Complex modulus information

Complex modulus may refer to: Modulus of complex number, in mathematics, the norm or absolute value, of a complex number: | x + i y | = x 2 + y 2 {\displaystyle...

Dynamic modulus (sometimes complex modulus) is the ratio of stress to strain under vibratory conditions (calculated from data obtained from either free...

French, specifically for the complex absolute value, and it was borrowed into English in 1866 as the Latin equivalent modulus. The term absolute value has...

(strain) to other kinds of stress: the shear modulus describes the response to shear stress, and Young's modulus describes the response to normal (lengthwise...

the complex modulus. The temperature of the sample or the frequency of the stress are often varied, leading to variations in the complex modulus; this...

Look up modulus in Wiktionary, the free dictionary. Modulus is the diminutive from the Latin word modus meaning measure or manner. It, or its plural moduli...

multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes called the Argand plane or Gauss plane. In complex analysis,...

mathematics, the maximum modulus principle in complex analysis states that if f {\displaystyle f} is a holomorphic function, then the modulus | f | {\displaystyle...

_{\mathrm {r} }^{2}+{\tilde {\varepsilon }}_{\mathrm {r} }^{2}}}} is the complex modulus. The wave impedance of a plane electromagnetic wave in a non-conductive...

only fixed points of conjugation. Conjugation does not change the modulus of a complex number: | z ¯ | = | z | . {\displaystyle \left|{\overline {z}}\right|=|z|...

In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following,...

in 1799.——S. Confalonieri (2015) Argand 1814, p. 204 defines the modulus of a complex number but he doesn't name it: "Dans ce qui suit, les accens, indifféremment...

polymers, such as rubber bands. The modulus is strongly dependent on temperature. Viscoelasticity describes a complex time-dependent elastic response, which...

be shown directly, or by using the multiplicative property of the modulus of complex numbers. The units of the ring of Gaussian integers (that is the Gaussian...

often taken over the complex numbers. The complex plane denoted by C is equipped with a notion of magnitude, the complex modulus |z|, which is defined...

materials. This is done by deriving the complex modulus (G*) from the storage modulus (elastic response, G') and loss modulus (viscous behaviour, G") yielding...

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...

always be diagonalized over the complex numbers to exhibit a full set of eigenvalues, all of which must have (complex) modulus 1. The inverse of every orthogonal...

with the provision that | ⋅ | {\displaystyle |\cdot |} denotes the complex modulus, i.e. | z | = z ∗ z {\displaystyle |z|={\sqrt {z^{*}z}}} . If ( a n...

manifold M: any holomorphic function on it is constant by the maximum modulus principle. Now if we had a holomorphic embedding of M into Cn, then the...

imaginary part, and modulus of the exponential function z = Re(ex + iy) z = Im(ex + iy) z = |ex + iy| Considering the complex exponential function as...

equations to common viscoelastic terms we get the storage modulus, G', and the loss modulus, G". G = G ′ + i G ″ {\displaystyle G=G'+iG''} A viscoelastic...