It should not be confused with a consolidated city-county[?], which is both a city and a county under the laws of the State (such as Denver, Colorado).
It should also not be confused with a city-state, a city that is fully independent and part of no other nation. (such as Singapore)
In the Commonwealth of Virginia, all cities are by law independent cities. In other states, they are relatively rare.
List of independent cities: (partial, add as known)
... of the DFT, the discrete cosine transform.)
(iii) Discrete Fourier transforms, especially in multidimensions, are often used to solve partial differential equations. ...
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