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1.1The positive square root of the sum of the squares of the real and imaginary parts of a complex number.
‘The concept of the modulus of a complex number is also due to Argand but Cauchy, who used the term later, is usually credited as the originator this concept.’
2A constant factor or ratio.
‘Such a material can be characterized by simple moduli (ratios of stress to strain): Young's modulus, E, and Poisson's ratio,.’
‘A cost from a cost function is calculated according to a constant modulus algorithm.’
‘Thus, they are characterized by two elastic constants, Young modulus E and Poisson ratio v.’
‘For example, in this case, it is easier to try to factor the modulus N than to perform an exhaustive key search on all possible decryption keys.’
2.1A constant indicating the relation between a physical effect and the force producing it.
‘The crosshatched regions in Fig.1 indicate the modulus of resilience for each steel.’
‘It is interesting to note that a considerable group of important structural materials have nearly the same ratio of modulus of elasticity to density.’
‘Flexible carbon fiber electrode with low modulus and high electrical conductivity, battery employing the carbon fiber electrode, and method of manufacture’
‘While heat treatment had little, if any effect of the modulus of elasticity of the composites, it did affect the transition into plastic flow.’
‘The modulus of elasticity in shear, or modulus of rigidity, is about 16 GPa, while Poisson's ratio is 0.35.’
3A number used as a divisor for considering numbers in sets, numbers being considered congruent when giving the same remainder when divided by a particular modulus.
‘This is known as using arithmetic modulo 26, and 26 is known as the modulus.’
‘His first notebook was on hypergeometric series, continued fractions, singular moduli, and many branches of number theory.’
‘Daemen and Rijmen picked x 8 + 1 as the modulus polynomial because it was simple-as simple as one could get.’
Origin
Mid 16th century (denoting an architectural unit of length): from Latin, literally ‘measure’, diminutive of modus.