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Mapping the nonzero digits to the alphabet and zero to the space is occasionally used to provide checksums for alphabetic data such as personal names, [54] to provide a concise encoding of alphabetic strings, [55] or as the basis for a form of gematria. [56] Compact notation for ternary. 28: Months timekeeping. 30: Trigesimal
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
Base36 is a binary-to-text encoding scheme that represents binary data in an ASCII string format by translating it into a radix-36 representation. The choice of 36 is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z (the ISO basic Latin alphabet). Each base36 digit needs less than 6 ...
The Franklin system is another Schauder basis for C([0, 1]), [12] and it is a Schauder basis in L p ([0, 1]) when 1 ≤ p < ∞. [13] Systems derived from the Franklin system give bases in the space C 1 ([0, 1] 2) of differentiable functions on the unit square. [14] The existence of a Schauder basis in C 1 ([0, 1] 2) was a question from Banach ...
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).
The classical normal basis theorem states that there is an element such that {():} forms a basis of K, considered as a vector space over F. That is, any element α ∈ K {\displaystyle \alpha \in K} can be written uniquely as α = ∑ g ∈ G a g g ( β ) {\textstyle \alpha =\sum _{g\in G}a_{g}\,g(\beta )} for some elements a g ∈ F ...
Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured data, possibly in high-dimensional spaces. The interpolant takes the form of a weighted sum of radial basis functions .
A projective basis is + points in general position, in a projective space of dimension n. A convex basis of a polytope is the set of the vertices of its convex hull. A cone basis [5] consists of one point by edge of a polygonal cone. See also a Hilbert basis (linear programming).