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1.
We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on
a compact manifold. The structure is not assumed to be unimodular, so an invariant measure may not exist. Ergodic stationary
measures always exist, and when such a measure has full support, we show the following:
An important ingredient in the proofs is a generalization of Gromov’s centralizer theorem beyond the case of invariant measures. 相似文献
1. | Either the manifold admits a smooth equivariant map onto a homogeneous projective variety, defined on an open dense conull invariant set, or the Lie algebra of the Zariski closure of the Gromov representation of the fundamental group contains a Lie subalgebra isomorphic to the Lie algebra of the acting group. As a corollary, a smooth non-trivial homogeneous projective factor does exist whenever the fundamental group of M admits only virtually solvable linear representations, and thus in particular when M is simply connected, regardless of the real rank. |
2. | There exist explicit examples showing that analytic rigid actions of certain simple real rank one groups may indeed fail to have a smooth projective factor. |
3. | It is possible to generalize Gromov’s theorem on the algebraic hull of the representation of the fundamental group of the manifold to the case of rigid non-unimodular structures, again for actions of groups of any real rank. |
2.
Clemens Heuberger 《Monatshefte für Mathematik》2001,132(4):325-339
In a recent paper [7] the author considered the family of parametrized Thue equations
for monic polynomials which satisfy
Under some technical conditions it could be proved that there is a computable constant such that for all integers the only integer solutions of the Diophantine equation satisfy .
In this paper, we give an explicit expression for depending on the polynomials .
(Received 5 September 2000; in revised form 30 December 2000) 相似文献
3.
Qiu Weisheng 《数学学报(英文版)》1994,10(1):49-58
The Multiplier Theorem is a celebrated theorem in the Design theory. The conditionp>λ is crucial to all known proofs of the multiplier theorem. However in all known examples of difference sets μ
p
. is a multiplier for every primep with (p, v)=1 andp‖n. Thus there is the multiplier conjecture: “The multiplier theorem holds without the assumption thatp>λ”. The general form of the multiplier theorem may be viewed as an attempt to partially resolve the multiplier conjecture,
where the assumption “p>λ” is replaced by “n
1>λ”. Since then Newman (1963), Turyn (1964), and McFarland (1970) attempted to partially resolve the multiplier conjecture
(see [7], [8], [9]). This paper will prove the following result using the representation theory of finite groups and the algebraic
number theory: LetG be an abelian group of orderv,v
0 be the exponent ofG, andD be a (v, k, λ)-difference set inG. Ifn=2n
1, then the general form of the multiplier theorem holds without the assumption thatn
1>λ in any of the following cases:
Supported by the scientific research finances of Peking University. 相似文献
2〈 | n 1; |
a | 2 Xn 1 and (v, 7)=1; |
2 Xn1, 7〈 | v, andt≡1 or 2 or 4 (mod 7). |
4.
GuangYan Jia 《中国科学A辑(英文版)》2009,52(4):785-793
In this paper, we prove that for a sublinear expectation ɛ[·] defined on L
2(Ω,), the following statements are equivalent:
Furthermore, we prove a sandwich theorem for subadditive expectation and superadditive expectation.
This work was supported by National Basic Research Program of China (973 Program) (Grant No. 2007CB814901) (Financial Risk)
and National Natural Science Foundation of China (Grant No. 10671111) 相似文献
(i) | ɛ is a minimal member of the set of all sublinear expectations defined on L 2(Ω,) |
(ii) | ɛ is linear |
(iii) | the two-dimensional Jensen’s inequality for ɛ holds. |
5.
Huili Liu Masaaki Umehara Kotaro Yamada 《Bulletin of the Brazilian Mathematical Society》2011,42(1):131-152
In a joint work with Saji, the second and the third authors gave an intrinsic formulation of wave fronts and proved a realization
theorem for wave fronts in space forms. As an application, we show that the following four objects are essentially the same:
– |
conformally flat n-manifolds (n ≥ 3) with admissible singular points (i.e. admissible GCF-manifolds) 相似文献
6.
Let (G, τ) be a commutative Hausdorff locally solid lattice group. In this paper we prove the following:
7.
8.
Ferenc Móricz 《Journal of Fourier Analysis and Applications》2001,7(6):601-614
A theorem of Fejér states that if a periodic function F is of bounded variation on the closed interval [0, 2π], then the nth
partial sum of its formally differentiated Fourier series divided by n converges to π-1[F(x+0)-F(x-0)] at each point x. The generalization of this theorem for Fourier-Stieltjes series of (nonperiodic) functions of bounded variation
is also well known.
The aim of the present article is to extend these results to the (m, n)th rectangular partial sum of double Fourier or Fourier-Stieltjes
series of a function F(x, y) of bounded variation over the closed square [0, 2π]×[0, 2π] in the sense of Hardy and Krause.
As corollaries, we also obtain the following results:
9.
Alain Togbé 《Bulletin of the Brazilian Mathematical Society》2008,39(4):537-554
In this paper, we solve a family of Diophantine equations associated with families of number fields of degree 3. In fact,
we use Baker’s method find all solutions to the Thue equation
10.
In the present paper, we prove an analog of Khinchin's metric theorem in the case of linear Diophantine approximations of plane curves defined over the ring of $p$ -adic integers by means of (Mahler) normal functions. We also prove some general assertions needed to generalize this result to the case of spaces of higher dimension. 相似文献
11.
Yuval Roichman 《Israel Journal of Mathematics》1997,97(1):305-316
Consider the two natural representations of the symmetric groupS
n
on the group algebra ℂ[S
n
]: the regular representation and the conjugacy representation (acting on the basis by conjugation). Letm(λ) be the multiplicity of the irreducible representationS
λ
in the conjugacy representation and letf
λ
be the multiplicity ofS
λ
in the regular representation. By the character estimates of [R1] and [Wa] we prove
12.
Bo Zhang 《Annali di Matematica Pura ed Applicata》1997,172(1):25-42
Consider the equation
13.
This paper introduces the concept of orthogonal vector measures, and gives the Yosida-Hewittdecomposition theorem for this kind of vector measures. The major results are(a) Any orthogonal vector measure can gain it countable additivity by enlarging its domain;(b) Every orthogonal vector measure can be represented as the sum of two orthogonal vectormeasures, one of which is countably additive, and the other is purely finitely additive. Furthermore,these vector measures are completely perpendicular to each other. 相似文献
14.
Laurent Bartholdi 《Israel Journal of Mathematics》2006,154(1):93-139
We develop the theory of “branch algebras”, which are infinite-dimensional associative algebras that are isomorphic, up to
taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees.
In particular, for every field
% MathType!End!2!1! we contruct a
% MathType!End!2!1! which
15.
Summary. We prove a functional central limit theorem for stationary random sequences given by the transformations
16.
N. K. Kosovskii T. M. Kosovskaya N. N. Kosovskii 《Vestnik St. Petersburg University: Mathematics》2016,49(2):111-114
Three series of number-theoretic problems with explicitly marked parameters that concerning systems of modulo m congruences and systems of Diophantine equations with solutions from the given segment are proposed. Parameter constraints such that any problem of each series is NP complete when they are met are proved. For any m1 and m2 (m1 < m2 and m1 is not a divisor of m2), the verification problem for the consistency of a system of linear congruences modulo m1 and m2 simultaneously, each containing exactly three variables, is proved to be NP complete. In addition, for any m > 2, the verification problem for the consistency on the subset, containing at least two elements, of the set {0, …, m–1} for the system of linear congruences modulo m, each of which contains exactly three variables, is proved to be NP complete. If P ≠ NP, one cannot replace the term 3-discongruence with the term 2-discongruence in the statement of the theorem. For systems of Diophantine linear equations, each of which contains exactly three variables, the verification problem for their consistency on the given segment of integers is proved to be NP complete. If P ≠ NP, one cannot replace the term 3-equation with the term 2-equation in the statement of the theorem. This problem can also have a simple geometrical interpretation concerning the NP completeness of the verification problem on whether there an integer point of intersection of the given hyperplanes exists that cuts off equivalent segments on three axes and are parallel to other axes inside of a multidimensional cube. The problems of the stated series include practically useful problems. Since the range of values for an integer computer variable can be considered integer values from a segment, if P ≠ NP, theorem 5 proves that any algorithm that solves these systems in the set of numbers of the integer type is nonpolynomial [6]. 相似文献
17.
It is shown that a non-degenerate curve in n satisfies a convergentGroshev theorem with a non-monotonic error function. In otherwords it is shown that if a volume sum converges the set ofpoints lying on the curve which satisfy a Diophantine conditionhas Lebesgue measure zero. 相似文献
18.
Marcel Erné 《Algebra Universalis》1993,30(4):538-580
We study several kinds of distributivity for concept lattices of contexts. In particular, we find necessary and sufficient conditions for a concept lattice to be
19.
A family of transitive modular Lie superalgebras with depth one 总被引:1,自引:0,他引:1
Wen-de LIU~ 《中国科学A辑(英文版)》2007,50(10):1451-1466
The embedding theorem is established for Z-graded transitive modular Lie superalgebras g=(?)satisfying the conditions: (i)g0(?)(g-1)and g0-module g-1 is isomorphic to the natural(?)(g-1)-module; (ii)dim g1=2/3n(2n~2 1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered. 相似文献
20.
We construct a self-avoiding process taking values in the finite Sierpinski gasket, and study its properties. We then study continuum limit processes that are suggested by the statistical mechanics of self-avoiding paths on the pre-Sierpinski gasket. We prove that there are three types of continuum limit processes according to the parameters defining the statistical mechanics of self-avoiding paths:
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