Báo cáo toán học: "On the function “sandwiched” between α(G) and χ(G) V Y" ppt

... u ∈ S then v  −− v  . Indeed, if  w∈S X wv  X wv  > 0 then Y v  v  > 0. Let V u = {u}∪ {v| v∈S,X uv > 0} for all u ∈ S and G (V u ) be the subgraph induced from G by leaving out ... G. (i) If v ∈ S then exists u ∈ S such that u −− v. Indeed, Y vv = 1 and X wv ≥ 0 for all w ∈ S. Hence,  w∈S X 2 wv = 1 and X uv > 0 for some u ∈ S. (ii) If v  ,v...

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... ×  a∈A U a ) ⊂ B R (0). 3. Proof of the Theorems In this section we prove the theorems; the proof is divided into 2 parts. Let f, f n be rational functions. We have the following lemma; see [1]. Lemma ... Y c l+1 ). From the Appendix 2 of [2], we have that z(c)=j c (c 0 ) is the dynamical continuation of the critical value c 0 and z  (c 0 ) = 1. The function z is de- fin...

Ngày tải lên: 06/08/2014, 05:20

... Fujimoto in [8]. When P is injective on the ro ots of its derivative P  , necessary and sufficient conditions were given in [5]. Recently, Khoai and Yang generalized the above studies by considering a ... polygons as the main tools, they gave some sufficient conditions on the degrees of P and Q for the problem (see [1]). After that, by using value distribution theory, in [2], Yan...

Ngày tải lên: 06/08/2014, 05:20

... B and v ∈ A let d B (v) denote the number of G-neighbours of v in B. The Minc conjecture then states that m(H) ≤  v A (d B (v) )! 1/d B (v) . Thus m(G) ≤ 1 2 ν  A,B  v A (d B (v) )! 1/d B (v) . ... chosen randomly from Ω and write k f =  v V 1 |K v | where K v is the weak component containing v. We will argue that Pr(|K v |≤k) ≤ k 2 (d − )n k ≥ 1. (21) Gi...

Ngày tải lên: 07/08/2014, 06:22

... < v p (k)sincev p (l) =v p (k) − min {v p (m) ,v p (k)}. This implies that v p (gcd(k, m)) = v p (m) =v p (δ). On the other hand, if the prime p does not divide gcd(l, m), then v p (δ)=0≤ v p (gcd(k, m)) and the proof is complete. Examples. ... that v p (δ)=  0ifp divides gcd(l, m) v p (m)ifp does not divide gcd(l, m). Suppose that p is a prime divisor of gcd(l,...

Ngày tải lên: 07/08/2014, 06:23

... θ d /θ u covers. Since the assignment t → ut gives a one to one correspondence between divisors of (d/u, n/u) and divisors of (d, n) which are divisible by u, the sum (3) is equal to (2), and we ... p)=1,τ the automorphism of order k which cyclically permutes the coordinate positions of V ,andG the group generated by V and τ (their semi-direct product, since τ normalize...

Ngày tải lên: 07/08/2014, 06:23

... most n. This is true for the first term N((λ 1 , ,λ n−1 )) by the inductive hypothesis. Each of the subsequent terms is itself a sum. By the inductive hypothesis, each summand in each term is a polynomial ... R(x)bethem × n matrix such that R ij =1if1≤ j ≤ x i and R ij = 0 otherwise. Then R lies in M and has row sums equal to x.Thisproves: Lemma 5 Let x =(x 1 , ,x m ) ∈ N m . Then...

Ngày tải lên: 07/08/2014, 13:21

... Figure 1: Density functions of sequences A, B and C. Figure 1 describes the behavior of the density function for the sequences A, B and C on one block for k = 1000 and a large value of m. More ... l)| l 2 , and s(k) = sup C s C (k). The following statement shows the equivalence between path Tur´an numbers and the numbers s(k) for a fixed k. Lemma 1.5 Let k ≥ 2. Then,...

Ngày tải lên: 07/08/2014, 15:23