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mathematics, moduli of smoothness are used to quantitatively measure smoothness of functions. Moduli of smoothness generalise modulus of continuity and are...

exactly two square roots. The square of the absolute value of a complex number is called its absolute square, squared modulus, or squared magnitude.[better source needed]...

value of function's best approximation by algebraic or trigonometric polynomials in terms of the modulus of continuity or modulus of smoothness of the function...

‖ . {\displaystyle \|x+y\|+\|x-y\|\leq 2+\epsilon \|y\|.} The modulus of smoothness of a normed space X is the function ρX defined for every t > 0 by...

carbide has an elastic modulus of approximately 400 GPa and a shear modulus of 188 GPa. Tool bits without tungsten content can be made of titanium carbide in...

is Young's modulus. This is similar to the expression for shear waves, save that Young's modulus replaces the shear modulus. This speed of sound for pressure...

uses a prime modulus p (with no trapdoor), and its security proof relies on the hardness of finding discrete logarithms of very smooth numbers modulo p...

the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects....

modulus of convexity and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense, the modulus of...

range of 0.5 to 0.9 MPa for articular cartilage, and the Young’s Modulus, which is typically 0.45 to 0.80 MPa. The aggregate modulus is “a measure of the...

and mechanical properties. Both values of hardness and related modulus like reduced modulus (Er) or elastic modulus (E) will significantly increase through...

values both of Young's modulus and of the shear modulus of elasticity. This contrasts with most liquids or fluids, which have a low shear modulus, and typically...

constant by the maximum modulus principle. Now if we had a holomorphic embedding of M into Cn, then the coordinate functions of Cn would restrict to nonconstant...

bundles have a high specific modulus of 2.07– 4.05 MPa⋅m3/kg, and their overall properties are improved when a high ratio of their cross sectional area...

arithmetic progression with modulus 9. In an arithmetic progression, all the numbers have the same remainder when divided by the modulus; in this example, the...

applied to study the modulus of silver nanowires, and again the modulus was found to be 88 GPa, very similar to the modulus of bulk Silver (85 GPa) These...

of the spring is thereby subjected to a bending moment, either reducing or increasing the helical radius. In this mode, it is the Young's Modulus of the...

scaling factor of the Haar measure, there exists a function Δ {\displaystyle \Delta } from the group to the positive reals, called the Haar modulus, modular...

used in many types of instruments for fingerboards, tailpieces, tuning pegs, and so forth due to its attractive appearance, smoothness to the touch, hardness...

smallest such bound is called the Lipschitz constant of the function (and is related to the modulus of uniform continuity). For instance, every function...