If " ? " and hence " M " are matrices rather than scalars this is a problem that in general does not admit an explicit solution.
12.
If " f " and hence " M " are matrices rather than scalars this is a problem that in general does not admit an explicit solution.
13.
At the left is the differential form; at the right is the explicit solution in terms of standard mathematical functions, which follows in this case from the differential form.
14.
Self-reducibility describes the phenomenon that, if we can quickly test whether a SAT instance is solvable, we can almost as quickly find an explicit solution to the instance.
15.
D . Talalaev solved the long-standing problem of the explicit solution for the full set of the quantum commuting conservation laws for the Gaudin model, discovering the following theorem.
16.
The general proof already given seems plausible to me ( although it's not really my area ), but an explicit solution for this particular case may be more convincing.
17.
However, if " A " is ill-conditioned, the explicit solution is a poor choice since it is sensitive to any noise in the data " y ".
18.
Jefimenko's equations ( or the closely related Li�nard Wiechert potentials ) are the explicit solution to Maxwell's equations for the electric and magnetic fields created by any given distribution of charges and currents.
19.
Almost all macroscale models are more complex than this example, in that they have multiple dimensions, lack explicit solutions in terms of standard mathematical functions, and must be understood from their differential forms ."
20.
Robert C . Merton showed that in independently and identically distributed through time, and with a risk-free asset, one can obtain an explicit solution for the demand for the unique optimal portfolio, and that demand is linear in initial wealth.
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