The product numerical range can be considered as a particular case of the decomposable numerical range defined for operators acting on a tensor product Hilbert space.
32.
In particular, Marcus introduced the notion of decomposable numerical range , the properties of which are a subject of considerable interest.
33.
The measures are both decomposable, showing that Tonelli's theorem fails for decomposable measures ( which are slightly more general than ?-finite measures ).
34.
The measures are both decomposable, showing that Tonelli's theorem fails for decomposable measures ( which are slightly more general than ?-finite measures ).
35.
Algorithmically computing the Grushko decomposition for specific classes of groups is a difficult problem which primarily requires being able to determine if a given group is freely decomposable.
36.
Since a general mixed dyadic tensor is a linear combination of decomposable tensors of the form f \ otimes v, the explicit formula for the dyadic case follows : let
37.
It is not enough to simply heap up soft, easily-decomposable green wastes from the garden, such as leaves and grass cuttings, into an unpleasant, soggy pile.
38.
It includes identifying who is poor by considering the range of deprivations they suffer, and aggregating that information to reflect societal poverty in a way that is robust and decomposable.
39.
In S-matrix theory, the S-matrix relates the infinite past to the infinite future in one step, without being decomposable into intermediate steps corresponding to time-slices.
40.
*A sum of indecomposable random variables is necessarily decomposable ( as it is a sum ), and in fact may a fortiori be an infinitely divisible distribution ( not just decomposable as the given sum ).
