Báo cáo toán học: "On Coloring the Odd-Distance Graph" pdf

... θ increases from 0 to π 2 . Also, the signs of these integrals alternate, so we can either throw out all of them or all but the first one, depending on whether the integral of h across R ⌊ r π ⌋ is positive ... establishes that the measurable chro matic number of the odd-distance graph is infinite. 4 Conclus i on and Open Problems The largest remaining question is whether or not...

Ngày tải lên: 07/08/2014, 21:21

... are indistinguishable to the naked eye. To tell them apart, he attaches a colored marker on each key. What is the fewest number of colored markers needed so he can distinguish the keys from each other? The answer ... [2] to generalize the original problem to arbitrary graphs. The vertices of a graph represented the keys and its edges indicate how the keys are connected to each...

Ngày tải lên: 07/08/2014, 13:21

... will prove the results stated in the previous section. Proof of Theorem 2.1 Upper Bound. The upper bound of Theorem 2.1 is obtained by setting r =3in the upper bound of Theorem 2.3. Therefore ... r  n 2  . Therefore we obtain the electronic journal of combinatorics 10 (2003), #R25 9 the equation 2x 1 −3x 2 + x 4 =0. ThenS consists of the set {1, 2, 4}. The trivial solutions...

Ngày tải lên: 07/08/2014, 07:21

... 1}, then Q(R) as defined in Section 2 is the Cayley table of the group Q × R represented on {0, 1, . . . , mn − 1}. Thus, if Q is taken as the Cayley table of C 2 , then the square Q(Q) gives the ... either contained in precisely one triple or one group, but not both. The vertices of the embedded graph K n,n,n form the points of each design, the tripartition determines the...

Ngày tải lên: 08/08/2014, 01:20

... mentioned, the upper bound follows immediately by combining Theorem 5 with the upper bound on δ(c) stated in Theorem 7, using the non-negativity of the o(1) term in Theorem 5. The proof of the lower ... P 8 in color 2. The precise strategy definition is given below in the proof of Proposition 12. The recursion defined in the following evaluates the performance of the str...

Ngày tải lên: 08/08/2014, 14:23

... expressions for the PDF, CDF, LCR, and ADF of the channel capacity. The mean channel capacity (or the ergodic capacity) can be obtained from the PDF of the channel capacity [27], while the CDF of the channel ... that increasing the relay gains increases the received SNR at the DMS, however the received SNR at the DMS is always less than or equal to the SNR at t...

Ngày tải lên: 20/06/2014, 20:20

... section is to establish the following result with the proof. Theorem 3.1. Let (A) and (B) be satisfied and assume that the initial vector x 0 belongs to the set S. Then the solution x(n; x 0 ), ... for the boundedness of the solution of (1.1) under the initial condition (1.2), but in the linear case of Volterra difference equation. The following result gives a sufficient condi...

Ngày tải lên: 20/06/2014, 20:20

... in the upper panels on the left showing the in-phase/quadrature (I/ Q) time domain traces. On the other hand, the DoL cir- cuit (the right-hand panels) improves the signal-to-noise ratio in the ... comparing the black lines in the upper panels of the figure, for the RC and the DoL circuits, one can see how the DoL circuit removes the impulsive noise by “trimming”...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 09:46