# Arbitrary function

Related to Arbitrary function: Arbitrary function generator
 See under Arbitrary.

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Host and Kra describe structures in an arbitrary measure-preserving system in order to decompose an arbitrary function into th sum of a function measurable with respect to such as a structure--a function that is orthogonal in some sense, and possibly a small-error function.
The AFG31000 series arbitrary function generators feature a 9-inch capacitive touchscreen and new user interface to solve increasingly complex test cases for debugging, troubleshooting, characterizing and validating devices under test.
The factors responsible for the growth of global signal generator market are increasing demand for signal generator in the market across various countries in developing regions around the world, also the hike in demand of arbitrary function generator in various application is driving the growth of global signal generator market, one of the important driver contributes in the growth of signal device market is rapid adoption of signal generator in application such as aerospace and defense.
We denote by [[DELTA].sub.[zeta]] the difference of f for an arbitrary function f defined on [R.sup.n] and [mathematical expression not reproducible]
where R([[epsilon].sub.3]t) is an arbitrary function of variable t; here, we suppose
where [F.sub.2](u, [x.sup.i]) is an arbitrary function and H is given by
Generally, the Jacobian  of the mapping [F.sup.e]([xi]) is required for the calculation of the integral of an arbitrary function h(x) over the element [[OMEGA].sup.e] through reference coordinates
The Lagrangian density is an arbitrary function of the torsion scalar T.
where a, b, c, d, e, and k are arbitrary constants and a(t) is an arbitrary function of t only.
These first integrals are obtained for the most general form of the equations in which they depend on an arbitrary function through an application of Nrether's theorem.
For an arbitrary function f, the q-differential is defined by
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