共查询到20条相似文献,搜索用时 10 毫秒
1.
Edith Adan-Bante 《Israel Journal of Mathematics》2008,168(1):93-100
Let G be a supersolvable group and A be a conjugacy class of G. Observe that for some integer η(AA
−1) > 0, AA
−1 = {ab
−1: a, b ∈ A} is the union of η(AA
−1) distinct conjugacy classes of G. Set C
G
(A) = {g ∈ G: a
g
= a for all a ∈ A. Then the derived length of G/C
G
(A) is less or equal than 2η(AA
−1) − 1. 相似文献
2.
Hong Lin Xiao-feng Guo 《应用数学学报(英文版)》2007,23(1):155-160
Let φ(G),κ(G),α(G),χ(G),cl(G),diam(G)denote the number of perfect matchings,connectivity,independence number,chromatic number,clique number and diameter of a graph G,respectively.In this note,by constructing some extremal graphs,the following extremal problems are solved:1.max{φ(G):|V(G)|=2n,κ(G)≤k}=k[(2n-3)!!],2.max{φ(G):|V(G)|=2n,α(G)≥k}=[multiply from i=0 to k-1(2n-k-i)[(2n-2k-1)!!],3.max{φ(G):|V(G)|=2n,χ(G)≤k}=φ(T_(k,2n))T_(k,2n)is the Turán graph,that is a complete k-partite graphon 2n vertices in which all parts are as equal in size as possible,4.max{φ(G):|V(G)|=2n,cl(G)=2}=n1,5.max{φ(G):|V(G)|=2n,diam(G)≥2}=(2n-2)(2n-3)[(2n-5)!!],max{φ(G):|V(G)|=2n,diam(G)≥3}=(n-1)~2[(2n-5)!!]. 相似文献
3.
Edward A. Bertram 《Israel Journal of Mathematics》1984,47(4):335-344
In 1955 R. Brauer and K. A. Fowler showed that ifG is a group of even order >2, and the order |Z(G)| of the center ofG is odd, then there exists a strongly real) elementx∈G−Z whose centralizer satisfies|C
G(x)|>|G|1/3. In Theorem 1 we show that every non-abeliansolvable groupG contains an elementx∈G−Z such that|C
G(x)|>[G:G′∩Z]1/2 (and thus|C
G(x)|>|G|1/3). We also note that if non-abelianG is either metabelian, nilpotent or (more generally) supersolvable, or anA-group, or any Frobenius group, then|C
G(x)|>|G|1/2 for somex∈G−Z. In Theorem 2 we prove that every non-abelian groupG of orderp
mqn (p, q primes) contains a proper centralizer of order >|G|1/2. Finally, in Theorem 3 we show that theaverage
|C(x)|, x∈G, is ≧c|G|
1/3 for metabelian groups, wherec is constant and the exponent 1/3 is best possible. 相似文献
4.
Lou Yuanren 《分析论及其应用》1990,6(1):46-64
Let f∈Ap. For any positive integer l, the quantity Δ1,n−1(f:z) has been studied extensively. Here we give some quantitative estimates for
and investigate some pointwise estimates of Δ
l,n−1
(r)
(f;z).
Supported by National Science Foundation of China 相似文献
5.
Xiao Yun CHENG Jian Guo XIA Hou Rong QIN 《数学学报(英文版)》2007,23(5):819-826
Let K2 be the Milnor functor and let Фn (x)∈ Q[X] be the n-th cyclotomic polynomial. Let Gn(Q) denote a subset consisting of elements of the form {a, Фn(a)}, where a ∈ Q^* and {, } denotes the Steinberg symbol in K2Q. J. Browkin proved that Gn(Q) is a subgroup of K2Q if n = 1,2, 3, 4 or 6 and conjectured that Gn(Q) is not a group for any other values of n. This conjecture was confirmed for n =2^T 3S or n = p^r, where p ≥ 5 is a prime number such that h(Q(ζp)) is not divisible by p. In this paper we confirm the conjecture for some n, where n is not of the above forms, more precisely, for n = 15, 21,33, 35, 60 or 105. 相似文献
6.
The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and of all edges having an end-vertex in common with e. Let f be a function on E(G), the edge set of G, into the set {−1, 1}. If
for each e ∈ E(G), then f is called a signed edge dominating function of G. The signed edge domination number γs′(G) of G is defined as
. Recently, Xu proved that γs′(G) ≥ |V(G)| − |E(G)| for all graphs G without isolated vertices. In this paper we first characterize all simple connected graphs G for which γs′(G) = |V(G)| − |E(G)|. This answers Problem 4.2 of [4]. Then we classify all simple connected graphs G with precisely k cycles and γs′(G) = 1 − k, 2 − k.
A. Khodkar: Research supported by a Faculty Research Grant, University of West Georgia.
Send offprint requests to: Abdollah Khodkar. 相似文献
7.
Let Ω be a bounded co.nvex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△ on Ω. Let hrp(Ω) = {f ∈ D'(Ω) :(E)F∈hp(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f→(△)2(Gf) for every f ∈ hrp(Ω) is obtained, where n/(n 1)<p≤1. 相似文献
8.
Mark L. Agranovsky 《Journal d'Analyse Mathématique》2011,113(1):305-329
Let C
t
= {z ∈ ℂ: |z − c(t)| = r(t), t ∈ (0, 1)} be a C
1-family of circles in the plane such that lim
t→0+
C
t
= {a}, lim
t→1−
C
t
= {b}, a ≠ b, and |c′(t)|2 + |r′(t)|2 ≠ 0. The discriminant set S of the family is defined as the closure of the set {c(t) + r(t)w(t), t ∈ [0, 1]}, where w = w(t) is the root of the quadratic equation ̅c′(t)w
2 + 2r′(t)w + c′(t) = 0 with |w| < 1, if such a root exists. 相似文献
9.
LetG be a finite group, andS a subset ofG \ |1| withS =S
−1. We useX = Cay(G,S) to denote the Cayley graph ofG with respect toS. We callS a Cl-subset ofG, if for any isomorphism Cay(G,S) ≈ Cay(G,T) there is an α∈ Aut(G) such thatS
α =T. Assume that m is a positive integer.G is called anm-Cl-group if every subsetS ofG withS =S
−1 and | S | ≤m is Cl. In this paper we prove that the alternating groupA
5 is a 4-Cl-group, which was a conjecture posed by Li and Praeger. 相似文献
10.
We assign to each pair of positive integers n and k ⩾ 2 a digraph G(n, k) whose set of vertices is H = {0, 1, ..., n − 1} and for which there is a directed edge from a ∈ H to b ∈ H if a
k
≡ b (mod n). We investigate the structure of G(n, k). In particular, upper bounds are given for the longest cycle in G(n, k). We find subdigraphs of G(n, k), called fundamental constituents of G(n, k), for which all trees attached to cycle vertices are isomorphic. 相似文献
11.
We study equidistribution properties of nil-orbits (b
n
x)
n∈ℕ when the parameter n is restricted to the range of some sparse sequence that is not necessarily polynomial. For example, we show that if X = G/Γ is a nilmanifold, b ∈ G is an ergodic nilrotation, and c ∈ ℝ \ ℤ is positive, then the sequence $
(b^{[n^c ]} x)_{n \in \mathbb{N}}
$
(b^{[n^c ]} x)_{n \in \mathbb{N}}
is equidistributed in X for every x ∈ X. This is also the case when n
c
is replaced with a(n), where a(t) is a function that belongs to some Hardy field, has polynomial growth, and stays logarithmically away from polynomials,
and when it is replaced with a random sequence of integers with sub-exponential growth. Similar results have been established
by Boshernitzan when X is the circle. 相似文献
12.
In 1990 G. T. Chen proved that if G is a 2-connected graph of order n and 2|N(x) ∪ N(y)| + d(x) + d(y) ≥ 2n − 1 for each pair of nonadjacent vertices x, y ∈ V (G), then G is Hamiltonian. In this paper we prove that if G is a 2-connected graph of order n and 2|N(x) ∪ N(y)| + d(x)+d(y) ≥ 2n−1 for each pair of nonadjacent vertices x, y ∈ V (G) such that d(x, y) = 2, then G is Hamiltonian. 相似文献
13.
Let Δ3 be the set of functions three times continuously differentiable on [−1, 1] and such that f″′(x) ≥ 0, x ∈ [−1, 1]. We prove that, for any n ∈ ℕ and r ≥ 5, there exists a function f ∈ C
r
[−1, 1] ⋂ Δ3 [−1, 1] such that ∥f
(r)∥
C[−1, 1] ≤ 1 and, for an arbitrary algebraic polynomial P ∈ Δ3 [−1, 1], there exists x such that
| f(x) - P(x) | 3 C?n \uprhonr(x), \left| {f(x) - P(x)} \right| \geq C\sqrt n {{\uprho}}_n^r(x), 相似文献
14.
A. V. Harutyunyan W. Lusky 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(3):128-135
Let U
n
be the unit polydisk in C
n
and S be the space of functions of regular variation. Let 1 ≤ p < ∞, ω = (ω
1, ..., ω
n
), ω
j
∈ S(1 ≤ j ≤ n) and f ∈ H(U
n
). The function f is said to be in holomorphic Besov space B
p
(ω) if
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