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In numerical analysis and approximation theory, basis functions are also called blending functions, because of their use in interpolation: In this application, a mixture of the basis functions provides an interpolating function (with the "blend" depending on the evaluation of the basis functions at the data points).
Conceptual blending is closely related to frame-based theories, but goes beyond these primarily in that it is a theory of how to combine frames (or frame-like objects). An early computational model of a process called "view application", which is closely related to conceptual blending (which did not exist at the time), was implemented in the 1980s by Shrager at Carnegie Mellon University and ...
Barycentric coordinates are strongly related to Cartesian coordinates and, more generally, affine coordinates.For a space of dimension n, these coordinate systems are defined relative to a point O, the origin, whose coordinates are zero, and n points , …,, whose coordinates are zero except that of index i that equals one.
In particular it is important to assure that for two given line segments, a new line segment can be constructed, such that its length equals the product of lengths of the other two. Similarly one needs to be able to construct, for a line segment of length , a new line segment of length . The intercept theorem can be used to show that for both ...
A mollifier (top) in dimension one. At the bottom, in red is a function with a corner (left) and sharp jump (right), and in blue is its mollified version. In mathematics, mollifiers (also known as approximations to the identity) are particular smooth functions, used for example in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via ...
In mathematics, the exterior algebra or Grassmann algebra of a vector space is an associative algebra that contains , which has a product, called exterior product or wedge product and denoted with , such that = for every vector in .
The "Demystified" series is introductory in nature, for middle and high school students, favoring more in-depth coverage of introductory material at the expense of fewer topics. The "Easy Way" series is a middle ground: more rigorous and detailed than the "Demystified" books, but not as rigorous and terse as the Schaum's series.
Euclid used the method of exhaustion to prove the following six propositions in the 12th book of his Elements. Proposition 2: The area of circles is proportional to the square of their diameters. [3] Proposition 5: The volumes of two tetrahedra of the same height are proportional to the areas of their triangular bases. [4]