Zhang. Alway...

Ngày tải lên: 07/08/2014, 13:21

... backtracking in H is equivalent to not backtracking on the corresponding path in B H . Once we know that backtracking isn’t an issue, having no tails also follows immediately since backtracking in ˜c 2 would ... actually be applied to graphs. One impediment to the Ihara-Selberg zeta function being truly useful as a graph invariant is that two k-regular graphs are cospectral—their adja...

Ngày tải lên: 07/08/2014, 13:21

... selecting an extreme node in each path of P we obtain in X(G) − W an independent set of nodes of cardinality at least εk. Since X(G) − W and ¯ G are isomorphic, this means that ¯ G has an independent ... problems and incompatible inapproximabilities. In Proc. 21st ACM-SIAM Symp. Discrete Algorithms, SODA ’10, pages 1258–1266, Philadelphia, PA, USA, 2010. Society for Industrial and Appli...

Ngày tải lên: 08/08/2014, 14:22

... Combinatorics 9 (2002), #R14. 4. Walter Stromquist, “Packing unit squares inside squares, I (six unit squares) ,” Daniel H. Wagner, Associates Memorandum, September 11, 1984 5. ——, “Packing unit squares ... “Packing unit squares inside squares, II (ten unit squares) ,” DHWA Memo- randum, October 15, 1984. 6. ——, “Packing unit squares inside squares, III (Cases with n...

Ngày tải lên: 07/08/2014, 07:21

... Suppose that a is an integer in the range x ≤ a ≤ y, and define b to be the smallest integer ≥ xy /a so that xy /a ≤ b<xy /a+ 1,and xy ≤ ab < xy + a. Therefore (a +1)b = ab +b<(xy + a) +(xy /a +1) ... + 1 in this range for a. Ifxy is an integer then ab ≤ xy + a −1, so that (a +1)b<xy+ a + xy /a ≤ xy + x + y. Thus both ab and (a +1)b are in J and therefore...

Ngày tải lên: 07/08/2014, 06:22

... William Staton considered this problem again. Because packing and covering are usually dual to each other, we discussed a problem of a minimal square-covering in [5]. In this paper, we generalize ... Erd˝os’ favorite problems. Keywords: packing, minimal covering Mathematics Subject Classification (2000): 52C15 1 Introduction Packing and covering are elementary but very important in c...

Ngày tải lên: 07/08/2014, 13:21

... GN6ASL in the ITS station architec- ture. Figure 2: IPv6 packet forwarding within an area, and a ected protocol layers. Figure 3: Geographical area partitioning and IPv6 virtual link abstraction. Figure ... vehicles distributed in a one-dimensional road, traveling at a pre-defined and constant speed, with an exponen- tial inter-vehicular distance and a maximum wireless radio coverag...

Ngày tải lên: 20/06/2014, 20:20

... Balk L, Vuorinen PJ, Karvinen H, Lang T: Biological indications of contaminant exposure in Atlantic cod (Gadus morhua) in the Baltic Sea. Can J Fish Aquat Sci 2008, 65: 1122-1134 21. Kammann ... Kategorie „rot“ in Abb.3 fallen. In Abb. 4 sind Monitoringdaten zu PAK-Metaboliten nach ihrer Kategorisierung anhand des BAC als prozen- tuale Anteile dargestellt. Der EAC für andere mari...

Ngày tải lên: 20/06/2014, 20:20