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A bounded operator: is not a bounded function in the sense of this page's definition (unless =), but has the weaker property of preserving boundedness; bounded sets are mapped to bounded sets (). This definition can be extended to any function f : X → Y {\displaystyle f:X\rightarrow Y} if X {\displaystyle X} and Y {\displaystyle Y} allow for ...
Maximum point-blank range is principally a function of a cartridge's external ballistics and target size: high-velocity rounds have long point-blank ranges, while slow rounds have much shorter point-blank ranges. Target size determines how far above and below the line of sight a projectile's trajectory may deviate.
In other words, all the functions in the family must be locally bounded, and around each point they need to be bounded by the same constant. This definition can also be extended to the case when the functions in the family U take values in some metric space, by again replacing the absolute value with the distance function.
A set with an upper (respectively, lower) bound is said to be bounded from above or majorized [1] (respectively bounded from below or minorized) by that bound. The terms bounded above ( bounded below ) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.
A subset S of a metric space (M, d) is bounded if there exists r > 0 such that for all s and t in S, we have d(s, t) < r. The metric space (M, d) is a bounded metric space (or d is a bounded metric) if M is bounded as a subset of itself. Total boundedness implies boundedness. For subsets of R n the two are equivalent.
A densely defined symmetric [clarification needed] operator T on a Hilbert space H is called bounded from below if T + a is a positive operator for some real number a. That is, Tx|x ≥ −a ||x|| 2 for all x in the domain of T (or alternatively Tx|x ≥ a ||x|| 2 since a is arbitrary). [8] If both T and −T are bounded from below then T is ...
Chilling surveillance video captured the moment a business owner in crime-ridden San Francisco was shot seven times at point-blank range in a random attack. Martin Olive, 47, had been taking a ...
A standard definition of an ellipse is the set of points for which the sum of a point's distances to two foci is a constant; if this constant equals the distance between the foci, the line segment is the result. A complete orbit of this ellipse traverses the line segment twice. As a degenerate orbit, this is a radial elliptic trajectory.