Báo cáo toán học: " Packing and covering a unit equilateral triangle with equilateral triangles" pot

... 3: a unit equilateral triangle covered by 3 smaller equilateral triangles Proposition 3.4. T 1 (5) < 9 4 . Proof. Consider a covering of a unit equilateral triangle T with one equilateral triangle ... they have great practical and theoretical significance. In this paper, we discuss a problem on packing and covering a unit equilateral triangle w...

Ngày tải lên: 07/08/2014, 13:21

... 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 either axis is at most ... quadrilateral with vertices (0, 0), (0, 1), (a, 0), and (a, b) must intersect the x-axis, the point (0, 1),orthepoint (a, b). The proofs are easier than in the general case and are...

Ngày tải lên: 07/08/2014, 07:21

... G, and otherwise, A is called aperiodic.WesaythatA is maximally H-periodic, if A is H-periodic, and H is the maximal subgroup for which A is periodic; in this case, H = {x ∈ G | x + A = A} ,andH is ... m.Suppose that n  ≥ m p − 1, that |S|≥m + m p + p − 3, and that P has at least n − n  cardinality one sets. Then either: (i) there exists an n-set partition A = A 1 ,A 2...

Ngày tải lên: 07/08/2014, 13:21

... amalgamates all numbers ≤ i, and all numbers > i. In particular, each A i] P is a Grassmannian puzzle . We will nee d to study a d eflation (of the single label 1) and an ambiguation together: A 1] × ... fourth says that e ach inequality de fining BDRY(n) (other than the chamber inequal- ities that say λ, µ, ν are decreasing) can be “blamed” on a Grassmannian puzzle. In [KnTaoW...

Ngày tải lên: 08/08/2014, 14:23

... −1)! Standard and Semistandard Tableaux. Let λ  n (i.e. λ is a partition of n). A tableau of shape λ, filled with 1, ···,n, is standard if the numbers in it are increasing both in rows and in ... of standard and semi-standard Young tableaux. When n →∞, the asymptotics of the number of such words is calculated. ∗ Work partially supported by N.S.F. Grant No. DMS-94-01197. Typeset by...

Ngày tải lên: 07/08/2014, 06:22

... related process, the random planar graph process (where at each step an edge is inserted if the graph remains planar) behaves differently. Gerke, Schlatter, Steger and Taraz [6] showed that a. a.s. ... binatorics and Computer Science , “Random Graphs ’93” (Pozna´n, 1993), volume 6, pages 309–318, 1995. [6] Stefanie Gerke, Dirk Schlatter, Angelika Steger, and Anusch Taraz. The random pla...

Ngày tải lên: 08/08/2014, 14:23

... on a nonlinear elastic foundation under localized external loads. Although their method app ears powerful as a mathematical procedure for beam deflections on nonlinear elastic foundation, in practice, ... beams which rest on an elastic foundation has received increased attention in a wide range of fields of engineering, because of its practical design applications, say, to highways and...

Ngày tải lên: 20/06/2014, 20:20

... Catalytic activity of dispersed CuO phases towards nitrogen oxides (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 ... be made available soon. Synthesis and characterization of CuO nanowires by a simple wet chemical method Nanoscale Research Letters 2012, 7:70 doi:10.1186/1556-276X-7-70 Anita SAGADEVA...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:21