# step function

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## step function

[′step ‚fəŋk·shən]
(mathematics)
A function ƒ defined on an interval [a,b ] so that [a,b ] can be partitioned into a finite number of subintervals on each of which ƒ is a constant. Also known as simple function.
More generally, a real function with finite range.
References in periodicals archive ?
From Figure 10, the velocity of the platform increases rapidly from 0 to expected value in the X, Z direction within 0.2 s, consistent with the variation trend of the defined STEP function. Then the velocity values in the X, Z direction fluctuate within a certain range.
In as much as F is regulated, there exists a sequence [F.sub.n] : [a,b] [right arrow] X, n = 1,2, ..., of step functions which converges uniformly to F, by Theorem 22; the integrals (HS) [[integral.sup.b.sub.a] B(Fn,dg) exist for each n = 1,2, ...
Residual variance were considered homogenous (hom) or heterogeneous (het) were modeled by step function with 7 (20 to 35, 36 to 50, 51 to 70, 71 to 85, 86 to 99, 100 to 120, and 121 to 140 months of age) and 10 (20 to 32, 33 to 44, 45 to 56, 57 to 69, 70 to 81, 82 to 93, 94 to 105, 106 to 117, 118 to 129, and 130 to 140 months of age) classes in total parities.
which, like (2), can also be understood as a kind of step functions with continuity and goes to the step function under the limit [l.sub.0] [right arrow] 0.
Approximated step functions [H.sub.1]([DELTA]), [H.sub.2]([d.sub.s]/[d.sub.n]), and [mathematical expression not reproducible] can yield a certain value (-1 to 1), which can be directly calculated to obtain the contact constraints without open-close iteration.
The exterior liquid pressure can be a step function pressure, where starting pressure has to be less than [P.sub.V] in order to produce equilibrium conditions.
This form of original activation function of MVN is a combination of multiple step functions, which can be approximated by stacking multiple sigmoid functions:
Let the step functions are [[psi].sub.1] = (1 - [e.sup.-(1/2)h])/(1/2), [[psi].sub.2] = ([e.sup.(1/2)h]-1)/(1/2), [[phi].sub.1] = (1-[e.sup.-(1/4)[DELTA]t])/(1/4) and [[phi].sub.2] = [e.sup.(1/4)[DELTA]t]-1)/(1/4), so [[phi].sub.1] = [2[psi].sub.1], and = [[phi].sub.2] = [2[psi].sub.2].
After introducing SAS, he covers creating variables conditionally, how the DATA step works, BY-group processing, writing loops, array processing, combining data sets, data input and output, data step functions, and useful SAS procedures.
As a result, hardware refresh every three to five years has resulted in large step functions in compute performance, resulting in consolidation of hardware for equivalent compute needs, but a simultaneous density increase (W/[ft.sup.2]).
(21) The analysis for any nondecreasing function can by treated by constructing a sequence of step functions that converges to b as K [right arrow] [infinity].
where 0 = [mu], [eta] < 1, then we say that the approximation is accurate to the order [gamma] with respect to the step functions on the time scale [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

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