Sentence examples for functional laws from inspiring English sources

In this paper, the authors obtain the strong approximations, the laws of the single logarithm, the functional laws of the single logarithm, and the limit law of the single logarithm for linear processes generated by arrays of independent and identically distributed random variables, and they show that they are all equivalent under the same moment conditions.

We need only augment the theory to include variables for the precise structural conditions in which the novel phenomena occur, and then draw up more complex functional laws of dynamical evolution that specify the 'ordinary' behavior when the new variables are not satisfied and the 'novel' behavior when the variables are satisfied.

"You can't legislate fine lines — that's just not a functional law".

But it cannot yet be satisfied with its efforts to help build a functional, law-abiding society there.

Lu and Qiu [3] obtained the functional law of the iterated logarithm for the one-side linear processes as follows.

And simplicity may militate in favour of this functional law being continuous, so even irrational-valued probabilities may be assigned.

On the other hand, since Chung's law and Strassen's functional law of the iterated logarithm appeared, the functional law of the iterated logarithm and its rates for some classes of Gaussian processes have been discussed by many authors (see, for example, Csörgö and Révész [9], Lin et al. [10], Dudley and Norvaiša [7], Malyarenko [11]).

The chances of a rare atom decaying in various time intervals may be determined by a more pervasive functional law, in which decay chances are given for a far wider range of atoms by plugging in a range of settings of some other magnitude (e.g., atomic number).

Then the process model of sustainable product function innovation was put forward by integrating sustainable design criteria, functional evolution laws and TRIZ into traditional function design.

Power-law distributions are known to have statistical self-similarity resulting in the probability density function obeying a functional scaling law which is a renormalization group property.

Finally, take (P^{epsilon}_{u_{0},n_{0}}) to be the probability density functional or law of the set of trajectories in ({mathcal{Y}}_{u_{0}}).