The notions of size, depth and width can be naturally extended to families of functions, becoming functions from \ mathbb { N } to \ mathbb { N }; for example, size ( n ) is the size of the n th circuit of the family.
32.
If \ epsilon _ 1 =-1 this is a 1-parameter family of functions where two critical points are created ( as t increases ), and for \ epsilon _ 1 = 1 it is a 1-parameter family of functions where two critical points are destroyed.
33.
If \ epsilon _ 1 =-1 this is a 1-parameter family of functions where two critical points are created ( as t increases ), and for \ epsilon _ 1 = 1 it is a 1-parameter family of functions where two critical points are destroyed.
34.
This notation can be produced by implementations of the " printf " family of functions following the C99 specification and ( Single Unix Specification ) IEEE Std 1003.1 POSIX standard, when using the " % a " or " % A " conversion specifiers.
35.
The main problem is that outliers ( that does not fit or does not match the selected model ) affect adjustment called least squares ( numerical analysis technique framed in mathematical optimization, which, given an set of ordered pairs : independent variable, dependent variable, and a family of functions, try to find the continuous function ).
36.
Although chirp signals have been known for many years in radar, pulse compression, and the like, the first published reference to the " chirplet transform " described specific signal representations based on families of functions related to one another by time varying frequency modulation or frequency varying time modulation, in addition to time and frequency shifting, and scale changes.
37.
The support for derived instances of Eq and Show makes their methods = = and show generic in a qualitatively different way from parametrically polymorphic functions : these " functions " ( more accurately, type-indexed families of functions ) can be applied to values of various types, and although they behave differently for every argument type, little work is needed to add support for a new type.
38.
Namely, the derivative of the value function with respect to the parameter equals the partial derivative of the objective function with respect to t holding the maximizer fixed at its optimal level . ( The term derives from describing the graph of V as the " upper envelope " of the graphs of the parameterized family of functions \ left \ { f \ left ( x, \ cdot \ right ) \ right \ } _ { x \ in X } .)
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