共查询到20条相似文献,搜索用时 93 毫秒
1.
Helmut Bender 《Israel Journal of Mathematics》1975,22(3-4):208-213
A solvableA-signalizer functor? assigns to any non-identity elementx of the abelian 2-subgroupA of the finite groupG anA-invariant solvable 2′-subgroupθ(C G(x)) ofC G(x) such thatθ(C G(x)) ∩C G(y) ??(C G(y)) for allx, y ∈ A #.θ is called complete ifG has a solvableA-invariant 2′-subgroupK=θ(G) such thatC k(x)=θ(C G(x)) for everyx ∈ A#. This note contains an alternate proof of the completeness theorem below. 相似文献
2.
If A∈T(m, N), the real-valued N-linear functions on Em, and σ∈SN, the symmetric group on {…,N}, then we define the permutation operator Pσ: T(m, N) → T(m, N) such that Pσ(A)(x1,x2,…,xN = A(xσ(1),xσ(2),…, xσ(N)). Suppose Σqi=1ni = N, where the ni are positive integers. In this paper we present a condition on σ that is sufficient to guarantee that 〈Pσ(A1?A2???Aq),A1?A2?? ? Aq〉 ? 0 for Ai∈S(m, ni), where S(m, ni) denotes the subspace of T(m, ni) consisting of all the fully symmetric members of T(m, ni). Also we present a broad generalization of the Neuberger identity which is sometimes useful in answering questions of the type described below. Suppose G and H are subgroups of SN. We let TG(m, N) denote all A∈T(m, N) such that Pσ(A) = A for all σ∈G. We define the symmetrizer G: T(m, N)→TG(m,N) such that . Suppose H is a subgroup of G and A∈TH(m, N). Clearly We are interested in the reverse type of comparison. In particular, if D is a suitably chosen subset of TH(m,N), then can we explicitly present a constant C>0 such that for all A∈D? 相似文献
3.
R. Nair 《Periodica Mathematica Hungarica》2012,64(1):39-51
Let S be a countable semigroup acting in a measure-preserving fashion (g ? T g ) on a measure space (Ω, A, µ). For a finite subset A of S, let |A| denote its cardinality. Let (A k ) k=1 ∞ be a sequence of subsets of S satisfying conditions related to those in the ergodic theorem for semi-group actions of A. A. Tempelman. For A-measureable functions f on the measure space (Ω, A, μ) we form for k ≥ 1 the Templeman averages \(\pi _k (f)(x) = \left| {A_k } \right|^{ - 1} \sum\nolimits_{g \in A_k } {T_g f(x)}\) and set V q f(x) = (Σ k≥1|π k+1(f)(x) ? π k (f)(x)|q)1/q when q ∈ (1, 2]. We show that there exists C > 0 such that for all f in L 1(Ω, A, µ) we have µ({x ∈ Ω: V q f(x) > λ}) ≤ C(∫Ω | f | dµ/λ). Finally, some concrete examples are constructed. 相似文献
4.
Let G be a connected simple graph, let X?V (G) and let f be a mapping from X to the set of integers. When X is an independent set, Frank and Gyárfás, and independently, Kaneko and Yoshimoto gave a necessary and sufficient condition for the existence of spanning tree T in G such that d T (x) for all x ∈ X, where d T (x) is the degree of x and T. In this paper, we extend this result to the case where the subgraph induced by X has no induced path of order four, and prove that there exists a spanning tree T in G such that d T (x) ≥ f(x) for all x ∈ X if and only if for any nonempty subset S ? X, |N G (S) ? S| ? f(S) + 2|S| ? ω G (S) ≥, where ω G (S) is the number of components of the subgraph induced by S. 相似文献
5.
Kai Wang 《Journal of Number Theory》1984,18(3):306-312
For a positive integer m, let and let n = |A|. For an integer x, let R(x) be the least positive residue of x modulo m and if (x, m) = 1, let x′ be the inverse of x modulo m. If m is odd, then |R(ab′)|a,b∈A = ?21?n(∏χ(Σa = 1m ? 1aχ(a))), where χ runs over all the odd Dirichlet characters modulo m. 相似文献
6.
Let G be a simple undirected graph of order n. For an independent set S ? V(G) of k vertices, we define the k neighborhood intersections Si = {v ? V(G)\S|N(v) ∩ S| = i}, 1 ≦ i ≦ k, with si = |Si|. Using the concept of insertible vertices and the concept of neighborhood intersections, we prove the following theorem. 相似文献
7.
8.
Let G be a connected graph, let ${X \subset V(G)}$ and let f be a mapping from X to {2, 3, . . .}. Kaneko and Yoshimoto (Inf Process Lett 73:163–165, 2000) conjectured that if |N G (S) ? X| ≥ f (S) ? 2|S| + ω G (S) + 1 for any subset ${S \subset X}$ , then there exists a spanning tree T such that d T (x) ≥ f (x) for all ${x \in X}$ . In this paper, we show a result with a stronger assumption than this conjecture; if |N G (S) ? X| ≥ f (S) ? 2|S| + α(S) + 1 for any subset ${S \subset X}$ , then there exists a spanning tree T such that d T (x) ≥ f (x) for all ${x \in X}$ . 相似文献
9.
Michel Las Vergnas 《Discrete Mathematics》1976,15(1):27-39
The main result of this paper is the following theorem: Let G = (X,E) be a digraph without loops or multiple edges, |X| ?3, and h be an integer ?1, if G contains a spanning arborescence and if d+G(x)+d?G(x)+d?G(y)+d?G(y)? 2|X |?2h?1 for all x, y?X, x ≠ y, non adjacent in G, then G contains a spanning arborescence with ?h terminal vertices. A strengthening of Gallai-Milgram's theorem is also proved. 相似文献
10.
A generalized matrix norm G dominates the spectral radius for all A?Mn(C) (i) if for some positive integer k the rule G(Ak) ? G(A)k holds for all A?Mn(C) and (ii) if and only if for each A?Mn(C) there exists a constant γA such that G(Ak) ? γAG(A)kfor all positive integers k. Other results and examples are also given concerning spectrally dominant generalized matrix norms. 相似文献
11.
Béla Uhrin 《Journal of Number Theory》1981,13(2):192-209
Given a lattice and a bounded function g(x), x ∈ Rn, vanishing outside of a bounded set, the functions ?(x)maxu∈Λg(u +x), ?(x)?Σu∈Λ g(u +x), and ?+(x)?Σu∈Λ maxv∈Λ min {g(v + x); g(u + v + x)} are defined and periodic mod Λ on Rn. In the paper we prove that ?(x) + ?+(x) ? 2?(x) ≥ ?(x) + h?+(x) ? 2?(x) holds for all x ∈ Rn, where h(x) is any “truncation” of g by a constant c ≥ 0, i.e., any function of the form h(x)?g(x) if g(x) ≤ c and h(x)?c if g(x) > c. This inequality easily implies some known estimations in the geometry of numbers due to Rado [1] and Cassels [2]. Moreover, some sharper and more general results are also derived from it. In the paper another inequality of a similar type is also proved. 相似文献
12.
Lawrence M. H. Ein David Ross Richman Daniel J. Kleitman James Shearer Dean Sturtevant 《Studies in Applied Mathematics》1981,65(3):269-274
Let S be a finite set, and fix K>2. Let F be a family of subsets of S with the property that whenever A1,...,Ak are sets in F, not necessarily distinct, and A1 ? ? ? Ak = ?, then A1 ? ? ? Ak = S. We prove here that the maximum size of such a family is 2|S|?1 + 1. If we require that the sets A1,...,Ak be distinct, then the maximum size of F is again 2|S|?1 + 1, provided that |S| ≥ log2(K?2)+3. 相似文献
13.
Finite-dimensional theorems of Perron-Frobenius type are proved. For A∈nn and a nonnegative integer k, we let wk (A) be the cone generated by Ak, Ak+1,…in nn. We show that A satisfies the Perron-Schaefer condition if and only if the closure k(A) of wk(A) is a pointed cone. This theorem is closely related to several known results. If k?v0(A), the index of the eigenvalue 0 in spec A, we prove that A has a positive eigenvalue if and only if wk(A) is a pointed nonzero cone or, equivalently k(A) is not a real subspace of nn. Our proofs are elementary and based on a method of Birkhoff's. We discuss the relation of this method to Pringsheim's theorem. 相似文献
14.
We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. LetS n(F) be the space of alln×n symmetry matrices over a fieldF with 2,3 ∈F *, thenT is an additive injective operator preserving rank-additivity onS n(F) if and only if there exists an invertible matrixU∈M n(F) and an injective field homomorphism ? ofF to itself such thatT(X)=cUX ?UT, ?X=(xij)∈Sn(F) wherec∈F *,X ?=(?(x ij)). As applications, we determine the additive operators preserving minus-order onS n(F) over the fieldF. 相似文献
15.
We associate a graph G ?(P) to a partially ordered set (poset, briefly) with the least element?0, as an undirected graph with vertex set P ?=P?{0} and, for two distinct vertices x and y, x is adjacent to?y in?G ?(P) if and only if {x,y} ? ={0}, where, for a subset?S of?P, S ? is the set of all elements x∈P with x≦s for all s∈S. We study some basic properties of?G ?(P). Also, we completely investigate the planarity of?G ?(P). 相似文献
16.
Let G be a graph and k ≥ 2 a positive integer. Let h: E(G) → [0, 1] be a function. If \(\sum\limits_{e \mathrel\backepsilon x} {h(e) = k} \) holds for each x ∈ V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e ∈ E(G): h(e) > 0}. A graph G is fractional independent-set-deletable k-factor-critical (in short, fractional ID-k-factor-critical), if G ? I has a fractional k-factor for every independent set I of G. In this paper, we prove that if n ≥ 9k ? 14 and for any subset X ? V (G) we have then G is fractional ID-k-factor-critical.
相似文献
$${N_G}(X) = V(G)if|X| \geqslant \left\lfloor {\frac{{kn}}{{3k - 1}}} \right\rfloor ;or|{N_G}(X)| \geqslant \frac{{3k - 1}}{k}|X|if|X| < \left\lfloor {\frac{{kn}}{{3k - 1}}} \right\rfloor ,$$
17.
Xin Min Hou 《数学学报(英文版)》2012,28(11):2161-2168
A graph G satisfies the Ore-condition if d(x) + d(y) ≥ | V (G) | for any xy ■ E(G). Luo et al. [European J. Combin., 2008] characterized the simple Z3-connected graphs satisfying the Ore-condition. In this paper, we characterize the simple Z3-connected graphs G satisfying d(x) + d(y) ≥ | V (G) |-1 for any xy ■ E(G), which improves the results of Luo et al. 相似文献
18.
T.-S. Chen 《代数通讯》2013,41(12):4457-4466
ABSTRACT Let A = A 0 ⊕ A 1 be an associative superalgebra over a commutative associative ring F, and let Z s (A) be its supercenter. An F-mapping f of A into itself is called supercentralizing on a subset S of A if [x, f(x)] s ∈ Z s (A) for all x ∈ S. In this article, we prove a version of Posner's theorem for supercentralizing superderivations on prime superalgebras. 相似文献
19.
Lutz Volkmann 《Central European Journal of Mathematics》2014,12(3):517-528
Let k ≥ 2 be an integer. A function f: V(G) → {?1, 1} defined on the vertex set V(G) of a graph G is a signed k-independence function if the sum of its function values over any closed neighborhood is at most k ? 1. That is, Σ x∈N[v] f(x) ≤ k ? 1 for every v ∈ V(G), where N[v] consists of v and every vertex adjacent to v. The weight of a signed k-independence function f is w(f) = Σ v∈V(G) f(v). The maximum weight w(f), taken over all signed k-independence functions f on G, is the signed k-independence number α s k (G) of G. In this work, we mainly present upper bounds on α s k (G), as for example α s k (G) ≤ n ? 2?(Δ(G) + 2 ? k)/2?, and we prove the Nordhaus-Gaddum type inequality $\alpha _S^k \left( G \right) + \alpha _S^k \left( {\bar G} \right) \leqslant n + 2k - 3$ , where n is the order, Δ(G) the maximum degree and $\bar G$ the complement of the graph G. Some of our results imply well-known bounds on the signed 2-independence number. 相似文献
20.
Given a graph G, a total k-coloring of G is a simultaneous coloring of the vertices and edges of G with k colors. Denote χve (G) the total chromatic number of G, and c(Σ) the Euler characteristic of a surfase Σ. In this paper, we prove that for any simple graph G which can be embedded in a surface Σ with Euler characteristic c(Σ), χve (G) = Δ (G) + 1 if c(Σ) > 0 and Δ (G) ≥ 13, or, if c(Σ) = 0 and Δ (G) ≥ 14. This result generalizes results in [3], [4], [5] by Borodin. 相似文献