共查询到20条相似文献,搜索用时 15 毫秒
1.
Let ρ be a real-valued function on [0, T], and let LSI(ρ) be a class of Gaussian processes over time interval [0, T], which need not have stationary increments but their incremental variance σ(s, t) is close to the values ρ(|t ? s|) as t → s uniformly in s ∈ (0, T]. For a Gaussian processesGfrom LSI(ρ), we consider a power variation V n corresponding to a regular partition π n of [0, T] and weighted by values of ρ(·). Under suitable hypotheses on G, we prove that a central limit theorem holds for V n as the mesh of π n approaches zero. The proof is based on a general central limit theorem for random variables that admit a Wiener chaos representation. The present result extends the central limit theorem for a power variation of a class of Gaussian processes with stationary increments and for bifractional and subfractional Gaussian processes. 相似文献
2.
Let V be a vector space over a field F. Assume that the characteristic of F is large, i.e. char(F)>dimV. Let T:V→V be an invertible linear map. We answer the following question in this paper. When doesVadmit a T-invariant non-degenerate symmetric (resp. skew-symmetric) bilinear form? We also answer the infinitesimal version of this question.Following Feit and Zuckerman 2, an element g in a group G is called real if it is conjugate in G to its own inverse. So it is important to characterize real elements in GL(V,F). As a consequence of the answers to the above question, we offer a characterization of the real elements in GL(V,F).Suppose V is equipped with a non-degenerate symmetric (resp. skew-symmetric) bilinear form B. Let S be an element in the isometry group I(V,B). A non-degenerate S-invariant subspace W of (V,B) is called orthogonally indecomposable with respect to S if it is not an orthogonal sum of proper S-invariant subspaces. We classify the orthogonally indecomposable subspaces. This problem is non-trivial for the unipotent elements in I(V,B). The level of a unipotent T is the least integer k such that (T-I)k=0. We also classify the levels of unipotents in I(V,B). 相似文献
3.
Let V be a nonsingular vector space over a field K of characteristic 2 with |K|>3. Suppose K is perfect and π is an element in the special orthogonal group SO(V)=Ω(V) with dimB(π)=2d. The length of π with respect to the symmetry commutators is d if B(π) is not totally isotropic; otherwise it is d+1. 相似文献
4.
Edward A Connors 《Journal of Number Theory》1973,5(6):477-501
Let V be a nondefective quadratic space over a field F of characteristic 2. Assume that V has dimension at least ten and that F has more than two elements. Let Δ be one of the groups O(V), O+(V), O′(V), or (the full orthogonal group, the rotation group, the spinorial kernel, or the commutator subgroup of O(V), respectively). Then Λ is an automorphism of Λ if and only if Λ(σ) = gσg?1 for all σ in Δ where g is a semilinear automorphism of V that preserves the quadratic structure of V in the sense that Q(gx) = αQ(x)u for all x in V where Q is the quadratic form, α is some nonzero element of F, and u is the field automorphism of F associated to g. 相似文献
5.
Let H be a Hopf algebra, B a bialgebra, and (B, ?, ρ) a right H-Hopf module. Assume that (B, ρ) is a right H-comodule algebra, (B, ?) is a right H-module coalgebra, and let A = B co H = {a ∈ B | ρ(a) = a ? 1}. Then we prove that B has a factorization of A□ ρ ? (the underlying space is A ? H) as a bialgebra, which generalizes Radford’s factorization of bialgebras with projection [12]. 相似文献
6.
Let ρ?Rn be a proper cone. From the theory of M-matrices (see e.g. [1]) it is known that if there exist α > 0 and a matrix B: ρ→ρ such that A = B?αI, then the following conditions are equivalent: (i) ? A is ρ-monotone,(ii) A is ρ-seminegative, (iii) Re[Spectrum(A)]<0. In this paper we show that while the condition (e) etAρ?ρ ?t≥0 is more general than the structural assumption A = B?αI, conditions (i)-(iii) are nevertheless all equivalent to (iv) {x∈ρ: Ax∈ρ}={0} when (e) holds. 相似文献
7.
<正> 1.设G是复数W平面上的一个凸形区域.假如通过G的一个境界点有一个圆周把G合在它的内部,那末这个圆周是 G 在此境界点的支持圆周.设在 G 的每一个境界点都有一个半径不超过ρ(ρ>0)的支持圆周,并且有一个点,其支持圆周的半径不能小于ρ,那末称 G 是一由半径为ρ的圆所支持的凸形区域.我们又简称这种区域为支持半径为ρ的区域.当ρ=∞时圆周化成直线,每一凸形区域都为一个半平面所支持. 相似文献
8.
Let R be a prime ring of char R≠2, d a non-zero derivation of R and ρ a non-zero right ideal of R such that [[d(x),d(y)]n [y,x]m] = 0 for all x,y ∈ ρ or [[d(x),d(y)]n d[y,x]m] = 0 for all x,y ∈ ρ, n, m ≥ 0 are fixed integers. If [ρ,ρ]ρ ≠ 0, then d(ρ)ρ = 0. 相似文献
9.
Put Zn = {1, 2,…, n} and let π denote an arbitrary permutation of Zn. Problem I. Let π = (π(1), π(2), …, π(n)). π has an up, down, or fixed point at a according as a < π(a), a > π(a), or a = π(a). Let be the number of π ∈ Zn with r ups, s downs, and t fixed points. Problem II. Consider the triple π?1(a), a, π(a). Let R denote an up and F a down of π and let B(n, r, s) denote the number of π ∈ Zn with r occurrences of π?1(a)RaRπ(a) and s occurrences of π?1(a)FaFπ(a). Generating functions are obtained for each enumerant as well as for a refinement of the second. In each case use is made of the cycle structure of permutations. 相似文献
10.
11.
Donald L McQuillan 《Journal of Number Theory》1976,8(4):438-445
Let R be a Dedekind domain, G a finite group of automorphisms of R, and A an ambiguous ideal of R i.e., σA = A for all σ ∈ G. The Tate groups Hn(G, A) are considered as RG-modules. A localization theorem is proved and the precise RG-module structure determined in a particular case. In addition some remarks are made concerning cohomological triviality. 相似文献
12.
Yoshinobu Kamishima 《Topology and its Applications》1985,19(2):189-199
This note will concern properly discontinuous actions of subgroups in real algebraic groups on contractible manifolds. Let (π,X,ρ) be such an action, where ρ:π→ Diff(X) is a homomorphism. We assume that ? extends to a smooth action of a real algebraic group G containing π. If such π has a nontrivial radical (i.e., unique maximal normal solvable subgroup), then we can apply the method of Seifert construction [14],[17] to yield that the quotient π\X supports the structure of an injective Seifert fibering with typical (resp. exceptional) fiber diffeomorphic to a solv (resp. infrasolv)-manifold (when π acts freely). When G is an amenable algebraic group, we can say about a uniqueness property for such actions. Namely, let (πi, Xi, ρi) be actions as above (i= 1,2). Then, given an isomorphism f of π1 onto ?2, there is a diffeomorphism h: X1→X2 such that h(ρ1(r)x)=ρ2(f(r)h(x).As an application, we try to decide the structure of affine motions of some euclidean space n. First we verify the conjecture of [17, 4 5], i.e., a compact complete affinely flat manifold admits a maximal toral action if its fundamental group has a nontrivial center. Second, a compact complete affinity flat manifold whose fundamental group is virtually polycyclic supports the structure of an infrasolvmanifold. This structure varies depending on its solvable kernel (if it is abelian or nilpotent, it must be a euclidean space form or an infranilmanifold respectively). If a group of the affine group A(n) acts properly discontinuously and with compact quotient of n, then it is called an affine crystallographic group. Finally, we can say so far as to a uniqueness property that two virtually polycyclic affine crystallographic groups are conjugate inside Diff(n) if they are isomorphic (cf.[8]). 相似文献
13.
Letq be a regular quadratic form on a vector space (V,F) and letf be the bilinear form associated withq. Then, \(\dot V: = \{ z \in V|q(z) \ne 0\} \) is the set of non-singular vectors ofV, and forx, y ∈ \(\dot V\) , ?(x, y) ?f(x, y) 2/(q(x) · q(y)) is theq-measure of (x, y), where ?(x,y)=0 means thatx, y are orthogonal. For an arbitrary mapping \(\sigma :\dot V \to \dot V\) we consider the functional equations $$\begin{gathered} (I)\sphericalangle (x,y) = 0 \Leftrightarrow \sphericalangle (x^\sigma ,y^\sigma ) = 0\forall x,y \in \dot V, \hfill \\ (II)\sphericalangle (x,y) = \sphericalangle (x^\sigma ,y^\sigma )\forall x,y \in \dot V, \hfill \\ (III)f(x,y)^2 = f(x^\sigma ,y^\sigma )^2 \forall x,y \in \dot V, \hfill \\ \end{gathered} $$ and we state conditions on (V,F,q) such thatσ is induced by a mapping of a well-known type. In case of dimV ∈N?{0, 1, 2} ∧ ∣F∣ > 3, each of the assumptions (I), (II), (III) implies that there exist aρ-linear injectionξ :V →V and a fixed λ ∈F?{0} such thatF x σ =F x ξ ?x ∈ \(\dot V\) andf(x ξ,y ξ)=λ · (f(x, y))ρ ?x, y ∈V. Moreover, (II) implies ρ =id F ∧q(x ξ) = λ ·q(x) ?x ∈ \(\dot V\) , and (III) implies ρ=id F ∧ λ ∈ {1,?1} ∧x σ ∈ {x ξ, ?x ξ} ?x ∈ \(\dot V\) . Other results obtained in this paper include the cases dimV = 2 resp. dimV ?N resp. ∣F∣ = 3. 相似文献
14.
Zhenqi Jenny Wang 《Israel Journal of Mathematics》2018,225(1):147-191
Suppose G is a higher-rank connected semisimple Lie group with finite center and without compact factors. Let G = G or G = G ? V, where V is a finite-dimensional vector space V. For any unitary representation (π,H) of G, we study the twisted cohomological equation π(a)f ? λf = g for partially hyperbolic element a ∈ G and λ ∈ U(1), as well as the twisted cocycle equation π(a1)f ? λ1f = π(a2)g ? λ2g for commuting partially hyperbolic elements a1, a2 ∈ G. We characterize the obstructions to solving these equations, construct smooth solutions and obtain tame Sobolev estimates for the solutions. These results can be extended to partially hyperbolic flows in parallel.As an application, we prove cocycle rigidity for any abelian higher-rank partially hyperbolic algebraic actions. This is the first paper exploring rigidity properties of partially hyperbolic that the hyperbolic directions don’t generate the whole tangent space. The result can be viewed as a first step toward the application of KAM method in obtaining differential rigidity for these actions in future works. 相似文献
15.
P Hanlon 《Journal of Combinatorial Theory, Series B》1985,38(3):226-239
We investigate the chromatic polynomial χ(G, λ) of an unlabeled graph G. It is shown that , where g is any labeled version of G, A(g) is the automorphism group of g and χ(g, π, λ) is the chromatic polynomial for colorings of g fixed by π. The above expression shows that χ(G, λ) is a rational polynomial of degree n = |V(G)| with leading coefficient . Though χ(G, λ) does not satisfy chromatic reduction, each polynomial χ(g, π, λ) does, thus yielding a simple method for computing χ(G, λ). We also show that the number N(G) of acyclic orientations of G is related to the argument λ = ?1 by the formula , where s(π) is the number of cycles of π. This information is used to derive Robinson's (“Combinatorial Mathematics V” (Proc. 5th Austral. Conf. 1976), Lecture Notes in Math. Vol. 622, pp. 28–43, Springer-Verlag, New York/Berlin, 1977) cycle index sum equations for counting unlabeled acyclic digraphs. 相似文献
16.
Olof Heden Juliane Lehmann Esmeralda N?stase Papa Sissokho 《Designs, Codes and Cryptography》2012,64(3):265-274
A subspace partition Π of V?= V(n, q) is a collection of subspaces of V such that each 1-dimensional subspace of V is in exactly one subspace of Π. The size of Π is the number of its subspaces. Let σ q (n, t) denote the minimum size of a subspace partition of V in which the largest subspace has dimension t, and let ρ q (n, t) denote the maximum size of a subspace partition of V in which the smallest subspace has dimension t. In this article, we determine the values of σ q (n, t) and ρ q (n, t) for all positive integers n and t. Furthermore, we prove that if n ≥?2t, then the minimum size of a maximal partial t-spread in V(n +?t ?1, q) is σ q (n, t). 相似文献
17.
Marian Nowak 《Indagationes Mathematicae》2009,20(1):151-403
Let Σ be a σ-algebra of subsets of a non-empty set Ω. Let X be a real Banach space and let X* stand for the Banach dual of X. Let B(Σ, X) be the Banach space of Σ-totally measurable functions f: Ω → X, and let B(Σ, X)* and B(Σ, X)** denote the Banach dual and the Banach bidual of B(Σ, X) respectively. Let bvca(Σ, X*) denote the Banach space of all countably additive vector measures ν: Σ → X* of bounded variation. We prove a form of generalized Vitali-Hahn-Saks theorem saying that relative σ(bvca(Σ, X*), B(Σ, X))-sequential compactness in bvca(Σ, X*) implies uniform countable additivity. We derive that if X reflexive, then every relatively σ(B(Σ, X)*, B(Σ, X))-sequentially compact subset of B(Σ, X)c~ (= the σ-order continuous dual of B(Σ, X)) is relatively σ(B(Σ, X)*, B(Σ, X)**)-sequentially compact. As a consequence, we obtain a Grothendieck type theorem saying that σ(B(Σ, X)*, B(Σ, X))-convergent sequences in B(Σ, X)c~ are σ(B(Σ, X)*, B(Σ, X)**)-convergent. 相似文献
18.
Conditions are given on maps A, C∈ L(X, V) and B, D ∈ L(Y, V) for which Cx∧Dy = Ax∧By for all x ∈ X and y ∈ Y, and, when X = Y, for which Cx∧Dx = Ax ∧Bx for all x ∈ X. 相似文献
19.
Kristopher Lee 《Journal of Mathematical Analysis and Applications》2011,375(1):108-117
Let A and B be uniform algebras on first-countable, compact Hausdorff spaces X and Y, respectively. For f∈A, the peripheral spectrum of f, denoted by σπ(f)={λ∈σ(f):|λ|=‖f‖}, is the set of spectral values of maximum modulus. A map T:A→B is weakly peripherally multiplicative if σπ(T(f)T(g))∩σπ(fg)≠∅ for all f,g∈A. We show that if T is a surjective, weakly peripherally multiplicative map, then T is a weighted composition operator, extending earlier results. Furthermore, if T1,T2:A→B are surjective mappings that satisfy σπ(T1(f)T2(g))∩σπ(fg)≠∅ for all f,g∈A, then T1(f)T2(1)=T1(1)T2(f) for all f∈A, and the map f?T1(f)T2(1) is an isometric algebra isomorphism. 相似文献
20.
Chu Yung-ching 《Discrete Mathematics》1980,29(3):251-255
Given n weights, w1, w2,…, wn, such that 0?w1?w2???w1, we examine a property of permutation π1, where π1=(w1, wn, w2, wn?1,…), concerning alphabetical binary trees.For each permutation π of these n weights, there is an optimal alphabetical binary tree corresponding to π, we denote it's cost by V(π). There is also an optimal almost uniform alphabetical binary tree, corresponding to π, we denote it's cost by Vu(π).This paper asserts that Vu(π1)?Vu(π)?V(π) for all π. This is a preliminary result concerning the conjecture of T.C. Hu. Hu's conjecture is V(π1)?V(π) for all π. 相似文献