共查询到20条相似文献,搜索用时 15 毫秒
1.
Benjamin M.S. Martin 《Indagationes Mathematicae》1999,10(4):555
Let R(F, G) be the variety of representations of a finitely generated group F into a connected reductive algebraic group G, and let C(F, G) be the variety of closed conjugacy classes of representations. We examine the question of whether an étale slice for the conjugation action of G exists through a representation ρR(F, G) when the ground field k has characteristic p > 0. We show that an étale slice through ρ may exist for the action of an enlarged group Ĝ, even when there is no étale slice for the G-action. As an application, we generalise a result known to hold in characteristic zero, which expresses the tangent space to C(F, G) at the conjugacy class of a suitable representation ρ as a subspace of the 1-cohomology H1 (F, %plane1D;524;(ρ)) of an F-module %plane1D;524;(ρ). A similar result holds in characteristic p, but with H1 (F%plane1D;524;(ρ)) replaced by a quotient of H1 (F%plane1D;524;(ρ)). 相似文献
2.
Bimal Kumar Sinha 《Journal of multivariate analysis》1976,6(4):617-625
Treated in this paper is the problem of estimating with squared error loss the generalized variance | Σ | from a Wishart random matrix S: p × p Wp(n, Σ) and an independent normal random matrix X: p × k N(ξ, Σ Ik) with ξ(p × k) unknown. Denote the columns of X by X(1) ,…, X(k) and set ψ(0)(S, X) = {(n − p + 2)!/(n + 2)!} | S |, ψ(i)(X, X) = min[ψ(i−1)(S, X), {(n − p + i + 2)!/(n + i + 2)!} | S + X(1) X′(1) + + X(i) X′(i) |] and Ψ(i)(S, X) = min[ψ(0)(S, X), {(n − p + i + 2)!/(n + i + 2)!}| S + X(1) X′(1) + + X(i) X′(i) |], i = 1,…,k. Our result is that the minimax, best affine equivariant estimator ψ(0)(S, X) is dominated by each of Ψ(i)(S, X), i = 1,…,k and for every i, ψ(i)(S, X) is better than ψ(i−1)(S, X). In particular, ψ(k)(S, X) = min[{(n − p + 2)!/(n + 2)!} | S |, {(n − p + 2)!/(n + 2)!} | S + X(1)X′(1)|,…,| {(n − p + k + 2)!/(n + k + 2)!} | S + X(1)X′(1) + + X(k)X′(k)|] dominates all other ψ's. It is obtained by considering a multivariate extension of Stein's result (Ann. Inst. Statist. Math. 16, 155–160 (1964)) on the estimation of the normal variance. 相似文献
3.
In this paper we define the vertex-cover polynomial Ψ(G,τ) for a graph G. The coefficient of τr in this polynomial is the number of vertex covers V′ of G with |V′|=r. We develop a method to calculate Ψ(G,τ). Motivated by a problem in biological systematics, we also consider the mappings f from {1, 2,…,m} into the vertex set V(G) of a graph G, subject to f−1(x)f−1(y)≠ for every edge xy in G. Let F(G,m) be the number of such mappings f. We show that F(G,m) can be determined from Ψ(G,τ). 相似文献
4.
We give conditions for orthonormal systems on the boundary of a plane Jordan domain which are necessary and sufficient for an arbitrary series in terms of this orthonormal system to be the Fourier series of some function in H∞(G) resp. EP(G)(1<p<∞). Our results contain a classical criterion of Fejér for the boundedness of a holomorphic function in the unit disk. 相似文献
5.
T.S. Quek 《Journal of Mathematical Analysis and Applications》1997,210(2):742
We extend the Littlewood–Paley theorem toLpw(G), whereGis a locally compact Vilenkin group andware weights satisfying the MuckenhouptApcondition. As an application we obtain a mixed-norm type multiplier result onLpw(G) and prove the sharpness of our result. We also obtain a sufficient condition for φ L∞(Γ) to be a multiplier on the power weightedLpα(G) in terms of its smoothness condition. 相似文献
6.
A Cayley graph Cay(G,S) of a groupGis called a CI-graph if wheneverTis another subset ofGfor which Cay(G,S) Cay(G,T), there exists an automorphism σ ofGsuch thatSσ = T. For a positive integerm, the groupGis said to have them-CI property if all Cayley graphs ofGof valencymare CI-graphs; further, ifGhas thek-CI property for allk ≤ m, thenGis called anm-CI-group, and a |G|-CI-groupGis called a CI-group. In this paper, we prove that Ais not a 5-CI-group, that SL(2,5) is not a 6-CI-group, and that all finite 6-CI-groups are soluble. Then we show that a nonabelian simple group has the 4-CI property if and only if it is A5, and that no nonabelian simple group has the 5-CI property. Also we give nine new examples of CI-groups of small order, which were found to be CI-groups with the assistance of a computer. 相似文献
7.
In this paper, it is proved that a finite group G is p-nilpotent if every minimal subgroup of P∩Op(G) is permutable in P and NG(P) is p-nilpotent, and when p=2 either [Ω2(P∩Op(G)),P]Ω1(P∩Op(G)) or P is quaternion-free, where p is a prime dividing the order of G and P is a Sylow p-subgroup of G. By using this result, we may get a series of corollaries for p-nilpotence, which contain some known results. Some other applications of this result are also given. 相似文献
8.
The object of this paper is to prove the following theorem: Let Y be a closed subspace of the Banach space X, (S,Σ,μ) a σ-finite measure space, L(S,Y) (respectively, L(S, X)) the space of all strongly measurable functions from S to Y (respectively, X), and p a positive number. Then L(S,Y) is pointwise proximinal in L(S,X) if and only if Lp(μ,Y) is proximinal in Lp(μ,X). As an application of the theorem stated above, we prove that if Y is a separable closed subspace of the Banach space X, p is a positive number, then Lp(μ,Y) is proximinal in Lp(μ,X) if and only if Y is proximinal in X. Finally, several other interesting results on pointwise best approximation are also obtained. 相似文献
9.
Duran A. J. 《Journal of Approximation Theory》1993,74(3)
The subspaces Gα, Gβ, and Gβα (α, β ≥ 0)of Schwartz′ space S+ in (0, + ∞) are associated with the Hankel transform in the same way as the Gel′fand-Shilov spaces Sα, Sβ, and Sβα are associated with the Fourier transform. Indeed, if we consider the Hankel transform Hγ (γ < −1) defined by
γ(ƒ)(t) =
∫∞0 (xt)−γ/2xγJγ([formula]) ƒ(x) dx then
γ is an isomorphism from Gα, Gβ, and Gβα onto Gα, Gβ, and Gαβ respectively. So. the spaces Gαα are invariant for
γ. In this paper, we characterize the spaces Gαα (α > 1) in terms of their Fourier-Laguerre coefficients. Also, we characterize the range of the Fourier-Laplace operator
D defined by
D(ƒ)(w) = ∫∞0 ƒ(t) e−(1/2)((1 + w)/(1 − w))t for w D = {w
: |w| ≤ 1} when it acts on the space Gαα. 相似文献
10.
On a simplex SRd, the best polynomial approximation is En()Lp(S)=Inf{Pn−Lp(S): Pn of total degree n}. The Durrmeyer modification, Mn, of the Bernstein operator is a bounded operator on Lp(S) and has many “nice” properties, most notably commutativity and self-adjointness. In this paper, relations between Mn−z.dfnc;Lp(S) and E[√n]()Lp(S) will be given by weak inequalities will imply, for 0<α<1 and 1≤p≤∞, En()Lp(S)=O(n-2α)Mn−z.dfnc;Lp(S)=O(n-α). We also see how the fact that P(D)εLp(S) for the appropriate P(D) affects directional smoothness. 相似文献
11.
Given a graph G and an ordering p of its vertices, denote by A(G, p) the number of colors used by the greedy coloring algorithm when applied to G with vertices ordered by p. Let , , Δ be positive constants. It is proved that for each n there is a graph Gn such that the chromatic number of Gn is at most n, but the probability that A(Gn, p) < (1 − )n/log2 n for a randomly chosen ordering p is O(n−Δ). 相似文献
12.
We prove that for f ε E = C(G) or Lp(G), 1 p < ∞, where G is any compact connected Lie group, and for n 1, there is a trigonometric polynomial tn on G of degree n so that f − tnE Crωr(n−1,f). Here ωr(t, f) denotes the rth modulus of continuity of f. Using this and sharp estimates of the Lebesgue constants recently obtained by Giulini and Travaglini, we obtain “best possible” criteria for the norm convergence of the Fourier series of f. 相似文献
13.
Valery Liskovets 《Journal of Algebraic Combinatorics》2003,18(3):189-209
We establish analytically several new identities connecting enumerators of different types of circulant graphs mainly of prime, twice prime and prime-squared orders. In particular, it is shown that the half-sum of the number of undirected circulants and the number of undirected self-complementary circulants of prime order is equal to the number of directed self-complementary circulants of the same order. Several identities hold only for prime orders p such that (p + 1)/2 is also prime. Some conjectured generalizations and interpretations are discussed. 相似文献
14.
I. V. Protasov 《Topology and its Applications》2003,130(3):1394
For a discrete group G, we consider βG, the Stone–
ech compactification of G, as a right topological semigroup, and G*=βGG as a subsemigroup of βG. We study the mappings λp* :G*→G*and μ* :G*→G*, the restrictions to G* of the mappings λp :βG→βG and μ :βG→βG, defined by the rules λp(q)=pq, μ(q)=qq. Under some assumptions, we prove that the continuity of λp* or μ* at some point of G* implies the existence of a P-point in ω*. 相似文献
15.
We prove the following analytic continuation theorem which applies to any virtual representation of any symmetric space (G, K, σ). The problem of passing from the Euclidean group to the Poincaré group appears first to have been addressed and solved this way by Klein and Landau. Let G be a Lie group, K a closed subgroup, and σ an involutive automorphism with K as fixed-point subgroup. If
=
+
is the corresponding symmetric Lie algebra, we form
* =
+
, and let G* denote the simply connected Lie group with
* as Lie algebra. We consider virtual representations π of G on a fixed complex Hilbert space
, adopting the definitions due to J. Fröhlich, K. Osterwalder, and E. Seiler; in particular, π(g−1) π(σ(g))* (possibly unbounded operators) for g in a neighborhood of e in G. We prove that every such π continues analytically to a strongly continuous unitary representation of G* on
. Our theorem extends results due to Klein-Landau, Fröhlich et al., and others, earlier, for special cases. Previous results were known only for special (G, K, σ), and then only for certain π. 相似文献
16.
Edward Minieka Niranjani H. Patel 《Journal of Algorithms in Cognition, Informatics and Logic》1983,4(4):345-352
A core of a graph G is a path P in G that is central with respect to the property of minizining d(P) = ΣυεV(G)d(υ, P), where d(υ, P) is the distance from vertex υ to path P. This paper explores some properties of a core of a specified length. 相似文献
17.
The undirected power graph G(S) of a semigroup S is an undirected graph whose vertex set is S and two vertices a,b∈S are adjacent if and only if a≠b and a
m
=b or b
m
=a for some positive integer m. In this paper we characterize the class of semigroups S for which G(S) is connected or complete. As a consequence we prove that G(G) is connected for any finite group G and G(G) is complete if and only if G is a cyclic group of order 1 or p
m
. Particular attention is given to the multiplicative semigroup ℤ
n
and its subgroup U
n
, where G(U
n
) is a major component of G(ℤ
n
). It is proved that G(U
n
) is complete if and only if n=1,2,4,p or 2p, where p is a Fermat prime. In general, we compute the number of edges of G(G) for a finite group G and apply this result to determine the values of n for which G(U
n
) is planar. Finally we show that for any cyclic group of order greater than or equal to 3, G(G) is Hamiltonian and list some values of n for which G(U
n
) has no Hamiltonian cycle. 相似文献
18.
In (Electron. J. Combin. 10 (2003); http://www.combinatorics.org/volume-10/Abstracts/v1oi1r28.html), the first author (Yuliya Gryshko) asked three questions. Is it true that every infinite group admitting a 2-coloring without infinite monochromatic symmetric subsets is either almost cyclic (i.e., have a finite index subgroup which is cyclic infinite) or countable locally finite? Does every infinite group G include a monochromatic symmetric subset of any cardinal <|G| for any finite coloring? Does every uncountable group G such that |B(G)|< |G| where B(G)={xG:x2=1}, admit a 2-coloring without monochromatic symmetric subsets of cardinality |G|? We answer the first question positively. Assuming the generalized continuum hypothesis (GCH), we give a positive answer to the second question in the abelian case. Finally, we build a counter-example for the third question and we give a necessary and sufficient condition for an infinite group G to admit 2-coloring without monochromatic symmetric subsets of cardinality |G|. This generalizes some results of Protasov on infinite abelian groups (Mat. Zametki 59 (1996) 468–471; Dopovidi NAN Ukrain 1 (1999) 54–57). 相似文献
19.
Jinxi Ma 《Journal of Mathematical Analysis and Applications》1998,220(2):769
For 0 < p < 1, letSpdenote the class of functionsf(z) meromorphic univalent in the unit disk
with the normalizationf(0) = 0,f′(0) = 1, andf(p) = ∞. LetSp(a) be the subclass ofSpwith the fixed residuea. In this note we determine the extreme points of the classSp(a). As an application, we solve the problem of minimizing the outer area overSp(a), which was posed by S. Zemyan (J. Analyse Math.39, 1981, 11–23). 相似文献
20.
For a finite group G and a prime p the poset Sp (G) of all subgroups H ≠ G of p-power index is studied. The Möbius number of the poset is given and the homotopy type of the poset is determined as a wedge of spheres. We describe the representation of G on the homology groups of the order complex of Sp (G) and show that this representation can be realized by matrices with entries in the set {+1, -1, 0}. Finally a CL-shellable subposet of Sp (G) is exhibited for odd primes p. 相似文献