Sentence examples for its characteristic function from inspiring English sources

If every real number is equivalently represented by its characteristic function, then it is easy to know that (mathbb{R}subset mathbb{R}_{mathcal{F}}).

It is defined as a compound Poisson process such that its characteristic function ψV t)(z) is given by [24], begin{array}{*{20}l} psi_{V t)} z) &:= mathrm{E}left[e^{izV t)}right] notag &= sum_{j=0}^{infty} e^{-t}frac{t^{,j}}{j!}left widehat{sigma} z) right)^{,j} notag &= exp(t widehat{sigma} z -1)), quad z in mat widehat{sigma} z -1

This paper presents an efficient probability analysis method using Fast Fourier transform taking into account that (1) a probability density function and its characteristic function are a pair of Fourier transforms, and (2) the characteristic function of the sum of statistically independent random variables is given by the product of the characteristic functions of each random variable.

Its characteristic function (CHF) can be obtained by (18).

Defining a power variable, its characteristic function [15] is given by (20).

For a μ-measurable set E, (chi_{E}) denotes its characteristic function.

The matter of a substance is the stuff it is composed of; the form is the way that stuff is put together so that the whole it constitutes can perform its characteristic functions.

It is interesting to note also the pass band ripple (Figure 7) of the characteristics from which the " " filter is the worst due to the discontinuity already in first derivative of its frequency characteristic function (7).

For the symmetry (V_{0}), its Lie characteristic function is W=- u_{x} and the conservation laws for Eq. (1) associated with (V_{0}) are begin{aligned}& X=uu_{t}-uR+R^{2}t-Rtu_{t}, & T=Rtu_{x}-u_{x}u.

This versatility of CD38 and its characteristic to function as dimers, multimers, or as part of multi-protein complexes makes it difficult to fully comprehend its biology.

The muscle, in particular the striated muscle, is well known by its unique structure consisting of a very well organized cytoskeleton that enables its characteristic contractile function.