Search results
Results From The WOW.Com Content Network
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 ...
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem. [1] As we change parameters of the objective, the envelope theorem shows that, in a certain sense, changes in the optimizer of the objective do not contribute to the change in ...
A back-of-the-envelope calculation is a rough calculation, typically jotted down on any available scrap of paper such as an envelope. It is more than a guess but less than an accurate calculation or mathematical proof. The defining characteristic of back-of-the-envelope calculations is the use of simplified assumptions.
In physics and engineering, the envelope of an oscillating signal is a smooth curve outlining its extremes. [1] 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 ...
Bregman–Minc inequality (discrete mathematics) Cauchy-Binet formula (linear algebra) Cayley–Hamilton theorem (Linear algebra) Dimension theorem for vector spaces (vector spaces, linear algebra) Euler's rotation theorem ; Exchange theorem (linear algebra) Gamas's Theorem (multilinear algebra) Gershgorin circle theorem (matrix theory)
For convex functions or quasiconvex functions, the upper envelope is again convex or quasiconvex. The lower envelope is not, but can be replaced by the lower convex envelope to obtain an operation analogous to the lower envelope that maintains convexity. The upper and lower envelopes of Lipschitz functions preserve the property of being Lipschitz.
In category theory and related fields of mathematics, an envelope is a construction that generalizes the operations of "exterior completion", like completion of a locally convex space, or Stone–Čech compactification of a topological space.
The postage stamp problem (also called the Frobenius Coin Problem and the Chicken McNugget Theorem [1]) is a mathematical riddle that asks what is the smallest postage value which cannot be placed on an envelope, if the latter can hold only a limited number of stamps, and these may only have certain specified face values.