This approach provides a closed-form explicit representation of \ check \ chi _ \ Omega ( \ cdot ) for general lattices, including optimal sampling lattices.
12.
One instance of this algorithm is the original Davis Putnam algorithm that was later refined into the DPLL algorithm that removed the need for explicit representation of the resolvents.
13.
Thus, since the liberation of the camps, artists who have wanted to express the Holocaust in their art have often chosen abstraction or symbolism, thus avoided any explicit representations.
14.
Such methods usually employ implicit solvation, which provides a continuous approximation of a solvent bath for a single protein molecule without necessitating the explicit representation of individual solvent molecules.
15.
In subsequent constitution making, federal states have often adopted bicameralism, and the solution remains popular when regional differences or sensitivities require more explicit representation, with the second chamber representing the constituent states.
16.
They used integral operators to obtain explicit representations, in terms of Painlev?transcendents, of the limiting distributions of the largest and smallest eigenvalues in many models of random matrices ( see Fredholm determinants ).
17.
This is largely a matter of taste, depending on whether one wishes to maintain an integer set of coefficients or prefers tighter formulas if the orthogonalization is involved . ) The explicit representation is
18.
A holistic perception of the face does not involve any explicit representation of local features ( i . e ., eyes, nose, mouth, etc . ), but rather considers the face as a whole.
19.
This results in the simulation effect of "'marked transformations "'that allow for the explicit representation of parallel processing, multiprocessing, and the implicit representation of deterioration of objects all unique to dualistic Petri nets.
20.
Artificial Intelligence and Law applications using an explicit representation of norms range from checking the compliance of business processes and the automatic execution of smart contracts to legal expert systems advising people on legal matters.
