In the case of an arithmetic manifold whose fundamental groups is commensurable with that of a manifold derived from a quaternion algebra over a number field F the invariant trace field equals F.
32.
The image of two spools, however, is of a homogeneous and commensurable thread, whereas, according to Bergson, no two moments can be the same, hence duration is heterogeneous.
33.
They used their results on weak-commensurability to obtain results on length-commensurable and isospectral arithmetic locally symmetric spaces, see [ 17 ], [ 18 ] and [ 19 ].
34.
If \ Gamma is an arithmetic Fuchsian group then k \ Gamma and A \ Gamma together are a number field and quaternion algebra from which a group commensurable to \ Gamma may be derived.
35.
Yet another is relativist ( Cultural relativism ), which sees different cultural groups as employing different conceptual schemes that are not necessarily compatible or commensurable, nor more or less in accord with external reality.
36.
No Doppelgangers applies in both the Conversation Theory's kinematic domain ( bounded by beginnings and ends ) where times are commensurable and in the eternal kinetic Interactions of Actors domain where times are incommensurable.
37.
If " this " constant is adopted as the Unit, instead of an individual Real Measure, then what were two incommensurable series are now made commensurable with each other in a common denominator.
38.
Although the Asean working group on forestry has been meeting for almost five years, Dr Lim said real achievement with regard to co-operation in forestry had not been commensurable with the agreed programmes and activities.
39.
Note that a theorem of Margulis implies that a lattice in \ mathrm { PSL } _ 2 ( \ mathbb C ) is arithmetic if and only if it is commensurable to infinitely many maximal Kleinian groups.
40.
Because no quantitative values were assigned to magnitudes, Eudoxus was then able to account for both commensurable and incommensurable ratios by defining a ratio in terms of its magnitude, and proportion as an equality between two ratios.
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