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 SquareDavid W. Boll Jerry Donovan Ronald L. Graham Boris D. LubachevskyHewlett-Packard Hewlett-Packard University of California ... journal of combinatorics (2000),#R46 5are 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 ... not careful! A more practical, but, perhaps, less convincing variant of the above procedure starts asabove with the set of equations with respect to zi. Instead of eliminating all the variables,...

Báo cáo toán học: "Repeated Patterns of Dense Packings of Equal Disks in a Square." pptx

... 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 SquareR. L. Graham, rlg@research.att.comB. D. Lubachevsky, bdl@research.att.comAT&T Bell LaboratoriesMurray Hill, New Jersey 07974, USASubmitted: ... square. In a recent paper, Nurmela and¨Osterg˚ard [NO] present various conjectured optimal packings of n equal disks in a square forup to 50 disks. They also point out certain patterns that...

Báo cáo toán học: " Eﬃcient packing of unit squares in a square" ppt

... many of the packings displayed in [2] show, by rotating by half a right-angle certainsquares from the trivial method of packing squares, we may be able to pack one extrasquare, 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 integer and 0 ≤ δ<1, ... construction that it is possible to have a packing so eﬃcient that the wastedarea is O(n7/11) for large n. By way of contrast, the ‘trivial’ packing of unit squaresgives a wasted area of (n + δ)2−...

Báo cáo toán học: "On the number of independent sets in a tree" pdf

... 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 theHosoya index, or the Z-index in mathematical chemistry. For a rooted ... showsthat for all a, (a, k) ∈ B which, by Proposition 7, implies that (k, a) ∈ B. Repeating theargument by increasing k, we conclude that B = Z2m.the electronic journal of combinatorics ... (1, a) , (a, 1 ) ∈ D. Applying Proposition 4, we have that each of the followingis in D.(1, a) µ−1⇒ (a − 1, 1)·(1,−1)⇒ (a − 1, −1)µ⇒ (−1, a − 2)·(−1,1)⇒ (1, a − 2) (a, 1 )µ⇒ (1, a +...

Báo cáo toán học: "Packing 10 or 11 Unit Squares in a Square" ppt

... 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 thedirection 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 sincethree of them are in one box, there cannot be 11 nonintersecting boxes. This completesthe proof of ... electronic journal of combinatorics 10 (2003), #R8 9Packing 10 or 11 Unit Squares in a SquareWalter StromquistDepartment of MathematicsBryn Mawr College, Bryn Mawr, Pennsylvania, USAwalters@chesco.comSubmitted:...

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

... also obtained in which all disks are Dense Packings of Equal Disks in an EquilateralTriangle: From 22 to 34 and BeyondR. L. GrahamB. D. LubachevskyAT&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 4Small black dots in the packing diagrams are ... bounded away from zero. In other words, packings of ∆(k )disks are so tight that any attempt to accommodate even one additional disk noticeably worsensthe packing in that L(n) increases by at least...

Báo cáo toán học: "Dense Packings of Equal Spheres in a Cube" pps

... Dense packings of equal disks in anequilateral 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 leastone point on every face of C (in ... frequency of obtaining f(P(n))withtwelve digits of accuracy, running Stochastic Billiard and the necessary average timeto reach them.Let us ﬁnally precise that the association of a small sample of...

Báo cáo khoa học: "Improving Machine Translation of Null Subjects in Italian and Spanish" pot

... (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 spokenand written Italian. In Manuscript.Marta Recasens and M. Ant`onia Mart´ı. 2010.AnCora-CO: Coreferentially Annotated Corporafor Spanish and Catalan. Language ... 2012.c2012 Association for Computational LinguisticsImproving Machine Translation of Null Subjects in Italian and SpanishLorenza Russo, Sharid Lo´aiciga, Asheesh GulatiLanguage Technology Laboratory...

Báo cáo toán học: " On the boundedness of the solutions in nonlinear discrete Volterra difference equations" pot

... discreteVolterra diﬀerence equationsIstv´an Gy˝ori∗1and Essam Awwad1,21Department of Mathematics, Faculty of Information Technology, University of Pannonia, Hungary2Department of Mathematics, Faculty ... κ.Competing interestsThe authors declare that they have no competing interests.Authors’ contributionsThis was a joint work in every aspect. All the authors have read and approved the ﬁnal manuscript.AcknowledgmentsThe ... some applications of our main result for sub-linear, linear, and super-linearVolterra diﬀerence equations. We study the boundedness of solutions of convolution cases and we get a result parallel...

Báo cáo toán học: " Synthesis and characterization of CuO nanowires by a simple wet chemical method" pdf

... 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 ... (N2O, NO, and NO2). 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 oxides of copper ... Synthesis and characterization of CuO nanowires by a simple wet chemical method Anita Sagadevan Ethiraj1 and Dae Joon Kang*1 1BK21 Physics Research Division, Department of Energy Science, Institute...

Xem thêm