scholarly journals A characterization of quaternionic Kleinian groups in dimension 2 with complex trace fields

2018 ◽  
Vol 18 (2) ◽  
pp. 957-974 ◽  
Author(s):  
Sungwoon Kim ◽  
Joonhyung Kim
Keyword(s):  
Kleinian Groups ◽  
Dimension 2 ◽  
Trace Fields

Derivations and Valuation Rings

2013 ◽  
Vol 56 (1) ◽  
pp. 31-38
Author(s):  
P. Fortuny Ayuso
Keyword(s):  
Complete Characterization ◽  
Valuation Rings ◽  
Dimension 2

AbstractA complete characterization of valuation rings closed for a holomorphic derivation is given, following an idea of Seidenberg, in dimension 2.

Zonoids, linear dependence, and size-biased distributions on the simplex

2003 ◽  
Vol 35 (04) ◽  
pp. 871-884 ◽  
Author(s):  
Marco Dall'Aglio ◽  
Marco Scarsini
Keyword(s):  
Random Vector ◽  
Linear Dependence ◽  
Copula Model ◽  
Convex Order ◽  
Dimension 2 ◽  
Concordance Order ◽  
Biased Distribution

The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it does characterize the size-biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.

Commensurability classes of arithmetic Kleinian groups and their Fuchsian subgroups

1987 ◽  
Vol 102 (2) ◽  
pp. 251-257 ◽  
Author(s):  
C. MacLachlan ◽  
A. W. Reid
Keyword(s):  
Kleinian Groups ◽  
Fuchsian Groups ◽  
Arithmetic Groups ◽  
Quaternion Algebras ◽  
Isomorphism Classes ◽  
Similar Characterization ◽  
One To One

Arithmetic Fuchsian and Kleinian groups can all be obtained from quaternion algebras (see [2,12]). In a series of papers ([8,9,10,11]), Takeuchi investigated and characterized arithmetic Fuchsian groups among all Fuchsian groups of finite covolume, in terms of the traces of the elements in the group. His methods are readily adaptable to Kleinian groups, and we obtain a similar characterization of arithmetic Kleinian groups in §3. Commensurability classes of Kleinian groups of finite co-volume are discussed in [2] and it is shown there that the arithmetic groups can be characterized as those having dense commensurability subgroup. Here the wide commensurability classes of arithmetic Kleinian groups are shown to be approximately in one-to-one correspondence with the isomorphism classes of the corresponding quaternion algebras (Theorem 2) and it easily follows that there are infinitely many wide commensurability classes of cocompact Kleinian groups, and hence of compact hyperbolic 3-manifolds.

Zonoids, linear dependence, and size-biased distributions on the simplex

2003 ◽  
Vol 35 (4) ◽  
pp. 871-884 ◽  
Author(s):  
Marco Dall'Aglio ◽  
Marco Scarsini
Keyword(s):  
Random Vector ◽  
Linear Dependence ◽  
Copula Model ◽  
Convex Order ◽  
Dimension 2 ◽  
Concordance Order ◽  
Biased Distribution

The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it does characterize the size-biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.

scholarly journals Some Properties of the Strong Primitivity of Nonnegative Tensors

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lihua You ◽  
Yafei Chen ◽  
Pingzhi Yuan
Keyword(s):  
Nonnegative Tensors ◽  
Dimension 2

We show that an order m dimension 2 tensor is primitive if and only if its majorization matrix is primitive, and then we obtain the characterization of order m dimension 2 strongly primitive tensors and the bound of the strongly primitive degree. Furthermore, we study the properties of strongly primitive tensors with n≥3 and propose some problems for further research.

TOPOLOGICAL CHARACTERIZATION OF STEIN MANIFOLDS OF DIMENSION >2

1990 ◽  
Vol 01 (01) ◽  
pp. 29-46 ◽  
Author(s):  
YAKOV ELIASHBERG
Keyword(s):  
Complex Structure ◽  
Topological Characterization ◽  
Stein Manifolds ◽  
Complex Dimension ◽  
Dimension 2

In this paper I give a completed topological characterization of Stein manifolds of complex dimension >2. Another paper (see [E14]) is devoted to new topogical obstructions for the existence of a Stein complex structure on real manifolds of dimension 4. Main results of the paper have been announced in [E13].

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