The frames definitions are reduced to apparent translations of the base frame and the computation is replaced with choosing an operator from a collection of six operators that cover all transformation possibilities.
A cochain mapping of (L·,d L )into (M·,d M ) means any collection of operators f i ∈ L ( L i, M i ), i ∈ Z Open image in new window such that d M i f i ∼ f i + 1 d L i Open image in new window for all i ∈ Z Open image in new window.
Let {T1,…,TJ} be a collection of differential operators with constant coefficients on the torus Tn.
The language of poly-modal or dynamic logic introduces a collection of modal operators □i, one for each program i (Harel, 1984).
We employ a collection of difference operators to capture signal variation at varying scales.
For example, if the operator in question is essentially a collection of m Schrödinger operators intertwined through boundary conditions then every incidence ray after reflection generates up to m reflected rays and we have branching Hamiltonian billiards.
The advanced call center operation of the 21st century consists of many elements and is not a collection of phones, computers, and operators only.
Recall that the Lorentz ideal C−p is the collection of operators A satisfying the condition ‖A‖p−="∑j="1∞j−(p−1)/psj(A)<∞.
We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators.
Travel Alliance Partners, a collection of 33 North American tour operators, put together a catalog of 64 guaranteed-to-run tours for 2006 that was so successful it rolled out another one for 2007 with 92 trips from its members.
Now if there exists a collection of these individual fractional-order operators driven by the same input, then their outputs can be combined F ( s ) = k 1 s q 1 X ( s ) + k 2 s q 2 X ( s ) + k 3 s q 3 X ( s ) + k 4 s q 4 X ( s ) + ⋯ = ∑ n = 1 N k n s q n X ( s ).
