共查询到20条相似文献,搜索用时 15 毫秒
1.
B.A.F. Wehrfritz 《Journal of Pure and Applied Algebra》2010,214(10):1898-1900
Let H be a subgroup of the polycyclic-by-finite group G and denote the automorphism group of G by Γ. We prove that there exists an integer d such that in the poset {?γ∈∑Hγ:∑ a subset of Γ} of all intersections of images Hγ of H under Γ, chains have length at most d. In particular the poset satisfies the minimal condition. This extends and improves a theorem of A.H. Rhemtulla. We also provide a very different proof of Rhemtulla’s theorem. 相似文献
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In this note we consider the Lüroth expansion of a real number, and we study the Hausdorff dimension of a class of sets defined in terms of the frequencies of digits in the expansion. We also study the speed at which the approximants obtained from the Lüroth expansion converge. In addition, we describe the multifractal properties of the level sets of the Lyapunov exponent, which measures the exponential speed of approximation obtained from the approximants. Finally, we describe the relation of the Lüroth expansion with the continued fraction expansion and the β-expansion. We remark that our work is still another application of the theory of dynamical systems to number theory. 相似文献
3.
Lu-Ming Shen 《Journal of Mathematical Analysis and Applications》2007,329(2):1440-1445
We introduce the error-sum function of Lüroth series. Some elementary properties of this function are studied. We also determine the Hausdorff dimension of the graph of this function. 相似文献
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B. Lindström 《Combinatorica》1985,5(3):237-239
The points of an algebraic combinatorial geometry are equivalence classes of transcendentals over a fieldk; two transcendentals represent the same point when they are algebraically dependent overk. The points of an algebraically closed field of transcendence degree two (three) overk are the lines (resp. planes) of the geometry.
We give a necessary and sufficient condition for two coplanar lines to meet in a point (Theorem 1) and prove the converse
of Desargues’ theorem for these geometries (Theorem 2). A corollary: the “non-Desargues” matroid is non-algebraic.
The proofs depend on five properties (or postulates). The fifth of these is a deep property first proved by Ingleton and Main
[3] in their paper showing that the Vámos matroid is non-algebraic. 相似文献
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Aequationes mathematicae - 相似文献
7.
Xiang-dong Hou 《Linear algebra and its applications》2007,426(1):214-227
In a previous paper [X. Hou, K.H. Leung, Q. Xiang, A generalization of an addition theorem of Kneser, J. Number Theory 97 (2002) 1-9], the following result was established: let E⊂K be fields such that the algebraic closure of E in K is separable over E. Let A,B be E-subspaces of K such that 0<dimEA<∞ and 0<dimEB<∞. Then dimEAB?dimEA+dimEB-dimEH(AB), where AB is the E-space generated by {ab:a∈A,b∈B} and H(AB)={x∈K:xAB⊂AB}. The separability assumption was essential in the proof of this result. However, even without the separability assumption, no counterexample is known. The present paper shows that no counterexample can be found if dimEA?5. 相似文献
8.
In this paper we study the concept of
-isologisms among the
-marginal extensions of groups, with respect to a given variety of groups
. We also give some equivalent conditions under which two extensions
are
-isologic.
Received: 9 January 2002 相似文献
9.
A recent comparison result ([3]) allows to get pointwise estimates for the solution of the Dirichlet problem for linear second–order elliptic equations in terms of the solution of a suitable "symmetrized" problem. In this paper we prove that equality is achieved only in the spherically symmetric situation. 相似文献
10.
William Kerby 《Aequationes Mathematicae》1986,31(1):247-252
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Subject to the continuum hypothesis, the Haar measure on a compact group of topological weight 2 admits a Baire strong lifting. 相似文献
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Mowaffaq Hajja 《代数通讯》2013,41(3):761-776
It is shown in [5, Theorem 3] that if s is an algebraic automorphism of a k-vector space V with minimalpolynomial μ(T) ∈ K[T], then the extension σ of s to a k-automorphism of the field of quotients of the symmetric k-algebra k(V) of V is completely determined by μ(T) (and dimkV). In Theorem 4 of this article, we show that σ is almost completely determined by the radical μ0(T) of μ(T) and we see in particular that if μ(T) is separable then the rationality of (the fixed field of) σ depends only on μ0(T). In Theorem 5, the rationality of σ is established under certain assumptions on the Galois group of μ0(T). 相似文献
17.
Sikui Wang 《Journal of Mathematical Analysis and Applications》2011,374(1):197-200
In this paper the sum-level sets for Lüroth expansion are introduced. We prove that the Lebesgue measure of these sum-level sets decays to zero as the level tends to infinity. 相似文献
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M. Van den Bergh 《Proceedings of the American Mathematical Society》2004,132(10):2857-2858
We give a proof avoiding spectral sequences of Deligne's decomposition theorem for objects in a triangulated category admitting a Lefschetz homomorphism.
20.
In this paper a new explicit upper bound in Schottky's theoremis given, which is sharp in a certain sense. 相似文献