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Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
The same direct relationship applies to gases and vapors diluted in air for example. Although, thorough mixing of gases and vapors may not be as easily accomplished. [citation needed] For example, if there are 10 grams of salt (the solute) dissolved in 1 litre of water (the solvent), this solution has a certain salt concentration . If one adds ...
The most prominent example of the classical two-body problem is the gravitational case (see also Kepler problem), arising in astronomy for predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars. A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful ...
For example, it was used in the analysis of the Markov equation back in 1879 and in the 1953 paper of Mills. [ 1 ] In 1988, the method came to the attention to mathematical olympiad problems in the light of the first olympiad problem to use it in a solution that was proposed for the International Mathematics Olympiad and assumed to be the most ...
In general, if the separation principle applies, then filtering also arises as part of the solution of an optimal control problem. For example, the Kalman filter is the estimation part of the optimal control solution to the linear-quadratic-Gaussian control problem.
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A new type of quarterback. Coming into the draft, Daniels was heralded for his dual-threat ability, providing as much threat as a rusher as he does through the air.
Hilbert's tenth problem: the problem of deciding whether a Diophantine equation (multivariable polynomial equation) has a solution in integers. Determining whether a given initial point with rational coordinates is periodic, or whether it lies in the basin of attraction of a given open set, in a piecewise-linear iterated map in two dimensions ...