Báo cáo toán học: "Maximum subsets of (0, 1] with no solutions to x + y = kz" pptx

... integer and y ∈  1, k 2  .Withy fixed, the function F y (m)=f(m, y) is an increasing linear function of m with root m (y) given by m (y) =k +3 − k(k − 1) − 2y y(k −2) . So the root m (y) ofF y (m) is ... value. Maximum subsets of (0, 1] with no solutions to x + y = kz FanR.K.Chung Department of Mathematics University of Pennsylvania Philadelph...

Ngày tải lên: 07/08/2014, 06:20

... polynomial T (G; x, y) , known as the Tutte polynomial of G, is defined as T (G; x, y) =  A⊆E (x − 1) r(E)−r(A) (y − 1) |A|−r(A) . (1) The Tutte polynomial of G has many interesting combinatorial interpretations ... T n (x, y) 1 + (x − 1)  n≥1 (y − 1) n T n (x, y) t n n! =   n≥0 y ( n 2 ) t n n!  (x 1) (y 1) (3) With these two general results it is ea...

Ngày tải lên: 07/08/2014, 15:22

... suppose D =( C+i)∪(C+j)andx, y ∈ C satisfy |x y| =diam(C). Let v = i−j =0 . Now | (x + i) − (y + j)| = | (x − y) +v| and | (x + j) − (y + i)| = | (x − y) − v| and one of these two norms is strictly greater ... set with A + C = B + C then A = B. Proof. Let A 0 = A \ B,letB 0 = B \ A,andsetR = A ∩ B.Nowforalli we have m...

Ngày tải lên: 07/08/2014, 06:20

... begin by defining f (x) =  4y, if 1 2y ∈ B and { 2y, 6y} ⊆ B, y, if 1 2y ∈ B and { 2y, 6y} ⊆ B. It remains to define f (x) when 1 2y ∈ B. Notice that then 2y ∈ B, since 9( 2y) = 3( 2y) + (1 2y) . If 2y ∈ ... homogeneous equations L 1 : x 1 + x 2 = 2x 3 , L 2 : x 1 + x 2 = x 3 + x 4 , L 3 : x 1 + x 2 = x 3 , where the corre...

Ngày tải lên: 07/08/2014, 15:23

... p + 1, , t − 1. Notice that S i + S j = {i + j, i + j + n/m, , i + j + 2qn/m} = i + j + n/m, (4) where the last equality follows because, from (3), 2qn/m ≥ n. Analogously, S i + ˜ S j = {i + ... H(kA). Then, h +kA = kA, which implies that h+(k +1 )A = (h +kA) + A = kA + A = (k + 1)A and the result follows...

Ngày tải lên: 07/08/2014, 21:21

... µ(H, x) , respectively. Then (a) µ(G ∪ H, x) = µ(G, x) µ(H , x) , (b) µ(G, x) = µ(G − e, x) −µ(G \ uv, x) where e = {u, v} is an edge of G, (c) µ(G, x) = x (G \u, x) −  v∼u µ(G \ uv, x) for any vertex ... mult( √ 3, G) = 2 and µ(P 7 , x) = x 7 − 6x 5 + 1 0x 3 − 4x. By Theorem 1.1, the maximum multiplicity of a root of µ(G, x) is 2. Also, G...

Ngày tải lên: 07/08/2014, 21:21

... respectively. Then (a) µ(G ∪ H, x) = µ(G, x) µ(H, x) , (b) µ(G, x) = µ(G − e, x) − µ(G \ uv, x) where e = {u, v} is an edge of G, (c) µ(G, x) = x (G \ u, x) −  v∼u µ(G \ uv, x) for any vertex u of G. Suppose ... well known that the maximum multiplicity of a root of the matching polynomial µ(G, x) is at most the minimum number of vertex disjoint paths need...

Ngày tải lên: 08/08/2014, 12:23

... determined by the power delay profile of the channel. Collecting the transmitted symbols into vectors x q = [x (0) q x (1) q x (N t −1) q ] T (q =0 ,1, ,N f − 1) with x (i) q denoting the data symbol ... have ⎡ ⎢ ⎢ ⎢ ⎣ y K 1 y K 2 . . . y K N c ⎤ ⎥ ⎥ ⎥ ⎦    y = ˜ H ˜ s 1 x 1 + ˜ H ˜ s 2 x 2 + + ˜ H ˜ s M x M + n =  ˆ H 1 ˆ H 2 ˆ...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:20