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Every vector space is a free module, [1] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. Given any set S and ring R, there is a free R-module with basis S, which is called the free module on S or module of formal R-linear combinations of the elements of S.
A sublinear modulus of continuity can easily be found for any uniformly continuous function which is a bounded perturbation of a Lipschitz function: if f is a uniformly continuous function with modulus of continuity ω, and g is a k Lipschitz function with uniform distance r from f, then f admits the sublinear module of continuity min{ω(t), 2r ...
In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle, [1] or extended ideal [2]) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to encode ramification data for abelian extensions of a global field.
Bulk modulus, a measure of compression resistance; Elastic modulus, a measure of stiffness; Shear modulus, a measure of elastic stiffness; Young's modulus, a specific elastic modulus; Modulo operation (a % b, mod(a, b), etc.), in both math and programming languages; results in remainder of a division; Casting modulus used in Chvorinov's rule.
In 1999, Judi Romijn compared two model checkers (CADP and SPIN) on the HAVi interoperability audio-video protocol for consumer electronics. [ 3 ] In 2003, Yifei Dong, Xiaoqun Du, Gerard J. Holzmann, and Scott A. Smolka published a comparison of four model checkers (namely: Cospan, Murphi , SPIN , and XMC) on a communication protocol, the GNU i ...
The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers.
The term "modulus" is borrowed from mathematics (or more specifically, moduli space is borrowed from algebraic geometry), where it is used synonymously with "parameter". The word moduli ( Moduln in German) first appeared in 1857 in Bernhard Riemann 's celebrated paper "Theorie der Abel'schen Functionen".
Both tests are the best of their kind. For the Dini-Lipschitz test, it is possible to construct a function f with its modulus of continuity satisfying the test with O instead of o, i.e. = (). and the Fourier series of f diverges. For the Dini test, the statement of precision is slightly longer: it says that for any function Ω such that