Although the above argument shows that \ varphi does not exist as a random element of H ^ 1 ( \ Omega ), it still could be that it is a random function on \ Omega in some larger function space.
32.
To create an AND-construction, we define a new family \ mathcal G of hash functions, where each function is constructed from random functions h _ 1, . . ., h _ k from \ mathcal F.
33.
To create an OR-construction, we define a new family \ mathcal G of hash functions, where each function is constructed from random functions h _ 1, . . ., h _ k from \ mathcal F.
34.
Matheron presented his " Stationary Random Function " at the first colloquium on geostatistics in the USA . He called on Brownian motion to conjecture the continuity of his Riemann integral but did not explain what Brownian motion and ore deposits have in common.
35.
Then, the random function with probability density proportional to \ exp (-H ( \ varphi ) ) with respect to the Lebesgue measure on \ R ^ { V \ setminus U } is called the discrete GFF with boundary " U ".
36.
It should be noted that a Kolmogorov random function has no representation smaller than a lookup table that contains a ( random ) value corresponding to each point in the search space; " any " function that can be expressed more compactly is, by definition, not Kolmogorov random.
37.
As the name suggests, CCM mode combines the well known CBC-MAC with the well known size block cipher, and for any size cryptographically strong pseudo-random function ( since in both counter mode and CBC-MAC, the block cipher is only ever used in one direction ).
38.
In the theory of hyper-random phenomena, the main mathematical entities ( models ) are hyper-random events, hyper-random variables, and hyper-random functions, which are, respectively, sets of non-interconnected random events, random variables, and stochastic functions considered as a whole.
39.
Basic mathematical objects ( models ) of it are " hyper-random phenomena " ( in particular " hyper-random events, hyper-random variables, and hyper-random functions " ) that represent " sets of unlinked random objects " regarded in complex as a comprehensive whole.
40.
Where \ mathbf { x } = \ { x _ i | 1 \ le i \ le k \ } is the set of unknowns, the f _ i and g _ i are arbitrary functions and the \ eta _ m are random functions of time, often referred to as " noise terms ".
