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In the aircraft example, the observer on the ground will observe unsteady flow, and the observers in the aircraft will observe steady flow, with constant streamlines. When possible, fluid dynamicists try to find a reference frame in which the flow is steady, so that they can use experimental methods of creating streaklines to identify the ...
The British imperial system uses a stone of 14 lb, a long hundredweight of 112 lb and a long ton of 2,240 lb. The stone is not a measurement of weight used in the US. The US customary system uses the short hundredweight of 100 lb and short ton of 2,000 lb. Where these systems most notably differ is in their units of volume.
In quantum mechanics, the measurement problem is the problem of definite outcomes: quantum systems have superpositions but quantum measurements only give one definite result. [ 1 ] [ 2 ] The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states.
Because = everywhere (e.g., see In terms of vector rotation), each streamline corresponds to the intersection of a particular stream surface and a particular horizontal plane. Consequently, in three dimensions, unambiguous identification of any particular streamline requires that one specify corresponding values of both the stream function and ...
For example Euclidean spaces of dimension n, and more generally n-dimensional Riemannian manifolds, naturally have the structure of a metric measure space, equipped with the Lebesgue measure. Certain fractal metric spaces such as the Sierpiński gasket can be equipped with the α-dimensional Hausdorff measure where α is the Hausdorff dimension .
A set of base units for a system of measurement is a conventionally chosen set of units, none of which can be expressed as a combination of the others and in terms of which all the remaining units of the system can be expressed. [5] For example, units for length and time are normally chosen as base units.
The International System of Units, internationally known by the abbreviation SI (from French Système international d'unités), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official status in nearly every country in the world, employed in science ...
An example of a measure on the real line with its usual topology that is not outer regular is the measure where () =, ({}) =, and () = for any other set .; The Borel measure on the plane that assigns to any Borel set the sum of the (1-dimensional) measures of its horizontal sections is inner regular but not outer regular, as every non-empty open set has infinite measure.