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The upper envelope or pointwise maximum is defined symmetrically. For an infinite set of functions, the same notions may be defined using the infimum in place of the minimum, and the supremum in place of the maximum. [1] For continuous functions from a given class, the lower or upper envelope is a piecewise function whose pieces are from the ...
The envelope thus generalizes the concept of a constant amplitude into an instantaneous amplitude. The figure illustrates a modulated sine wave varying between an upper envelope and a lower envelope. The envelope function may be a function of time, space, angle, or indeed of any variable. Envelope for a modulated sine wave.
In mathematics, the lower convex envelope ˘ of a function defined on an interval [,] is defined at each point of the interval as the supremum of all convex functions that lie under that function, i.e.
In geometry, an envelope of a planar family of curves is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope. Classically, a point on the envelope can be thought of as the intersection of two " infinitesimally adjacent" curves, meaning the limit of intersections of ...
The convex hull or lower convex envelope of a function on a real vector space is the function whose epigraph is the lower convex hull of the epigraph of . It is the unique maximal convex function majorized by . [30]
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A Davenport–Schinzel sequence of order 3 formed by the lower envelope of line segments. The lower envelope of a set of functions ƒ i (x) of a real variable x is the function given by their pointwise minimum: ƒ(x) = min i ƒ i (x). Suppose that these functions are particularly well behaved: they are all continuous, and any two of them are ...
Real estate investing has historically seen high returns. Residential homes typically have lower returns than commercial properties, but they can still be valuable assets in many investment...