The Multiple Arbitrary Function Generator ( or MARF ) goes well beyond what a typical sequencer is capable of performing and is capable of acting as an envelope generator, voltage quantizer or tracking generator.
32.
DCTs are also closely related to Chebyshev polynomials, and fast DCT algorithms ( below ) are used in Chebyshev approximation of arbitrary functions by series of Chebyshev polynomials, for example in Clenshaw Curtis quadrature.
33.
However, these definitions characterize distinct classes since there are uncountably many subsets of the natural numbers that can be enumerated by an arbitrary function with domain & omega; and only countably many computable functions.
34.
In general, deducing whether some arbitrary function terminates is called the halting problem and it is unsolvable ( there is provably no algorithm that can do it, as has even been proved in verse ).
35.
Hence, when they are used as a basis for expanding an arbitrary function, they represent behaviors of the function on different timescales ( and at different time offsets for different " k " ).
36.
Because \ lambda ( \ phi ) \; is an arbitrary function of the scalar field, it can be set to give an acceleration that is large in the early universe and small at the present epoch.
37.
It is used to specify animation options such as " duration ", " easing ", and " complete " ( an arbitrary function to execute once the animation has completed ):
38.
By using the ADM decomposition and introducing extra auxiliary fields, in 2009 Deruelle et al . found a method to find the boundary term for " gravity theories whose Lagrangian is an arbitrary function of the Riemann tensor ."
39.
Conversely, a CRF can loosely be understood as a generalization of an HMM that makes the constant transition probabilities into arbitrary functions that vary across the positions in the sequence of hidden states, depending on the input sequence.
40.
Here f and \ tilde f are arbitrary functions selected to give Newtonian and MOND behaviour in the correct limits, and l _ 0 = c ^ 2 / a _ 0 \; is the MOND length scale.
