首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 10 毫秒
1.
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, bA} is the union of η(AA −1) distinct conjugacy classes of G. Set C G (A) = {gG: a g = a for all aA. Then the derived length of G/C G (A) is less or equal than 2η(AA −1) − 1.  相似文献   

2.
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.
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.
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.
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 eE(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.
Let C t = {z ∈ ℂ: |zc(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}, ab, 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 aH to bH 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, bG 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 xX. 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, yV (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, yV (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 fC 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.
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 ≤ jn) and fH(U n ). The function f is said to be in holomorphic Besov space B p (ω) if
$ \left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}} {{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty } $ \left\| f \right\|_{B_p (\omega )}^p = \int_{U^n } {\left| {Df(z)} \right|^p \prod\limits_{j = 1}^n {\frac{{\omega _j (1 - |z_j |)}} {{(1 - |z_j |^{2 - p} )}}} dm_{2n} (z) < + \infty }   相似文献   

15.
In the paper, the equation
is considered in the scale of the weighted spaces H β s (ℝ n ) (q > 1, a ∈ ℂ). We prove that if the expression
does not vanish on the set {ξ ∈ ℝ n ∖ 0, |z| ≤ q βs+n /2−2m}, then this equation has a unique solution uH β s+2m (ℝ n ) for every function fH β s (ℝ n ) provided that β, s ≠ ∈ ℝ, βsn/2 + p, and βs − 2m ≠ − n/2 − p (p = 0, 1, ...). __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 37–55, 2007.  相似文献   

16.
An extension of a classical theorem of Rellich to the exterior of a closed proper convex cone is proved: Let Γ be a closed convex proper cone inR n and −Γ′ be the antipodes of the dual cone of Γ. Let be a partial differential operator with constant coefficients inR n, whereQ(ζ)≠0 onR niΓ′ andP i is an irreducible polynomial with real coefficients. Assume that the closure of each connected component of the set {ζ∈R niΓ′;P j(ζ)=0, gradP j(ζ)≠0} contains some real point on which gradP j≠0 and gradP j∉Γ∪(−Γ). LetC be an open cone inR n−Γ containing both normal directions at some such point, and intersecting each normal plane of every manifold contained in {ξ∈R n;P(ξ)=0}. Ifu∈ℒ′∩L loc 2 (R n−Γ) and the support ofP(−i∂/∂x)u is contained in Γ, then the condition implies that the support ofu is contained in Γ.  相似文献   

17.
A lower bound on the total signed domination numbers of graphs   总被引:4,自引:0,他引:4  
Let G be a finite connected simple graph with a vertex set V(G)and an edge set E(G). A total signed domination function of G is a function f:V(G)∪E(G)→{-1,1}.The weight of f is W(f)=∑_(x∈V)(G)∪E(G))f(X).For an element x∈V(G)∪E(G),we define f[x]=∑_(y∈NT[x])f(y).A total signed domination function of G is a function f:V(G)∪E(G)→{-1,1} such that f[x]≥1 for all x∈V(G)∪E(G).The total signed domination numberγ_s~*(G)of G is the minimum weight of a total signed domination function on G. In this paper,we obtain some lower bounds for the total signed domination number of a graph G and compute the exact values ofγ_s~*(G)when G is C_n and P_n.  相似文献   

18.
In this paper, we show the equivalence of somequasi-random properties for sparse graphs, that is, graphsG with edge densityp=|E(G)|/( 2 n )=o(1), whereo(1)→0 asn=|V(G)|→∞. Our main result (Theorem 16) is the following embedding result. For a graphJ, writeN J(x) for the neighborhood of the vertexx inJ, and letδ(J) andΔ(J) be the minimum and the maximum degree inJ. LetH be atriangle-free graph and setd H=max{δ(J):JH}. Moreover, putD H=min{2d H,Δ(H)}. LetC>1 be a fixed constant and supposep=p(n)≫n −1 D H. We show that ifG is such that
(i)  deg G (x)≤C pn for allxV(G),
(ii)  for all 2≤rD H and for all distinct verticesx 1, ...,x rV(G),
,
(iii)  for all but at mosto(n 2) pairs {x 1,x 2} ⊆V(G),
, then the number of labeled copies ofH inG is
.
Moreover, we discuss a setting under which an arbitrary graphH (not necessarily triangle-free) can be embedded inG. We also present an embedding result for directed graphs. Research supported by a CNPq/NSF cooperative grant. Partially supported by MCT/CNPq through ProNEx Programme (Proc. CNPq 664107/1997-4) and by CNPq (Proc. 300334/93-1 and 468516/2000-0). Partially supported by NSF Grant 0071261. Supported by NSF grant CCR-9820931.  相似文献   

19.
Let G be a finite group. We extend Alan Camina’s theorem on conjugacy classes sizes which asserts that if the conjugacy classes sizes of G are {1, p a , q b , p a q b }, where p and q are two distinct primes and a and b are integers, then G is nilpotent. We show that let G be a group and assume that the conjugacy classes sizes of elements of primary and biprimary orders of G are exactly {1, p a , n,p a n} with (p, n) = 1, where p is a prime and a and n are positive integers. If there is a p-element in G whose index is precisely p a , then G is nilpotent and n = q b for some prime qp.  相似文献   

20.
Summary Letf: (x, z)∈R n×Rn→f(x, z)∈[0, +∞] be measurable inx and convex inz. It is proved, by an example, that even iff verifies a condition as|z| p≤f(x, z)≤Λ(a(x)+|z|q) with 1<p<q,aL loc s (R n),s>1, the functional that isL 1(Ω)-lower semicontinuous onW 1,1(Ω), does not agree onW 1,1(Ω) with its relaxed functional in the topologyL 1(Ω) given by inf
Riassunto Siaf: (x, z)∈R n×Rn→f(x, z)∈[0, +∞] misurabile inx e convessa inz. Si mostra con un esempio che anche sef verifica una condizione del tipo|z| p≤f(x, z)≤Λ(a(x)+|z|q) con 1<p<q,aL loc s (R n),s>1, il funzionale , che èL 1(Ω)-semicontinuo inferiormente suW 1,1(Ω), non coincide suW 1,1(Ω) con il suo funzionale rilassato nella topologiaL 1(Ω) definito da inf
  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号