The stretched exponential function f β ( t ) = e − t β {\displaystyle f_{\beta }(t)=e^{-t^{\beta }}} is obtained by inserting a fractional power law into...

In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio...

include the power-law distribution, that is a basis for the stretched exponential function, and parabolic fractal distribution. The King effect has been...

a power law distribution, or less well-known ones such as a stretched exponential function or parabolic fractal distribution, at least approximately for...

spectra. Depending on application, the Fourier transform of the stretched exponential function can be a viable alternative that has one parameter less. For...

charge response corresponds to the stretched exponential function or the Kohlrausch–Williams–Watts (KWW) function, for small time arguments. Cole–Cole...

The gamma function is related to the stretched exponential function. For instance, the moments of that function are ⟨ τ n ⟩ ≡ ∫ 0 ∞ t n − 1 e − ( t τ...

asymmetric broadening. Kohlrausch–Williams–Watts function Fourier transform of stretched exponential function. Curie–von Schweidler law This shows the response...

distribution. Its complementary cumulative distribution function is a stretched exponential function. The Weibull distribution is related to a number of other...

process. The lifetime of oxide cathodes can be evaluated with a stretched exponential function. The survivability of electron emission sources is significantly...

also a characteristic feature of the Fourier transform of the stretched exponential function it has been considered as an approximation of the latter, although...

refer to: The Kohlrausch-Williams-Watts function is the Fourier transform of the stretched exponential function Katosi Water Works, water treatment facility...

distribution function will be real. In the simplest case β = 0 {\displaystyle \beta =0} , the characteristic function is just a stretched exponential function; the...

is the co-discoverer of the Kohlrausch-Williams-Watts [KWW] stretched-exponential function for modelling molecular-relaxation processes in condensed media...

maximum human lifespan to be around 125 years using a modified stretched exponential function for human survival curves. In another study, researchers claimed...

Science at the University of Manchester: co-discoverer of the KWW stretched-exponential function for relaxation phenomena in condensed media and expert on photopolymerised...

Kohlrausch introduced the relaxation phenomena, and used the stretched exponential function to explain relaxation effects of a discharging Leyden jar (capacitor)...

secure cryptographic hash functions but do not usually have a strong connection to practical security. For example, an exponential-time algorithm can sometimes...

tests of the Arrhenius law. Another common modification is the stretched exponential form[citation needed] k = A exp ⁡ [ − ( E a R T ) β ] , {\displaystyle...

be regarded as its norm.] However for another inverse function of the complex exponential function (and not the above defined principal value), the branch...

maps a function from its original function space into another function space via integration, where some of the properties of the original function might...

distributions not only forms an exponential family (EF), but in fact forms a natural exponential family (NEF) with quadratic variance function (NEF-QVF). Many properties...

characteristic function Φ of the probability density function f of a random variable X of continuous type is defined without a negative sign in the exponential, and...

2 , {\textstyle \omega _{1}=\omega _{0}{\sqrt {1-\zeta ^{2}}},} the exponential decay of the underdamped harmonic oscillator is given by λ = ω 0 ζ ....

particular importance in statistical physics when the convex function is an exponential, giving: e E ⁡ [ X ] ≤ E ⁡ [ e X ] , {\displaystyle e^{\operatorname...

distribution Dagum distribution Erlang distribution ExGaussian distribution Exponential power distribution Fréchet distribution Gamma distribution Generalized...

for some function of t {\textstyle t} that goes to zero more rapidly than t 2 / n {\textstyle t^{2}/n} . By the limit of the exponential function ( e x =...

1137/070710111. S2CID 9155618. Laherrère, J.; Sornette, D. (1998). "Stretched exponential distributions in nature and economy: "fat tails" with characteristic...

studies and the history of technology, accelerating change is the observed exponential nature of the rate of technological change in recent history, which may...

which it breaks down, suffering from unavoidable reflections or even exponential growth. One caveat with perfectly matched layers is that they are only...